A Nearly Optimal Inspection Policy

This paper is concerned with an easily computable inspection policy for the detection of the failure of a system. A one-parameter policy is suggested and it is shown that this policy has the property of decreasing (increasing) intervals between successive inspection times if the system has an increasing (decreasing) failure rate. Cost comparisons, using linear cost functions, with a computationally difficult optimal policy which has a minimium expected cost show that the proposed policy compares quite well with the optimal policy.     

An Inspection Policy for the Weibull Case

This paper is concerned with the detection of failure of a system when the time to failure is a Weibull variate. The suggested inspection policy depends on a single meaningful parameter. Graphical aids for computing an appropriate inspection policy on the basis of costs, or on the basis of mean time between failure and its detection are given.     

Approximate Calculation of Optimal Inspection Times

This paper considers an inspection model whose failure is known only through checking. A new approximate calculation of optimal checking procedures is suggested. This computes successive check times backwards, supposing that an appropriate check time is previously given after a large number of checks. This policy is simple to compute and compares fairly well with the optimal policy.     

一可修系统的最优检测更新模型

本文研究了由一个部件和一个修理工组成的检测更新模型。部件不能“修复如新”。其寿命和修理时间均服从一般分布。在假设最大的修理次数为K—1的条件下,证明了最优检测时间T的存在,此时模型取得最大经济效益。     

Optimally maintaining a Markovian deteriorating system with limited imperfect repairs

We consider the problem of optimally maintaining a periodically inspected system that deteriorates according to a discrete-time Markov process and has a limit on the number of repairs that can be performed before it must be replaced. After each inspection, a decision maker must decide whether to repair the system, replace it with a new one, or leave it operating until the next inspection, where each repair makes the system more susceptible to future deterioration. If the system is found to be failed at an inspection, then it must be either repaired or replaced with a new one at an additional penalty cost. The objective is to minimize the total expected discounted cost due to operation, inspection, maintenance, replacement and failure. We formulate an infinite-horizon Markov decision process model and derive key structural properties of the resulting optimal cost function that are sufficient to establish the existence of an optimal threshold-type policy with respect to the system’s deterioration level and cumulative number of repairs. We also explore the sensitivity of the optimal policy to inspection, repair and replacement costs. Numerical examples are presented to illustrate the structure and the sensitivity of the optimal policy.     

被检测系统的可靠性和最优检测策略

研究被检测系统的一个模型,假定系统有4种运行状态(正常工作、异常工作、正常故障和异常故障)．系统故障时不需检测,系统工作时必须经过检测才能知道它是正常还是异常．系统开始工作后,每隔一段随机时间对它检测一次,直到系统故障或检测出系统处于异常状态为止．利用概率分析和随机模型的密度演化方法,导出了系统的一些新的可靠性指标和最优检测策略．     

修理工可单重休假的预防维修更换策略

本文研究了一个修理工带有单重休假的单部件可修系统.为了延长系统的使用寿命,在系统故障前考虑了预防维修,且假定预防维修能够“修复如新”,而故障维修为“修复非新”时,以系统的故障次数N为更换策略.通过更新过程和几何过程理论,得出系统经长期运行单位时间内期望费用的明显表达式,并对预防维修的定长间隔时间T及更换策略N进行了讨论,最后,通过实例分析,求出最优策略N’,使得目标函数取得最优值.     

Optimal lot size and inspection policy for products sold with warranty

This paper develops a mathematical model to jointly determine the optimal lot size and product inspection policy for a deteriorating production system, when products are sold with free minimal repair warranty. Due to system deterioration, a last-K product inspection scheme is proposed, under which the last K products in a production lot are inspected and nonconforming products found are reworked. Based on the model, we show that there exist a unique optimal lot size and a corresponding inspection policy such that the expected total cost per unit time is minimized. Since there is no closed-form expression for the optimal lot size, an upper bound and approximate solutions are obtained to facilitate the search process. Furthermore, an algorithm is provided to efficiently search for the optimal policy and the performance of the optimal policy is evaluated through numerical examples.     

Availability and maintenance modeling for systems subject to dependent hard and soft failures

This paper develops availability and maintenance models for single‐unit systems subject to dependent hard and soft failures. A hard failure stops the system immediately, whereas a soft failure only reduces the performance capacity of the system. Dependence between these 2 types of failures is reflected in the fact that each soft failure directly increases the hazard rate of the hard failure. On the basis of such interaction, we derive recursive equations for the system reliability and availability functions. To detect both types of failures, inspections are executed periodically. Furthermore, we investigate the optimal inspection policy via the minimization of the expected cost per unit time. The applicability of the developed availability and maintenance models is validated by a case study on an electrical distribution system.     

带有多重休假及预防维修的冲击模型二维更换策略

研究了修理工带有多重休假且定期检测的累积冲击模型.为了延长系统的运行时间,在检测时考虑了预防维修.将事后维修和预防维修结合起来运用于可修系统,且假定预防维修能够"修复如新",而事后维修为"修复非新".以系统的检测周期和故障次数为二维决策变量,选取系统经长期运行单位时间内期望费用为目标函数.并通过数值分析,求出了最优策略.     

Simple expressions for finding recovery system inventory control parameter values

In recent years considerable effort has been devoted to the development of inventory control models for joint manufacturing and remanufacturing. Optimality of control policies is analyzed and algorithms for the determination of parameter values have been developed. However, there is still a lack of formulae or algorithms that allow for an easy computation of optimal or near optimal policy parameter values. This paper addresses the problem of computing the produce-up-to level S and the remanufacture-up-to level M in a periodic review inventory control model. We provide simple formulae for the policy parameter values, which can easily be implemented within spreadsheet applications. The approach is to derive news-vendor-type formulae that are based on underage and overage cost considerations. We propose different formulae depending on whether lead times for production and remanufacturing are identical or not. A numerical study shows that the obtained solutions provide relatively small cost deviations compared to the optimal solution within the investigated class of inventory control policies.     

Optimizing System Availability Under Minimal Repair with Non-Negligible Repair and Replacement Times

Availability measures are given for a repairable system under minimal repair with constant repair times. A new policy and an existing replacement policy for this type of system are discussed. Each involves replacement at the first failure after time T, with T representing total operating time in the existing model and total elapsed time (i.e. operating time + repair time) in the new model. Optimal values of T are found for both policies over a wide range of parameter values. These results indicate that the new and administratively easier policy produces only marginally smaller optimal availability values than the existing policy.     

Inspection scheduling for imperfect production processes under free repair warranty contract

The paper considers scheduling of inspections for imperfect production processes where the process shift time from an ‘in-control’ state to an ‘out-of-control’ state is assumed to follow an arbitrary probability distribution with an increasing failure (hazard) rate and the products are sold with a free repair warranty (FRW) contract. During each production run, the process is monitored through inspections to assess its state. If at any inspection the process is found in ‘out-of-control’ state, then restoration is performed. The model is formulated under two different inspection policies: (i) no action is taken during a production run unless the system is discovered in an ‘out-of-control’ state by inspection and (ii) preventive repair action is undertaken once the ‘in-control’ state of the process is detected by inspection. The expected sum of pre-sale and post-sale costs per unit item is taken as a criterion of optimality. We propose a computational algorithm to determine the optimal inspection policy numerically, as it is quite hard to derive analytically. To ease the computational difficulties, we further employ an approximate method which determines a suboptimal inspection policy. A comparison between the optimal and suboptimal inspection policies is made and the impact of FRW on the optimal inspection policy is investigated in a numerical example.     

Basic optimality results for Bayesian group replacement policies

The optimal structure of Bayesian group replacement policies for a parallel system of n items with exponential failure times and random failure parameter is presented. The paper contains a proof of the fact that it is optimal to observe the system only at failure times. For the case of two items operating in parallel the exact form of the policy is derived.     

Utilizing an approximative solution to obtain the real optimal solution for a production and inspection model

Previous studies have proposed an integrated production and inspection model for a deteriorating production system whose process is characterized by an exponential distribution. Since the simultaneous determination of the optimal scheduled inspection times and the optimal production run length is difficult, an approximative production and inspection solution is obtained under the condition that the optimal inspection policy is equally-spaced. That is, obtaining an approximative production run length and number of inspections. This study further investigates this approximative solution and demonstrates that how to utilize it to obtain the real optimal solution more efficiently.     

考虑不完全检测的冲击模型最优维修策略

针对制造系统中设备检测不完全的情形,研究基于不完全检测的冲击模型的周期检测、维修联合策略．通过定期检测获知系统的劣化状态以进行必要的预防性维修．在假设系统是退化的且有k个不同故障状态的条件下,以最小化系统运行成本为目标,以检测周期T、系统更换前故障次数Ⅳ为联合决策变量,利用更新过程理论建立了系统平均费用率C（T,N）的数学模型,并且给出最优联合策略的数值算法．最后借助数值例子演示了该模型,分析了检测水平对系统运行成本的影响．     

Comparison of Inspection Policies

In this paper, we compare an optimal inspection policy by Barlow et al. with nearly optimal ones by Kaio and Osaki, Munford and Shahani, and Nakagawa and Yasui. We obtain the result that, for the Weibull and gamma distributions, there are no significant differences between the optimal and nearly optimal inspection policies. We recommend the simpler-to-compute policy of Kaio and Osaki since it is nearly optimal.     

Optimal inspection policy for three-state systems monitored by control charts

This paper presents the formulations of the expected long-run cost per time unit for a system monitored by a static control chart and by an adaptive control chart respectively. The static chart has a fixed sampling interval and a fixed sample size. The adaptive chart has a fixed sample size but variable sampling intervals. The system is supposed to have three states, normal working state, failure delay time state, and failed state. Two levels of repair are used to maintain the system. A minor repair is used to restore the system if a detectable defect is confirmed by an inspection. A major repair will be performed if the system fails. The expected cost per time unit for maintaining such a system is obtained. The objective of such analysis is to find an optimal sampling policy for the inspection process. An artificially generated data example and a real data example are used to compare the expected cost per time unit for both the static and adaptive control charts.     

Optimal policy and stability regions for the single product periodic review inventory problem,with stationary demands

In this paper we present rules concerning the optimal policy and stability regions for the single product periodic review inventory problem with stationary demands, over a finite horizon. The key parameter to the whole study is the Lot-Sizing Index (LSI) introduced by Blackburn and Millen. Two algorithms are presented. The first one constructs stability regions which are expressed as intervals of the LSI parameter, covering the whole range of its values. The proposed algorithm is very simple to understand and implement, and most importantly, it provides a solution table which can be used by the decision maker to easily determine the optimal policy for any problem with a given horizon and any possible combination of its cost parameters, namely any LSI value. The second proposed algorithm determines the optimal policy for any given LSI value; it constitutes a completely different approach to that of the Wagner–Whitin algorithm and requires very little computational effort.