Professor Shaomin Wu

Professor Shaomin Wu is currently Programme Director for the MSc Business Analytics and coordinates the Student Implant Scheme. He received his PhD and MSc in Applied Statistics. Professor Wu serves on the editorial board of several journals, including IISE Transactions, Reliability Engineering and System Safety, and IMA Journal of Management Mathematics. He has co-chaired 3 international conferences, has been invited to act as scientific committee members by more than 18 international conferences has edited 3 special issues, has been invited to review research proposals for four countries, and has published over 60 papers in academic journals. Professor Wu has also won research funding from the EPSRC as the PI and a Co-I, respectively. He is currently undertaking a research project funded by the ESRC as a co-investigator.

Research interests

Applied Stochastic Processes, Business Data Analysis, Statistical Data Analysis, Data Mining, and Risk Management.
Shaomin has considerable experience in a range of research areas, and his research has received a good number of citations. 

Teaching

Professor Wu has teaching experience in various subjects Statistical Data Analysis, Data Mining, and Risk Management in higher education institutions. He is currently teaching statistics and data mining.

Supervision

Shaomin is interested in Applied Stochastic Processes, Statistical Data Analysis, Data Mining, and Risk Management.
He welcomes applicants with a background relating to computing sciences or mathematical sciences. Supervision topicsBig data analytics and applications in industrial engineeringWarranty management and asset management related topicsRecurrent event data analytics such as actuarial/warranty data analysisReliability mathematics and relevant topicsData mining and applications in industrial engineeringCurrent SuperviseesYu Ye: Developing and Managing Performance Tree - A New Performance Management FrameworkJinhao Xie: Managing risk and uncertainty of extended warranty servicingPast superviseesAhmed Aljazea: Warranty Risk Management for the Consumer Durable ManufacturersDarshana Sabhi Appanna: Reliability Modeling for Asset Management in the Southeast WaterBin Liu: Reliability analysis and maintenance optimisation for complex systems (Bin is a visiting PhD student from The City University of Hong Kong)Sheraz Malik: Optimising supermarket promotions of fast moving consumer goods using disaggregated sales data: A case study of Tesco and their small and medium sized suppliers (University of Kent)Martyn Davies: Modelling Fireside Corrosion of Heat ExchangerYanhong Tang: Transboundary environmental risk management based on multi-network collaborative theoryYi Zheng: Theory and Action Research on a new Framework and Approach of Performance ManagementMohammad Asgaryan: Prediction of the remaining service life of superheater and reheater tubes in coal/biomass fired power plants (Cranfield University)Ming Luo: Learning from the Actuarial Science Modeling Methods to Improve Warranty Data Analysis

Professional

Professor Wu was a senior data analyst for a company in Shanghai after his PhD graduation. He subsequently sought new experiences and moved to the UK for a postdoctoral research position in machine learning from the University of Bristol, where he gained expertise through research and industrial projects, and then a research position in reliability analysis and risk management at the University of Reading.
After a short spell in a credit card company, of which the responsibilities in statistical data analysis is worthy of mention, he moved to Cranfield University for a lecturer position in risk and decision analysis in July 2007 and then was appointed as a senior lecturer in July 2012. 

Publications

Showing 50 of 132 total publications in the Kent Academic Repository. View all publications.

Article

• Wu, D., Yang, X., Peng, R. and Wu, S. (2020). Risk-attitude-based defense strategy considering proactive strike, preventive strike and imperfect false targets. Reliability Engineering and System Safety [Online] 196:106778. Available at: https://doi.org/10.1016/j.ress.2019.106778.
This paper analyzes the optimal strategies for the attacker and the defender in an attack–defense game, considering the risk attitudes of both parties. The defender moves first, allocating its limited resources to three different measures: launching a proactive strike or preventive strike, building false targets, and protecting its genuine object. It is assumed that (a) launching a proactive strike has limited effectiveness on its rival and does not expose the genuine object itself, (b) a false target might be correctly identified as false, and (c) launching a preventive strike consumes less resources than a proactive strike and might expose the genuine object. The attacker moves after observing the defender's movements, allocating its limited resources to three measures: protecting its own base from a proactive strike or preventive strike, building false bases, and attacking the defender's genuine object. For each of the defender's given strategies, the attacker chooses the attack strategy that maximizes its cumulative prospect value, which accounts for the players’ risk attitudes. Similarly, the defender maximizes its cumulative prospect value by anticipating that the attacker will always choose the strategy combination that maximizes its own cumulative prospect value. Backward induction is used to obtain the optimal defense, attack strategies, and their corresponding cumulative prospect values. Our results show that the introduction of risk attitudes leads the game to a lose-lose situation under some circumstances and benefits one party in other cases.
• Peng, R., Wu, D., Sun, M. and Wu, S. (2020). An attack-defense game on interdependent networks. Journal of Operational Research Society [Online]. Available at: https://doi.org/10.1080/01605682.2020.1784048.
This paper analyzes the optimal strategies for an attacker and a defender in an attack-defense game on a network consisting of interdependent subnetworks. The defender moves first and allocates its resource to protect the network nodes. The attacker then moves and allocates its resources to attack the network nodes. The binary decision diagram is employed to obtain all potential states of the network system after attack. Considering each of its opponent’s strategies, the game player tries to maximize its own cumulative prospect value. The backward induction method is employed to obtain the game players’ optimal strategies, respectively. Different resource relationships are analyzed to testify the robustness of the main conclusions and players’ risk attitudes are also investigated. Numerical examples are used to illustrate the analysis.
• Wu, D., Gong, M., Peng, R., Yang, X. and Wu, S. (2020). Optimal Product Substitution and Dual Sourcing Strategy considering Reliability of Production Lines. Reliability Engineering and System Safety [Online]. Available at: https://dx.doi.org/10.1016/j.ress.2020.107037.
Most of the supply chain literature assumes that product substitution is an effective method to mitigate supply chain disruptions and that all production lines either survive or are disrupted together. Such assumptions, however, may not hold in the real world: (1) when there is a shortfall of all products, product substitution may be inadequate unless it is paired with other strategies such as dual sourcing; and (2) production lines do not survive forever and may fail. To relax such assumptions, this paper therefore investigates the situations that the manufacturer may optimize substitution policy and dual sourcing policy to cope with supply chain disruptions. The paper obtains and compares the optimal policies for both deterministic and stochastic demands. A real-world case is also studied to verify the effectiveness of the proposed model.
• Gao, K., Peng, R., Qu, L. and Wu, S. (2020). Jointly optimizing lot sizing and maintenance policy for a production system with two failure modes. Reliability Engineering and System Safety [Online]. Available at: https://doi.org/10.1016/j.ress.2020.106996.
In the reliability literature, there are studies that jointly study maintenance and production and that is typically restricted to one failure mode, and fail to address the case where multiple failure modes exist. This study in-vestigates the problem of joint optimization of lot sizing and maintenance policy for a multi-product produc-tion system subject to two failure modes. The failure of the first mode refers to the soft failure that occurs af-ter defects arrive. The failure of the second mode is a hard failure that occurs without any early warning sig-nals. Products are sequentially produced by the system and a complete run of all products forms a production cycle. The system needs to be re-set up before producing a different product. Both the production cycle and the set-up point depend on the lot sizes of products. Models are proposed for two maintenance policies: 1) arranging the maintenance to be at the end of each production cycle; 2) arranging the maintenance to be at set-up points. The expected profit per unit time is formulated to obtain the optimal lot sizing and maintenance policy. Some properties of proposed models are proved, which show that the optimal lot sizing and mainte-nance policy can be obtained under certain conditions. Case studies and sensitivity analyses are presented to illustrate the proposed models of two maintenance policies. Basically, the results show that the producer will gain the most profit if the optimal lot sizing and maintenance policy are adopted. The results of comparing both maintenance policies reveal that the excessive maintenance is not economic. The sensitivity analyses il-lustrate that reducing the cost caused by failures and improving system reliability are effective ways to in-crease the expected profit per unit time.
• Wu, D., Peng, R. and Wu, S. (2020). A review of the extensions of the geometric process, applications, and challenges. Quality and Reliability Engineering International [Online] 36:436-446. Available at: http://dx.doi.org/10.1002/qre.2587.
Modelling the failure process of a repairable system is vitally important in many industrial sectors such as the offshore industry and the transport industry, in which properly maintaining assets is needed. Among the various models, the geometric process (GP) has been widely applied, mainly in the reliability and maintenance engineering, since its introduction. A book on the GP was published in 2007 and included the GP-related research by that year. However, since then, much research has been conducted, which creates a necessity to review the existing publications relating to the GP, its various extensions and applications since 2007. This paper serves for this purpose.
• Wu, S. and Castro, I. (2020). Maintenance policy for a system with a weighted linear combination of degradation processes. European Journal of Operational Research [Online] 280:124-133. Available at: https://doi.org/10.1016/j.ejor.2019.06.048.
This paper develops maintenance policies for a system under condition monitoring. We assume that a number of defects may develop and the degradation process of each defect follows a gamma process. The system is said failed if a linear combination of the degradation processes exceeds a pre-specified threshold. Preventive maintenance is performed. The system is renewed after several preventive maintenance activities have been performed. The main objective of this paper is to optimise the time between preventive maintenance actions and the number of the preventive maintenance. Numerical examples are given to illustrate the results.
• Yang, X., Qiu, H., Peng, R. and Wu, S. (2020). Optimal configuration of a power grid system with a dynamic performance sharing mechanism. Reliability Engineering and System Safety [Online] 193:1-10. Available at: https://doi.org/10.1016/j.ress.2019.106613.
Performance sharing is an effective policy for a power grid system to satisfy the power demand of different districts to greatest extent. Through transmission lines, the districts with sufficient power can share the redundant power with the districts with power deficit. The existing research has incorporated the performance sharing mechanism into systems with simple structures such as parallel systems and series-parallel systems. However, little concentration has been spent on more complex structures. This necessitates the need of this paper that models a power distribution with a more complex reliability structure. We assume that the system is composed of generators and nodes. Both the performance of each generator and the demand of each node in the network are assumed to be random variables. This paper first proposes a dynamic performance sharing policy to minimize the unsupplied demand for a given system with fixed capacity and demand. The optimal allocation of generators, which minimizes the expected system unsupplied demand, is then studied. Numerical examples are proposed to illustrate the applications of the proposed procedures.
• Syamsundar, A., Naikan, V. and Wu, S. (2020). Alternative scales in reliability models for a repairable system. Reliability Engineering and System Safety [Online] 193:1-11. Available at: https://dx.doi.org/10.1016/j.ress.2019.106599.
In an industry, the lifetime of a technical system is often assessed according to its accumulated throughput/usage e.g., the performance of a Blast Furnace in terms of accumulated quantity of its product, the lifetime of a vehicle in terms of accumulated number of miles it has travelled. Most of these systems are repairable systems. The failure process of a repairable system is conventionally measured in the time domain also termed as a time scale in the literature. Nevertheless, the lifetime of some repairable systems and their failures may be measured in terms of their throughput/usage. Therefore, it makes sense to quantify their failure processes in terms of throughput/ usage which may be better indicators than time, of system failure and reliability. Time, usage or a combination of both time and usage may be used as alternative domains/scales of measurement for modelling the failure process of a repairable system. This paper proposes such alternative scales in reliability models for a repairable system. A method is devised in the paper to identify the better alternative scale to model the failure process and thus identify the appropriate scale to assess the system reliability. Industrial failure data are used to illustrate the proposed method.
• Aljazea, A. and Wu, S. (2019). Managing Risk for Auto Warranties. International Journal of Quality & Reliability Management [Online] 36:1088-1105. Available at: http://dx.doi.org/10.1108/IJQRM-08-2018-0221.
Purpose - This paper aims to (1) analyse the existing work of warranty risk management (WaRM); (2) develop a generic WaRM framework; and (3) design a generic taxonomy for warranty hazards from a warranty chain perspective.

Design/methodology/approach – To understand the top warranty hazards, we designed a questionnaire, received 40 responses from the warranty decision makers (WDM) in the automotive industry in the UK and then analysed the responses.

Findings – The assembly process capability at suppliers is the top contributor to warranty incidents from the suppliers’ and original equipment manufacturers (OEMs’) viewpoints. The human error at different stages of the product lifecycle contributes to the occurrence of warranty incidents. The collaboration among parties, particularly, the accessibility to warranty-related data between parties (i.e., suppliers, OEM and dealers), is limited. Customers’ fraud contributes more to warranty costs than warranty services providers’ (WSPs) fraud. The top contributors to customer dissatisfaction relating to warranty are the warranty service time and service quality.

Research limitations/implications – The questionnaires were used to collect data in the UK, which implies the research outcomes of this paper may only reflect the UK area.
Practical implications – The WaRM framework and taxonomy proposed in this paper provide warranty decision makers with a holistic view to identifying the top contributors to warranty incidents. With them, the decision makers will be able to allocate the required fund and efforts more effectively.
Originality/value – This paper contributes to the literature by providing the first work of systematically analysing the top contributors to warranty incidents and costs and by providing a WaRM framework.
• Wu, D., Yang, X., Peng, R. and Wu, S. (2019). Optimal defence-attack strategies between one defender and two attackers. Journal of the Operational Research Society [Online]. Available at: https://doi.org/10.1080/01605682.2019.1630332.
This paper analyses the optimal strategies for one defender and two attackers in a defence-attack game, where a) the defender allocates its resource into defending against and attacking the two attackers, and b) the two attackers, after observing the action of the defender, allocate their resources into attacking and defending against the defender, on either a cooperative or non-cooperative basis. On a cooperative basis, for each of the defender’s given strategies, the two attackers work together to maximise the sum of their cumulative prospect values while anticipating the eight possible game outcomes. On a non-cooperative basis, for each of the defender’s given strategies, each attacker simultaneously yet independently tries to maximise their own cumulative prospect value. In both cases, the defender maximises its cumulative prospect value while anticipating the attackers’ actions. Backward induction is employed to obtain the optimal defence and attack strategies for all scenarios. Numerical examples are performed to illustrate the applications of the strategies. In general, we find two opposing effects considering the attackers’ strategies and analyse the alteration of strategies for the participants under two different risk preferences: risk-averse and risk seeking. The reasons for the alteration are also performed to illustrate the practical applications.
• Luo, M. and Wu, S. (2019). A comprehensive analysis of warranty claims and optimal policies. European Journal of Operational Research [Online] 276:144-159. Available at: https://dx.doi.org/10.1016/j.ejor.2018.12.034.
Nowadays many products, such as 3C products (Computer, Communication and Consumer Electronics) and cars, consist of software and hardware. The causes of warranty claims of such products may be attributed to software specific failures, hardware specific failures, software-hardware interaction failures and human errors. Apparently, those causes may be dependent. For example, one may claim warranty due to the malfunction of the embedded software in a product item and then the entire item may be replaced. Nevertheless, the existing research on warranty management studies mainly concentrates on warranty analysis of hardware subsystems, assuming that the warranty claims are statistically independent of those caused by the failures of software subsystems or human factors, that is, the interactions between those causes are neglected. This paper investigates warranty costs incurred due to those three subsystems with a focus on their interactions. It estimates the costs due to different cause, develops integrated warranty cost models and optimises warranty policies considering the above possible combinations. Numerical examples are given to illustrate the proposed models.
• Wu, S. (2019). A failure process model with the exponential smoothing of intensity functions. European Journal of Operational Research [Online] 275:502-513. Available at: https://doi.org/10.1016/j.ejor.2018.11.045.
This paper proposes a new model and investigates its special case model, both of which model the failure process of a series system composed of multiple components. We make the following assumption: (1) once the system fails, the failed component can be immediately identified and replaced with a new identical one, and (2) once the system fails, only the time of the failure is recorded; but the component that causes the system to fail is not known. The paper derives a parameter estimation method and compares the performance of the proposed models with nine other models on artificially generated data and fifteen real-world datasets. The results show that the two new models outperform the nine models in terms of the three most commonly used penalised model selection criteria, the Akaike's information criterion (AIC), corrected Akaike's information criterion (AICc) and Bayesian information criterion (BIC), respectively.
• Longhurst, P., Tompkins, D., Pollard, S., Hough, R., Chambers, B., Gale, P., Tyrrel, S., Villa, R., Taylor, M., Wu, S., Sakrabani, R., Litterick, A., Snary, E., Leinster, P. and Sweet, N. (2019). Risk assessments for quality-assured, source-segregated composts and anaerobic digestates for a circular bioeconomy in the UK. Environment International [Online] 127:253-266. Available at: https://doi.org/10.1016/j.envint.2019.03.044.
A circular economy relies on demonstrating the quality and environmental safety of wastes that are recovered and reused as products. Policy-level risk assessments, using generalised exposure scenarios, and informed by stakeholder communities have been used to appraise the acceptability of necessary changes to legislation, allowing wastes to be valued, reused and marketed. Through an extensive risk assessment exercise, summarised in this paper, we explore the burden of proof required to offer safety assurance to consumer and brand-sensitive food sectors in light of attempts to declassify, as wastes, quality-assured, source-segregated compost and anaerobic digestate products in the United Kingdom. We report the residual microbiological and chemical risks estimated for both products in land application scenarios and discuss these in the context of an emerging UK bioeconomy worth £52bn per annum. Using plausible worst case assumptions, as demanded by the quality food sector, risk estimates and hazard quotients were estimated to be low or negligible. For example, the human health risk of E. coli 0157 illness from exposure to microbial residuals in quality-assured composts, through a ready-to-eat vegetable consumption exposure route, was estimated at ~10-8 per person per annum. For anaerobic digestion residues, 7 x10-3 cases of E. coli 0157 were estimated per annum, a potential contribution of 0.0007 percent of total UK cases. Hazard quotients for potential chemical contaminants in both products were insufficient in magnitude to merit detailed quantitative risk assessments. Stakeholder engagement and expert review was also a substantive feature of this study. We conclude that quality assured, source-segregated products applied to land, under UK quality protocols and waste processing standards, pose negligible risks to human, animal, environmental and crop receptors, providing that risk management controls set within the standards and protocols are adhered to.
• Zhang, G., Chen, Y., Yu, Y., Hu, H. and Wu, S. (2019). Intelligent Swarm Firefly Algorithm for the Prediction of China’s National Electricity Consumption. International Journal of Bio-Inspired Computation [Online] 13:111-118. Available at: https://doi.org/10.1504/IJBIC.2019.098407.
China’s energy consumption is the world’s largest and is still rising, leading to concerns of energy shortage and environmental issues. It is, therefore, necessary to estimate the energy demand and to examine the dynamic nature of the electricity consumption. In this paper, we develop a nonlinear model of energy consumption and utilise a computational intelligence approach, specifcally a swarm fre?y algorithm with a variable population, to examine China’s electricity consumption with historical statistical data from 1980 to 2012. Prediction based on these data using the model and the examination is verifed with a bivariate sensitivity analysis, a bias analysis and a forecasting exercise, which all suggest that the national macroeconomic performance, the electricity price, the electricity consumption efciency and the economic structure are four critical factors determining national electricity consumption. Actuate prediction of the consumption is important as it has explicit policy implications on the electricity sector development and planning for power plants.
• Luo, M. and Wu, S. (2018). A value-at-risk approach to optimisation of warranty policy. European Journal of Operational Research [Online] 267:513-522. Available at: https://dx.doi.org/10.1016/j.ejor.2017.11.062.
In the real world, a manufacturer may produce many products, which may have common components installed. Consequently, the frequencies of the warranty claims of those products are statistically dependent. Warranty policy optimisation in the existing research, however, has not considered such statistical dependence, which may increase bias in decision making. This paper is the first attempt to collectively optimises warranty policy for a set of different products, produced by one manufacturer, whose failures are statistically dependent, using tools borrowed from financial mathematics (i.e., value-at-risk theory and copula). We prove the existence of the optimal solutions for different scenarios. Numerical examples are used to validate the applicability of the proposed methods.
• Wu, S. and Wang, G. (2018). The semi-geometric process and some properties. IMA Journal of Management Mathematics [Online] 29:229-245. Available at: https://doi.org/10.1093/imaman/dpx002.
The geometric process has been widely applied in reliability engineering and other areas since its introduction. One of its assumptions is that the times between occurrences of events are independent. This assumption is rather restrictive and can limit its application in the real world. This paper extends the geometric process to a new process, which we call the semi-geometric process, by relaxing this assumption. Some probabilistic properties of the process are derived and parameter estimation is described. A numerical example, based on a real-world dataset, is used to illustrate the model and validate the estimation methodology.
• Luo, M. and Wu, S. (2018). A mean-variance optimisation approach to collectively pricing warranty policies. International Journal of Production Economics [Online] 196:101-112. Available at: https://doi.org/10.1016/j.ijpe.2017.11.013.
Warranty policy can influence the profit and cost of a product. In practice, a manufacturer commonly produces more than one product, or a portfolio of products, and provides warranty servicing for them. Many authors have attempted to optimise warranty policy to maximise the profit or minimise the cost of each individual product. Warranty claims of the products produced by the same manufacturer, however, may be due to common causes, since the products may be designed by the same engineer team or using the same type of components. This implies that the numbers of warranty claims of different products may be related, and optimisation of warranty policies for each individual product may therefore cause biased decisions. To overcome this disadvantage, this paper aims to collectively optimise a manufacturer's total profit for a portfolio of different products by using a mean-variance optimisation approach. A tool from the probability theory, {\it copulas}, is used to depict the dependence among the warranty claims of different products. Numerical examples are provided to illustrate the application of the proposed methods.
• Wu, S. (2018). Doubly geometric processes and applications. Journal of the Operational Research Society [Online] 69:66-77. Available at: http://dx.doi.org/10.1057/s41274-017-0217-4.
The geometric process has attracted extensive research attention from authors in reliability mathematics since its introduction. However, it possesses some limitations, which include that: (1) it can merely model stochastically increasing or decreasing inter-arrival times of recurrent event processes, and (2) it cannot model recurrent event processes where the inter-arrival time distributions have varying shape parameters. Those limitations may prevent it from a wider application in the real world.

In this paper, we extend the geometric process to a new process, the doubly geometric process, which overcomes the above two limitations. Probability properties are derived and two methods of parameter estimation are given. Application of the proposed model is presented: one is on fitting warranty claim data and the other is to compare the performance of the doubly geometric process with the performance of other widely used models in fitting real world datasets, based on the corrected Akaike information criterion.
• Wu, X. and Wu, S. (2017). An elitist quantum-inspired evolutionary algorithm for the flexible job-shop scheduling problem. Journal of Intelligent Manufacturing [Online] 28:1441-1457. Available at: http://dx.doi.org/10.1007/s10845-015-1060-6.
The flexible job shop scheduling problem (FJSP) is vital to manufacturers especially in today’s constantly changing environment. It is a strongly NP-hard problem and therefore metaheuristics or heuristics are usually pursued to solve it. Most of the existing metaheuristics and heuristics, however, have low efficiency in convergence speed. To overcome this drawback, this paper develops an elitist quantum-inspired evolutionary algorithm. The algorithm aims to minimise the maximum completion time (makespan). It performs a global search with the quantum-inspired evolutionary algorithm and a local search with a method that is inspired by the motion mechanism of the electrons around an atomic nucleus. Three novel algorithms are proposed and their effect on the whole search is discussed. The elitist strategy is adopted to prevent the optimal solution from being destroyed during the evolutionary process. The results show that the proposed algorithm outperforms the best-known algorithms for FJSPs on most of the FJSP benchmarks.
• Ahmadi, R. and Wu, S. (2017). A novel data-driven approach to optimizing replacement policy. Reliability Engineering and System Safety [Online] 167:506-516. Available at: http://dx.doi.org/10.1016/j.ress.2017.06.027.
Parallel systems are a commonly used structure in reliability engineering. A common characteristic of such systems is that the failure of a component may not cause its system to fail. As such, the failure may not be immediately detected and the random (disruption) time at which the number of failed components reaches a certain predefined number may therefore be unknown. For such systems, scheduling maintenance policy is a difficult task, which is tackled in this paper. The paper assumes that times between inspections conform to a modulated Poisson process. This assumption allows the frequency of inspection responds to the variation of the disruption state. The paper then estimates the disruption time on the basis of inspection point process observations in the framework of filtering theorem. The paper develops a unified cost structure to jointly optimise inspection frequency and replacement time for the system when the lifetime distribution of a component follows the Pareto or exponential distribution. Numerical results are provided to show the application of the proposed model.
• Liu, B., Wu, S., Xie, M. and Kuo, W. (2017). A condition-based maintenance policy for degrading systems with age- and state-dependent operating cost. European Journal of Operational Research [Online] 263:879-887. Available at: http://dx.doi.org/10.1016/j.ejor.2017.05.006.
Most of the maintenance policies in existing publications assume that no cost is incurred as long as the system can undertake missions while little consideration has been devoted to the operating cost during system operation. However, in practice, the operating cost increases while the system ages and degrades even if a system is in a functioning state. This paper proposes a maintenance policy for a degrading system with age- and state-dependent operating cost, which increases with system age and degradation levels. Under such a setting, a replacement model is first developed to investigate the optimal preventive replacement policy. The replacement model is then extended to a repair-replacement model, in which imperfect repair is assumed to restore the system to the operating condition. Particularly, the repair model with controllable and uncontrollable repair levels is considered separately. The paper proves that the optimal maintenance policy is actually a monotone control limit policy, where the optimal control limits decrease monotonically with system age. Finally, a numerical example along with sensitivity analysis is presented to illustrate the optimal maintenance policy. The proposed model implies a more conservative maintenance policy, compared with the traditional model without the age- and state-dependent operating cost.
• Dui, H., Si, S., Wu, S. and Yam, R. (2017). An importance measure for multistate systems with external factors. Reliability Engineering and System Safety [Online] 167:49-57. Available at: http://dx.doi.org/10.1016/j.ress.2017.05.016.
Many technical systems are operated under the impact of external factors that may cause the systems to fail. For such systems, an interesting question is how those external factors and their impacts on the system can be identified at an earlier stage. Importance measures in reliability engineering are used to prioritise weak components (or states) of a system. Component failures and the impact of external factors in the real world may be statistically dependent as external factors may affect system performance. This paper proposes a new importance measure for analysing the impact of external factors on system performance. The measure can evaluate the degree of the impact of external factors on the system and can therefore help engineers to identify the factors with the strong impact on the system performance. A real-world case study is used to illustrate its applicability.
• Wu, S. and Scarf, P. (2017). Two new stochastic models of the failure process of a series system. European Journal of Operational Research [Online] 257:763-772. Available at: http://dx.doi.org/10.1016/j.ejor.2016.07.052.
Consider a series system consisting of sockets into each of which a component is inserted: if a component fails, it is replaced with a new identical one immediately and system operation resumes. An interesting question is: how to model the failure process of the system as a whole when the lifetime distribution of each component is unknown? This paper attempts to answer this question by developing two new models, for the cases of a specified and an unspecified number of sockets, respectively. It introduces the concept of a virtual component, and in this sense, we suppose that the effect of repair corresponds to replacement of the most reliable component in the system. It then discusses the probabilistic properties of the models and methods for parameter estimation. Based on six datasets of artificially generated system failures and a real-world dataset, the paper compares the performance of the proposed models with four other commonly used models: the renewal process, the geometric process, Kijima's generalised renewal process, and the power law process. The results show that the proposed models outperform these comparators on the datasets, based on the Akaike information criterion.
• Dui, H., Chen, L. and Wu, S. (2017). Generalized integrated importance measure for system performance evaluation: application to a propeller plane system. Maintenance and Reliability [Online] 19:279-286. Available at: http://dx.doi.org/10.17531/ein.2017.2.16.
The integrated importance measure (IIM) evaluates the rate of system performance change due to a component changing from one state to another. The IIM simply considers the scenarios where the transition rate of a component from one state to another is constant. This may contradict the assumption of the degradation, based on which system performance is degrading and therefore the transition rate may be increasing over time. The Weibull distribution describes the life of a component, which has been used in many different engineering applications to model complex data sets. This paper extends the IIM to a new importance measure that considers the scenarios where the transition rate of a component degrading from one state to another is a time-dependent function under the Weibull distribution. It considers the conditional probability distribution of a component sojourning at a state is the Weibull distribution, given the next state that component will jump to. The research on the new importance measure can identify the most important component during three different time periods of the system lifetime, which is corresponding to the characteristics of Weibull distributions. For illustration, the paper then derives some probabilistic properties and applies the extended importance measure to a real-world example (i.e., a propeller plane system).
• Wu, S., Coolen, F. and Liu, B. (2016). Optimization of maintenance policy under parameter uncertainty using portfolio theory. IISE Transactions [Online] 49:711-721. Available at: http://dx.doi.org/10.1080/24725854.2016.1267881.
In reliability mathematics, optimisation of maintenance policy is derived based on reliability indexes such as the reliability or its derivatives (e.g., the cumulative failure intensity or the renewal function) and the associated cost information. The reliability indexes, also referred to as models in this paper, are normally estimated based on either failure data collected from the field or lab data. The uncertainty associated with them is sensitive to factors such as the sparsity of data. For a company that maintains a number of different systems, developing maintenance policies for each individual system separately and then allocating maintenance budget may not lead to optimal management of the model uncertainty and may lead to cost ineffective decisions. To overcome this limitation, this paper uses the concept of risk aggregation. It integrates the uncertainty of model parameters in optimisation of maintenance policies and then collectively optimises maintenance policies for a set of different systems, using methods from portfolio theory. Numerical examples are given to illustrate the application of the proposed methods.
• Luo, M. and Wu, S. (2016). An overview of approaches to insurance data analysis and suggestions for warranty data analysis. Recent Patents on Engineering [Online] 10:138-145. Available at: http://dx.doi.org/10.2174/1872212110666160617092705.
Warranty shares similarities with insurance in many aspects. Research on insurance data analysis has attracted much more attention than on warranty data analysis. This paper provides a general comparison between warranty and insurance in terms of their coverages, policies and data collection. It then reviews existing approaches to insurance data analysis with regard to modelling of claim frequency, modelling of claim size and policy pricing. Some recent patents relating statistical models are also discussed. The paper concludes with suggestions for improving warranty data analysis.
• Wu, S., Chen, Y., Wu, Q. and Wang, Z. (2016). Linking component importance to optimisation of preventive maintenance policy. Reliability Engineering and System Safety [Online] 146:26-32. Available at: http://dx.doi.org/10.1016/j.ress.2015.10.008.
In reliability engineering, time on performing preventive maintenance (PM) on a component in a system may affect system availability if system operation needs stopping for PM. To avoid such an availability reduction, one may adopt the following method: if a component fails, PM is carried out on a number of the other components while the failed component is being repaired. This ensures PM does not take system’s operating time. However, this raises a question: Which components should be selected for PM? This paper introduces an importance measure, called Component Maintenance Priority (CMP), which is used to select components for PM. The paper then compares the CMP with other importance measures and studies the properties of the CMP. Numerical examples are given to show the validity of the CMP.
• Wu, Q. and Wu, S. (2016). Optimization of replacement policy for a one-component system subject to Poisson shocks. International Journal of Systems Science [Online] 3:114-127. Available at: http://dx.doi.org/10.1080/23302674.2015.1066898.
In reliability engineering, system failures may occur due to intrinsic or extrinsic factors. For example, drinking water systems may fail due to ageing and deterioration (i.e., intrinsic factors) or flooding (i.e., extrinsic factors). An interesting question is: for such systems, how should preventive maintenance be scheduled? This paper investigates this question.

The paper develops a maintenance policy for repairable systems subject to extrinsic shocks. It assumes that a system may fail due to either intrinsic factors or extrinsic factors. Reliability indexes and the expected long run cost rate are then derived. A numerical example is given to illustrate the theoretical results.
• Wu, S. and Scarf, P. (2015). Decline and repair, and covariate effects. European Journal of Operational Research [Online] 244:219-226. Available at: http://dx.doi.org/10.1016/j.ejor.2015.01.041.
The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive statistical properties of the failure processes for such systems.

Book section

• Wu, S. (2019). Superimposed Renewal Processes in Reliability. In: Ruggeri, F. ed. Wiley StatsRef: Statistics Reference Online. Wiley. Available at: https://doi.org/10.1002/9781118445112.stat08228.
This paper reviews the existing literature on the superimposed renewal process, with its foci on probabilistic and statistical properties, statistical inference, and applications in reliability analysis and maintenance policy optimisation. It then proposes future research topics.
• Ahmadi, R. and Wu, S. (2018). An optimal maintenance policy based on partial information. In: Haugen, S., Barros, A., van Gulijk, C., Kongsvik, T. and Vinnem, J. E. eds. Safety and Reliability – Safe Societies in a Changing World: Proceedings of ESREL 2018. London, UK: CRC Press, pp. 511-518. Available at: http://dx.doi.org/10.1201/9781351174664-63.
This paper proposes an integrated model for maintenance scheduling of parallel systems whose failures are detected by inspections. A common characteristic of such systems is that the system failures are detected only by inspections and the failure of a component may not cause its system to fail. As such, the failure may not be immediately detected and the random (disruption) time at which the number of failed components reaches a certain predefined number d may therefore be unknown. For such systems, scheduling maintenance policy is a difficult task, which is tackled in this paper. The main issue considered here is to get an estimate of the disruption time on the basis of inspection point process observations in the framework of filtering theorem. The paper develops a unified cost structure to jointly optimise inspection frequency and replacement time for the system when the lifetime distribution of a component follows the Weibull distribution. Numerical results are provided to show the application of the proposed model. In addition, a sensitivity analysis is performed to examine the effect of maintenance parameters on the model.
• Aljazea, A., Luo, M. and Wu, S. (2018). Mitigating Warranty Risk for Automotive Industry. In: Scarf, P., Wu, S. and Do, P. eds. Proceedings of the 10th IMA International Conference on Modelling in Industrial Maintenance and Reliability. UK: Institute of Mathematics and its Applications, pp. 19-24. Available at: https://doi.org/10.19124/ima.2018.001.04.
Warranty is offered by manufacturers as protection and promotional tools. It also gives customers a certain degree of insurance against product failures for a certain period. Although bringing those benefits, it involves various risks originating from various perspectives of the product lifetime cycle. To prepare risk mitigation plans is therefore needed, which is challenging due to the increasing complexity of the product designs and the long warranty period. Accordingly, the decision made to select the mitigation plan involves a high level of uncertainty. This paper develops a plan to mitigate warranty risk based on cumulative prospect theory, which helps warranty decision makers in selecting the optimal mitigation plan.
• Wu, S., Gitzel, R. and Turrin, S. (2016). On assumptions in optimisation of warranty policies. In: Proceedings of the 9thIMA International Conference on Modellingin Industrial Maintenance and Reliability. Institute of Mathematics and its Applications.
Optimisation of warranty policy has been a hot research topic in both operations research and statistics communities since warranty providers hope to balance cost-benefit analysis in the nowadays competitive market. Some assumptions are inevitably needed for such research. Most of the existing publications, however, make assumptions that may not be true in practice, based on which biased decision may be made. This paper discusses pitfalls in the assumptions, which include causes of warranty claims, pattern of warranty claims, warranty claim models, field reliability vs product reliability, the relationship between usage and age in 2-dimensional warranty. A real-world example is used to elaborate the arguments.
• Gitzel, R., Turrin, S., Maczey, S., Wu, S. and Schmitz, B. (2016). A Data Quality Metrics Hierarchy for Reliability Data. In: Proceedings of the 9thIMA International Conference on Modellingin Industrial Maintenance and Reliability. Institute of Mathematics and its Applications.
In this paper, we describe an approach to understanding data quality issues in field data used for the calculation of reliability metrics such as availability, reliability over time, or MTBF. The focus lies on data from sources such as maintenance management systems or warranty databases which contain information on failure times, failure modes for all units. We propose a hierarchy of data quality metrics which identify and assess key problems in the input data. The metrics are organized in such a way that they guide the data analyst to those problems with the most impact on the calculation and provide a prioritised action plan for the improvement of data quality. The metrics cover issues such as missing, wrong, implausible and inaccurate data. We use examples with real-world data to showcase our software prototype and to illustrate how the metrics have helped with data preparation. Using this way, analysts can reduce the amount of wrong conclusions drawn from the data to mistakes in the input values.

Conference or workshop item

• Wu, D., Xiangbin, Y., Peng, R., Wu, S. and Gao, K. (2019). Optimal preventive strike strategy vs. optimal attack strategy in a defense-attack game. In: 2019 Prognostics and System Health Management Conference. IEEE. Available at: http://dx.doi.org/10.1109/PHM-Qingdao46334.2019.8943047.
This paper analyzes an attack-defense game between one defender and one attacker. Among, the defender moves first and allocates its resources to three different methods: employing a preventive strike, founding false targets, and protecting its genuine object. The preventive strike may expose the genuine object, and different from previous literature, a false target may also be detected to be false. The attacker, observing the actions taken by the defender and allocating its resources to three methods: protecting its own base from the preventive strike, founding false bases, and attacking the defender's genuine object. Similarly, a false base may be correctly identified. Different from previous methods in evaluating the potential outcome, for each of the defender's given strategies, the attacker tries to maximize its cumulative prospect value considering different possible outcomes. Similarly, the defender maximizes its cumulative prospect value, assuming that the attacker chooses the strategy to maximize the attacker's cumulative prospect value. Numerical examples are presented to illustrate the optimal number of bases to attack by preventive strike, and the optimal number of targets to attack by attacker.
• Annamraju, S., Naikan, V. and Wu, S. (2019). Assessing the Restoration / Improvement Factor for Imperfect Maintenance of a Repairable System. In: Xie, M. ed. the 11th International Conference on Mathematical Methods in Reliability (MMR2019).
A repairable system on failure is repaired / maintained to mitigate the damage that has occurred while in use to restore its functionality. This causes a change in the system ageing or its failure intensity in proportion to the maintenance carried out. Various methods have been proposed to estimate the effect of maintenance on the repairable system other than the usual statistical method. This work studies the various methods to assess the effect of maintenance and helps arrive at a better measure for the same.
• Annamraju, S., Naikan, V. and Wu, S. (2019). Assessing the Reliability of a Repairable System in a Usage or Combined Time Scale. In: the 11th International Conference on Mathematical Methods in Reliability (MMR2019).
Repairable systems age with use and their failure intensities and reliability are assessed on a time scale based on their ageing. A common time scale for ageing of systems is chronological time. However, it is often seen that the same systems exhibit different failure behaviour and reliability in chronological time owing to different usages. Hence usage or a combined scale of chronological time and usage can form a better time scale to assess the reliability of a repairable system in such a case. This work presents a methodology to identify the better time scale to assess the reliability of a repairable system.
• Peng, R., Wu, D., Wu, S. and Zhai, Q. (2019). Optimal Attack Strategy to a Network Consisting of Interdependent Subnetworks. In: the 11th International Conference on Mathematical Methods in Reliability (MMR2019).
This paper analyzes the optimal strategies for the attacker in an attack-defense game on a network consisting of interdependent subnetworks. The defender moves first and evenly allocates the scarce resource to protect the network nodes. The attacker moves after observing the actions taken by the defender, allocating its limited resources to attack the network nodes. Binary Decision Diagram is employed to obtain all potential states of a given interdependent network after attack. For each of the defender's given strategies, the attacker tries to maximize its cumulative prospect value considering all possible outcomes. Illustrative example is solved to show the applications
• Xie, J. and Wu, S. (2019). Optimisation of Extended Warranty Price with Usage Rate Being Considered. In: the 11th International Conference on Mathematical Methods in Reliability (MMR2019).
Optimisation of extended warranty has attracted considerable attention in the literature. Its focuses are on optimisation of the length and/or the price of the ex-tended warranty. Such research is done by good mathematicians with some unrealistic assumptions. For example, in the real world, the length of extended warranty is usually a positive integer, which may be 6 months, 12 months, etc, but it is seldom 3.5623 months. In this paper, we take into consideration of this fact and assume that the buyers may decide to purchase a different number of the base periods of extended warranty. We then propose a novel method of optimising the price of extended warranty.
• Aljazea, A. and Wu, S. (2019). A Framework of Warranty Risk Management. In: The Ninth International Conference on Business Intelligence and Technology. pp. 1-6. Available at: https://www.thinkmind.org/index.php?view=article&articleid=bustech_2019_1_10_90014.
Warranty is a useful tool for a manufacturer to reflect its product quality and combat competition. It, however, introduces various risks that may have a direct impact on the profitability and reputation of the manufacturer. Although managing such risks is crucial in reducing the number of warranty incidents and warranty related cost, little research has systematically investigated warranty risk management (WaRM). As such, this paper aims to (1) analyse the existing literature on warranty-related risks; (2) develop a generic WaRM framework; (3) investigate the existing WaRM techniques and methods by surveying the warranty decision makers in the automotive industry in the UK, and then (4) propose a warranty hazard identification tool through utilising social media data.
• Wu, S. (2017). Three models for the failure process of a repairable system. In: The 10th International Conference on Mathematical Methods in Reliability. Available at: http://mmr2017.imag.fr/invited_sessions/.
Development of models for the failure process of a repairable system has been an interesting research topic for decades. There have been many models developed in the literature. However, more research is still needed to deal with various difficulties raised in the practical applications, which includes the cases that most real systems are composed of more than one component and that the failure process may not be stochastically monotone. For such cases, we have recently developed three models, which are briefly discussed in this paper.
• Wu, S. and Luo, M. (2017). Optimisation of warranty policy considering the interplay of product subsystems. In: The 10th International Conference on Mathematical Methods in Reliability. Available at: http://mmr2017.imag.fr/invited_sessions/.
Development of warranty policy has attracted attention from researchers from both reliability and supply chain communities. Two conventionally assumed contexts in optimisation of warranty policy are reliability mathematics and game theory. In both scenarios, the causes of warranty claims are usually assumed to be hardware systems only. In reality, however, user behaviour, software failure, and hardware failure may cause warranty claims, which may be handled differently. In addition, some subsystems/components may be installed in different products. The existing research focuses on individual systems/products and little attention has been paid to the effect of the interplay of different systems and that of different subsystems. This work investigates the consequences of such interplay and reports our recent work.

Edited book

• Wu, S. (2018). Proceedings of the 10th IMA International Conference on Modelling in Industrial Maintenance and Reliability. [Online]. Scarf, P., Wu, S. and Do, P. eds. Institute of Mathematics and its Applications. Available at: https://doi.org/10.19124/ima.2018.001.
The 10th International Conference on Modelling in Industrial Maintenance and Reliability (MIMAR) took place in Manchester, UK from 13 – 15 June 2018. This event is the premier maintenance and reliability modelling conference in the UK and builds upon a very successful series of previous conferences. It is an excellent international forum for disseminating information on the state-of-the-art research, theories and practices in maintenance and reliability modelling and offers a platform for connecting researchers and practitioners from around the world.

Edited journal

• Wu, S. and Do, P. eds. (2017). Maintenance Modelling. Reliability Engineering & System Safety [Online] 168:1-364. Available at: https://doi.org/10.1016/j.ress.2017.09.004.
• Wang, W. and Wu, S. eds. (2017). Guest Editorial. IMA Journal of Management Mathematics [Online] 28:339-466. Available at: https://academic.oup.com/imaman/issue/28/3.

Thesis

• Aljazea, A. (2020). Warranty Risk Management For the Consumer Durable Manufacturers.
Warranty is a contractual obligation for maintenance upon failures of sold items during a warranty period. Warrantors utilise warranty as a strong promotional tool. Although warranty can bring some benefits, it involves various types of risks that may lead to negative impact (such as economic loss) on the warrantor. Systematic analysis of such risks can protect warrantors from potential losses. Based on a critical and comprehensive analysis of the existing warranty literature, very few studies discuss warranty risk management (WaRM). This thesis therefore aims to investigate WaRM from several perspectives and it makes contributions to the literature and practice, as shown below.
Firstly, a WaRM framework was developed. The framework was thoroughly analysed.
Secondly, a questionnaire was designed to gain an in-depth understanding of WaRM. From analysing the survey in the UK automotive industry, the following findings were obtained:
(a) the most commonly used tool for identifying warranty hazards is the root cause analysis technique;
(b) the most commonly used tool for assessing warranty risks is the failure mode effect and criticality analysis technique;
(c) the top contributors to warranty incidents and costs were human error related, which mainly include: (1) human error at different stages of the product life cycle; (2) product modification at suppliers and original equipment manufacturer (OEM); (3) customers' fraud (4) insufficient collaboration between parties (suppliers, OEM and warranty services providers). Based on these findings, two generic warranty hazard taxonomies were designed.
Thirdly, the selection of methods to mitigate WaR (warranty risk) is important but includes uncertainty. The thesis investigates the warranty risk mitigation process and analyses the main criteria that can be influenced. A selection method is developed based on the joint application of the cumulative prospect theory (CPT) and the analytic hierarchy process method (AHP). The new method can guide decision makers to the selection of mitigation methods over their conflicting views and their attitudes towards risks.
Fourthly, a warranty policy includes both warranty price and duration. Optimisation of warranty policies is therefore vitally important. The thesis also developed a CPT-based warranty model to optimise warranty price considering the warrantor's and buyers' risk attitudes. A numerical example is provided to illustrate the proposed models and the sensitivity of the profit to different risk attitudes for the parties. Accordingly, the main findings are: (1) The warrantor's risk attitude has less impact on the profit compared to the buyers' risk attitudes; (2) the increase in the repair cost may lead buyers to accept higher warranty price; and (3) the higher the buyers perceive the product failure rate, the more likely they will be willing to buy the extended warranty.
The theoretical implications of this thesis are listed as follows:
(a) Develop a framework for WaRM.
(b) Determine the top contributors to warranty hazards and hence two taxonomies were developed.
(c) Develop a decision model to select the optimal mitigation plan to respond to the emergent warranty risk.
(d) Develop a mathematical model to optimise warranty price considering the buyer and warrantor point of views towards the expected repair cost and claims cost, respectively.
The practical implications of this thesis are listed as follows:
(a) The WaRM framework will provide warranty practitioners with the required guidelines to manage warranty risks.
(b) The result of using the streaming data as an early warning tool has shown its efficiency in highlighting the warranty issues.
(c) The warranty hazards taxonomies might help warranty practitioners in improving the process, procedures or technologies which are required to reduce the occurrence of warranty risks.
(d) The development of WaRM-CPT model may aid the decision makers in selecting the optimal mitigation plan to respond to an emergent warranty risk.
(e) The determination of the optimal warranty price can be achieved when the warrantor and buyers views are considered. To this end, a mathematical model is provided.
• Luo, M. (2018). Learning from Actuarial Science: Approaches to Collectively Optimising Warranty Policies.
This research starts from the comparison between warranty and insurance in their coverages, policies, data and, particularly, policy optimisation techniques. Based on abundant literature in related areas, the result of this comparison indicates that warranty policy optimisation can be improved by considering the application of the portfolio theory, dependence modelling and risk measures that are widely used in the actuarial science and the financial discipline. In the following chapters, Chapter 1 introduces the Importance of this research and lists its aim and objectives. Chapter 2 mainly conducts a critical and comprehensive literature review relating to warranty management and actuarial science and summarised the knowledge gaps identified. Chapter 3 establishes a collective warranty policy optimisation framework, with the benefits of the modern portfolio theory borrowed from the actuarial and financial disciplines and copulas from the probability and statistics. With progressing of this research, the disadvantage of the symmetric risk measure, variance, is uncovered in dealing with the extreme events. Chapter 4 proposes using two of the downside risk measures used in the financial discipline, Value-at-Risk and Conditional Value-at-Risk, into the optimisation of warranty policy and a new portfolio optimisation framework of warranty optimisation based on copulas. Chapter 5 investigates the interplay among the hardware, software and users of individual products under different scenarios relating to the warranty claims. Considering such an interplay, it then develops a more comprehensive framework for warranty policy optimisation. This fits the trend that that more and more products can be considered as a system composed of three subsystems: hardware, software and user subsystems and considers that the existing warranty policy optimisation methods in the literature merely focus on products composed of hardware systems. Even though the above chapters have developed warranty policy optimisation frameworks collectively and comprehensively, this research can also be improved in many aspects. As such, in Chapter 6, the sale volume modelling, renewing warranty policy optimisation and copula selection are discussed. Chapter 7 wraps up the research and discusses future research.
• Zheng, Y. (2017). Theory and Action Research on a New Framework and Approach of Performance Management.
Today, the activities relevant to performance management (PM) can be found in every corner of business, and its importance could be described by a famous business motto that whether a company measures its workforce in hundreds or thousands, its success relies solely on performance. Despite its importance as an enabler of successful business, some issues and shortcomings still exist in the performance management research and its implementation, which can be largely categorized into two main challenges.
The first challenge is reflected in the PM dilemma of SMEs. Most existing PM frameworks focus on mechanistic organisations of significant size, yet small and medium enterprises, which comprise 99 percent of business in the UK and 94.15 percent in China, benefit little from the extant PM research. The second PM challenge is combining PM with business and management process innovations. Even for an organisation with simple operating cores, current PM frameworks provide little guidance on how to introduce innovations during performance management system (PMS) building up and management. This issue further causes difficulties in managing performance in complex operating cores, which is exemplified by the challenges of carrying out PM in an R&D unit.
The above challenges are quite typical and should be dealt with in the level of performance management framework. We believe that existing PM frameworks are not built around an organisation's performance generation processes and therefore may not be able to handle many issues effectively, including those outlined above. Thus, the research objectives of this thesis are to develop a PM framework that is built around performance generation and also has mechanisms to address the above issues. Furthermore, we need to develop implemental approaches within the framework that can effectively deal with these challenges in real business cases.
To accomplish the aforementioned research objectives, a comprehensive typological literature review was carried out to analyze the characteristics and features of the existing PM frameworks. Next, based on the literature research, a new PM framework, namely as the performance tree (PT) framework was introduced in Chapter five, which focuses on the performance generation processes of organisations and also contains mechanisms to accommodate different approaches for a wide range of organisations. In addition, two implemental approaches of PT frameworks were developed in the thesis for the sake of solving the pressing PM issues in SMEs and R&D unit.
This research has the following four main contributions:
1. A significant research gap was identified that the existing PM frameworks largely ignored the procedures of performance generation which could lead organisations to be near-sighted, unsustainable, and even experience strategic failure.
2. A new performance management framework, PT framework was developed in this thesis. The PT framework adopts a performance-based perspective to explain performance generation and management processes; also it contains mechanisms to accommodate different approaches for a wide range of organisations seeking to handle the pressing PM issues
3. An implemental approach of PT for classic Chinese manufacturer SMEs was developed in the thesis. Comparing with the existing PM approaches, the new one fully considers the managerial and operational characteristics of SMEs, such as fast-changing organisational chart and high demand for organisational adjustments.
4. An implemental approach of PT for Chinese R&D units under was developed in the thesis. The approach considers both the characteristics of R&D management and the specific PM needs, and hence a PMS in accordance with core operation of R&D units can be developed under its guidance. Meanwhile, a behavioural evidence-based performance measurement system is accommodated in the approach to better measure and evaluate R&D staff's performance.
• Malik, S. (2015). Optimising Supermarket Promotions of Fast Moving Consumer Goods Using Disaggregated Sales Data: A Case Study of Tesco and Their Small and Medium Sized Suppliers.
The use of price promotions for fast moving consumer goods (FMCG’s) by supermarkets has increased substantially over the last decade, with significant implications for all stakeholders (suppliers, service providers & retailers) in terms of profitability and waste. The overall impact of price promotions depends on the complex interplay of demand and supply side factors, which has received limited attention in the academic literature. There is anecdotal evidence that in many cases, and particularly for products supplied by small and medium sized enterprises (SMEs), price promotions are implemented with limited understanding of these factors, resulting in missed opportunities for sales and the generation of avoidable promotional waste. This is particularly dangerous for SMEs who are often operating with tight margins and limited resources.
A better understanding of consumer demand, through the use of disaggregated sales data (by shopper segment and store type) can facilitate more accurate forecasting of promotional uplifts and more effective allocation of stock, to maximise promotional sales and minimise promotional waste. However, there is little evidence that disaggregated data is widely or routinely used by supermarkets or their suppliers, particularly for those products supplied by SMEs. Moreover, the bulk of the published research regarding the impact of price promotions is either focussed on modelling consumer response, using claimed behaviour or highly aggregated scanner data or replenishment processes (frameworks and models) that bear little resemblance to the way in which the majority of food SMEs operate.
This thesis explores the scope for improving the planning and execution of supermarket promotions, in the specific context of products supplied by SME, through the use of dis-aggregated sales data to forecast promotional sales and allocate promotional stock. An innovative case study methodology is used combining qualitative research to explore the promotional processes used by SMEs supplying the UK’s largest supermarket, Tesco, and simulation modelling, using supermarket loyalty card data and store level sales data, to estimate short term promotional impacts under different scenarios and derive optimize stock allocations using mixed integer linear programming (MILP).
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The results suggest that promotions are often designed, planned and executed with little formalised analysis or use of dis-aggregated sales data and with limited consideration of the interplay between supply and demand. The simulation modelling and MILP demonstrate the benefits of using supermarket loyalty card data and store level sales data to forecast demand and allocate stocks, through higher promotional uplifts and reduced levels of promotional waste

Forthcoming

• Sabhi Appanna, D. (2019). Reliability Modelling For Asset Management in South East Water.
Over the years, the reliability modelling of water assets has generated increasing interest among both researchers and practitioners. Statistical methods and software packages for assessing asset reliability have been developed in order to improve asset availability, indirectly reduce water losses, and hence improve the efficiency of water assets. OFWAT, which is the economic regulator of the water sector in England and Wales, aims to ensure that water companies operate under their statutory functions and have sufficient financial means to perform these functions adequately. Water companies need to prepare a five-year business plan for OFWAT, in order to certify they have enough capital and are transparent when carrying out their statutory functions. Hence, this thesis aims to analyse the reliability of two selected types of assets at South East Water to help plan their future investments on vehicles and future maintenance costs on borehole assets.

This thesis will provide an extensive literature review on reliability modelling in water distribution networks. An MS Excel-based decision support system will be developed for both vehicles and borehole assets, using data collected from South East Water. For the transport model, a block replacement policy will be developed by using Visual Basic, to obtain the optimum time of replacing a vehicle. Performance analysis will be conducted on the borehole data to pinpoint the worst performers among the 16 boreholes under analysis.
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