On defect propagation in multi-machine stochastically deteriorating systems with incomplete information

In many manufacturing environments, costly job inspection provides information about the random deterioration of the machines. The resulting maintenance and inspection problem is extensively studied for a single machine system by using the framework of Partially Observable Markov Decision Processes (POMDPs). In this work, this concept is extended to multiple operations and multiple job types by considering two process flow topologies: (i) re-entrant flow, (ii) hybrid flow. The resulting (significantly large sized) POMDPs are solved using a point based method called PERSEUS, and the results are compared with those obtained by conventionally used periodic policies.     

Optimal replacement policy for a deteriorating production system with preventive maintenance

This paper presents a new policy for determining the optimal replacement time of a deteriorating production system. The optimal replacement time is expressed in terms of the accumulated number of failures that the system has experienced. The provision of preventive maintenance is incorporated in the system model and the objective function is cost efficiency (i.e. the long-run average cost per unit working time). A numerical example is given in the paper. The basic concept used in this paper parallels the geometric process replacement policy N introduced by Lam in 1988. The work in this paper generalizes and modifies Lam's 1988 work.     

全寿命周期下退化的大规模系统预防性维修策略优化

单元退化情形下,考虑全寿命周期的大规模系统可靠性设计与预防性维修策略的综合优化问题将变得更为复杂.针对单元失效服从威布尔分布的情形,考虑多单元联合的预防性维修模式,构建可靠性约束下大规模系统全寿命周期成本优化模型.单元数量众多带来的组合规模指数增长问题将导致非线性择优困难,利用遗传算法编程快速求解全局最优解,包括设计阶段的单元可靠性和使用阶段的系统预防性维修周期.最后通过典型算例分析验证模型与算法的正确性和有效性,探究维修改善因子、单元可靠性和预防性维修周期等决策变量间的相互关系.研究成果有助于简化系统工程师的可靠性工程设计过程,具有一定的理论和应用价值.     

Integrated production planning and preventive maintenance in deteriorating production systems

This paper discusses the issue of integrating production planning and preventive maintenance in manufacturing production systems. In particular, it tackles the problem of integrating production and preventive maintenance in a system composed of parallel failure-prone production lines. It is assumed that when a production line fails, a minimal repair is carried out to restore it to an ‘as-bad-as-old’ status. Preventive maintenance is carried out, periodically at the discretion of the decision maker, to restore the production line to an ‘as-good-as-new’ status. It is also assumed that any maintenance action, performed on a production line in a given period, reduces the available production capacity on the line during that period. The resulting integrated production and maintenance planning problem is modeled as a nonlinear mixed-integer program when each production line implements a cyclic preventive maintenance policy. When noncyclical preventive maintenance policies are allowed, the problem is modeled as a linear mixed-integer program. A Lagrangian-based heuristic procedure for the solution of the first planning model is proposed and discussed. Computational experiments are carried out to analyze the performance of the method for different failure rate distributions, and the obtained results are discussed in detail.     

Optimal maintenance model for a multistate deteriorating system: a geometric process approach

A monotone process model is introduced for a deteriorating system with k+1 states (k working states and one failure state). We prove that the model is equivalent to a geometric process model for a two-state system, in the sense that both systems have the same long-run average cost per unit time and the same optimal maintenance policy. Finally, an optimal maintenance policy for the deteriorating system is determined analytically.     

Model-based testing of stochastically timed systems

Innovations in Systems and Software Engineering - Many systems are inherently stochastic: they interact with unpredictable environments or use randomised algorithms. Classical model-based testing...     

A condition-based maintenance policy and input parameters estimation for deteriorating systems under periodic inspection

This paper combines an optimization model and input parameters estimation from empirical data, in order to propose condition-based maintenance policies. The system deterioration is described by discrete states ordered from the state “as good as new” to the state “completely failed”. At each periodic inspection, whose outcome might not be accurate, a decision has to be made between continuing to operate the system or stopping and performing its preventive maintenance. We explore the problem of how to estimate the model input parameters, i.e., how to adequate the model inputs to the empirical data available. For this purpose, we use the Hidden Markov Model theory. The literature has not explored the combination of optimization techniques and model input parameters, through historical data, for problems with imperfect information such as the one considered in this paper. We thoroughly discuss our approach, illustrate it with empirical data and also point out directions for future research.     

Unrelated parallel-machine scheduling with deteriorating maintenance activities

We study the problem of unrelated parallel-machine scheduling with deteriorating maintenance activities. Each machine has at most one maintenance activity, which can be performed at any time throughout the planning horizon. The length of the maintenance activity increases linearly with its starting time. The objective is to minimize the total completion time or the total machine load. We show that both versions of the problem can be optimally solved in polynomial time.     

Optimal design of series-parallel systems considering maintenance and salvage value

A reliability based design (RBD) model is developed for a series-parallel system with deteriorating components in order to minimize the life cycle cost of the system. The effects of fixed asset depreciation, preventive maintenance and minimal repair are incorporated in the model. We also propose equations to model the effects of preventive maintenance on the system's failure rate and the salvage value as functions of time. Genetic algorithms (GAs) are used to perform constrained optimization of the system cost function subject to both active and non-active constraints. The results are useful for engineering economists, reliability engineers, and system designers.     

Machine scheduling with deteriorating and resource-dependent maintenance activity

In this paper we investigate scheduling problems with a deteriorating and resource-dependent maintenance activity on a single machine. The duration of the maintenance is assumed to be dependent both on its starting time and on the resource allocated to it. The objective is determining the job sequence, the position to perform a maintenance activity and the amount of additional resource allocated to it such that the total cost of related measure and resource is minimized. The considered measures are the makespan, flowtime, maximum tardiness and combination of earliness, tardiness and due-date. Analysis results show that all the considered problems are polynomially solvable.     

Stability analysis of systems with stochastically varying delays

A stability analysis of linear systems with stochastically varying delay is performed. It is assumed that the delay function has the form of a sawtooth with switches occurring at the arrival times of a homogeneous Poisson process. Several notions of stochastic stability are considered and corresponding stability criteria are derived. For two examples the different criteria are compared and the effect on stability of various deterministic approximations is examined.     

Optimal spares and preventive maintenance frequencies for constrained industrial systems

The research investigates the influence of an effective maintenance system on the efficient performance of any industrial system. The core concept of the research explains that the simultaneous focus on the spares inventory subsystem as well as on the preventive maintenance subsystem must be considered when developing a quality maintenance programme. Considering and developing such aspects separately will lead to suboptimal performance since there exists a trade-off between overstocking and undersupplying spares for preventive maintenance activities. Details on the technique chosen are discussed, namely simulation modelling as well as recent developments such as agent based modelling. Advantages of this technique are the flexibility in representing complex relationships within a system without knowing the exact form. The optimisation heuristic, a genetic algorithm, which was used to solve the research problem is explained. Finally a case study is used to demonstrate the aptness and success of the research approach, namely an annual 44% maintenance cost saving and 3% increase in production output.     

Optimal maintenance policy for multi-component systems under Markovian environment changes

In this paper, we study multi-component systems, which environmental conditions and opportunistic maintenance (OM) involve. Environmental conditions will exert an influence on deterioration processes of the components in the system. For each component, the worse the environmental conditions are, the faster its deterioration speed is. We want to determine when to preventively maintain each component under such environmental influence. Our purpose is to minimize its long-run average maintenance cost. We decompose such a multi-component system into mutually influential single-component systems, and formulate the maintenance problem of each component as a Markov decision process (MDP). Under some reasonable assumptions, we prove the existence of the optimal (n_r, N_r) type policy for each component. A policy iteration method is used to calculate its optimal maintenance policy. Based on the method, we develop an iterative approximation algorithm to obtain an acceptable maintenance policy for a multi-component system. Numerical examples find that environmental conditions and OM pose significant effects on a maintenance policy.     

Joint optimization of preventive maintenance and inventory policies for multi-unit systems subject to deteriorating spare part inventory

The interconnection of maintenance and spare part inventory management often puzzles managers and researchers. The deterioration of the inventory affects decision-making and increases losses. Block replacement and periodic review inventory policies were here used to evaluate a joint optimization problem for multi-unit systems in the presence of inventory deterioration. The deterministic deteriorating inventory (DDI) model was used to describe deteriorating inventory when deteriorating inventory data were available and the stochastic deteriorating inventory (SDI) model was used when they were not. Analytical joint optimization models were established, and the preventive replacement interval and the maximum inventory level served as decision variables to minimize the expected system total cost rate. This work proved the existence of the optimal maximum inventory level and gave the uniqueness condition under the DDI model. Numerical experiments based on the electric locomotives in Slovenian Railways were performed to confirm the effectiveness of the proposed models. Results showed the total cost rate to be sensitive to the maximum inventory level, which indicates that the research of this work is necessary. Further, the optimal preventive replacement interval was reduced and the optimal maximum inventory level was increased to balance the influence of deteriorating inventory. Monte Carlo experiments were used to show that the proposed policy is better than policies that do not take deteriorating inventory into account.     

Optimal and suboptimal solutions to stochastically uncertain problems of quintile optimization

In this paper, problems of stochastic optimization under incomplete information on distribution of random perturbations with the quintile and probability criteria are considered. The minimax approach is used when optimal solutions are chosen. Conditions for equivalency of direct and inverse problems of stochastic optimization under incomplete statistical information are studied. The solution method for statistically uncertain problems of optimization with the quintile criterion basing on the use of generalized confidence sets for statistically uncertain random quantities is proposed. The use of confidence sets for finding suboptimal solutions to the problem of stochastic optimization under incomplete information is considered. Examples of the application of obtained relations are represented.     

Optimal maintenance policies for systems subject to a Markovian operating environment

Many stochastic models of repairable equipment deterioration have been proposed based on the physics of failure and the characteristics of the operating environment, but they often lead to time to failure and residual life distributions that are quite complex mathematically. The first objective of our study is to investigate the potential for approximating these distributions with traditional time to failure distribution. We consider a single-component system subject to a Markovian operating environment such that the system’s instantaneous deterioration rate depends on the state of the environment. The system fails when its cumulative degradation crosses some random threshold. Using a simulation-based approach, we approximate the time to first failure distribution for this system with a Weibull distribution and assess the quality of this approximation. The second objective of our study is to investigate the cost benefit of applying a condition-based maintenance paradigm (as opposite to a scheduled maintenance paradigm) to the repairable system of interest. Using our simulation model, we assess the cost benefits resulting from condition-based maintenance policy, and also the impact of the random prognostic error in estimating system condition (health) on the cost benefits of the condition-based maintenance policy.     

Patient scheduling with periodic deteriorating maintenance on single medical device

In this paper, we study a patient scheduling problem with periodic deteriorating maintenance. The objective is to minimize the number of tardy medical treatment of all the patients. A binary integer programming model is developed to characterize the problem. A three-phase heuristic based on Moore׳s algorithm is proposed for the problem. Numerical experiments are performed to demonstrate the effectiveness of the proposed heuristic. Results show that the proposed heuristic is able to obtain a relatively good solution in a short computation time. The impact of the key parameters on the performance of the proposed heuristic is discussed. Finally, we develop an earliest due date (EDD) rule based heuristic to optimize another objective, the maximum tardiness, which is more applicable when fairness among patients is considered.     

Optimal inventory policies for deteriorating complementary and substitute items

The optimal production for an inventory control system of deteriorating multi-items where items are either complementary and/or substitute is formulated with a resource constraint. Here, the production function is unknown and considered as a control variable. Also, the deterioration rates of the items are either stock dependent or constant. The demand is stock dependent, shortages are not allowed and deteriorated items are salvaged. The total profit, which consists of the sales proceeds, production cost, inventory holding cost, salvage value, is formulated as a Pontryagin's Optimal Control problem for both steady and transient states and evaluated using Taylor's theorem, generalised reduced gradient technique and optimal control theory satisfying the Generalised Legendre conditions. The model is formulated in general form for n-items, and in particular, is illustrated with three items for some numerical data. The optimum results are presented both in tabular form and graphically.     

Optimal dynamic pricing for deteriorating items with reference-price effects

In this paper, a dynamic pricing problem for deteriorating items with the consumers’ reference-price effect is studied. An optimal control model is established to maximise the total profit, where the demand not only depends on the current price, but also is sensitive to the historical price. The continuous-time dynamic optimal pricing strategy with reference-price effect is obtained through solving the optimal control model on the basis of Pontryagin's maximum principle. In addition, numerical simulations and sensitivity analysis are carried out. Finally, some managerial suggestions that firm may adopt to formulate its pricing policy are proposed.