Bounds to optimal burn‐in and optimal work size

Burn‐in is a widely used method to improve the quality of products or systems after they have been produced. In this paper, we consider the problem of determining the optimal burn‐in time and optimal work size maximizing the long‐run average amount of work saved per time unit in the computer applications. Assuming that the underlying lifetime distribution of the computer has an initially decreasing or/and eventually increasing failure rate function, an upper bound for the optimal burn‐in time is derived for each fixed work size and a uniform (with respect to the burn‐in time) upper bound for the optimal work size is also obtained. Furthermore, it is shown that a non‐trivial lower bound for the optimal burn‐in time can be derived if the underlying lifetime distribution has a large initial failure rate. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficiency consideration of generalized age replacement policy

Under the generalized age replacement policy, the system is replaced either at the predetermined age or upon failure if its corresponding repair time exceeds the threshold, whichever comes first. In this paper, we investigate the optimal choice of the pre‐determined preventive replacement age for a nonwarranted system, which minimizes the expected cost rate during the life cycle of the system from the customer's perspective under certain cost structures. Furthermore, we discuss several properties of such a generalized age replacement policy in comparison with the traditional age replacement policy. An efficiency, which represents the fractional time that the system is on, is defined under the proposed generalized age replacement policy and its monotonicity properties are investigated as well. The main objective of this study is to investigate the advantageous features of the generalized age replacement policy over the traditional age replacement policy with regard to the availability of the repairable system. Assuming that the system deteriorates with age, we illustrate our proposed optimal policies numerically and observe the impact of relevant parameters on the optimal preventive replacement age.     

Long-term optimal operation of a parallel multireservoir power system

Long-term optimal operation of a multireservoir system is complex because it is a dynamic problem (present decisions for one reservoir depend on future decisions for all reservoirs); the optimal operating policy for one reservoir depends not only on its own energy content, but also on the corresponding content of each one of the other reservoirs; it is a highly stochastic problem with respect to the reservoir inflows and it is a nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system consisting of multireservoirs on a multiriver system taking into account the stochasticity of the river flows. Functional optimization techniques and minimum norm formulation have been used. Results for a numerical example composed of three rivers with four reservoirs, three reservoirs, and two reservoirs on each river, respectively, are presented.This work was supported by the National Research Council of Canada, Grant. No. A4146.     

单部件可修系统的一个几何过程维修模型

本文研究了单部件、一个修理工组成的可修系统的最优更换问题,假定系统不能修复如新,以系统年龄T为策略,利用几何过程求出了最优的策略T^*,使得系统经长期运行单位时间内期望效益达到最大,并求出了系统经长期运行单位时间内期望效益的显式表达式。在一定条件下证明了T^*的唯一存在性。最后还证明了策略T^*比文献[6]中的策略T^*优。     

Optimal operation of multireservoir power systems

The optimal monthly operating policy of a multireservoir hydroelectric power system is a stochastic nonlinear problem. This paper presents a new method for determining the optimal monthly operating policy of a power system ofn reservoirs in series on a river taking into account the stochasticity of the river flows. Functional optimization techniques and minimum-norm formulation have been used to find the optimal release policy of the system. Results for a numerical example composed of four reservoirs are presented.This work was supported by the National Research Council of Canada, Grant No. A4146.     

一个可修系统的最优更换模型

本文考虑了单部件、一个修理工组成的可修系统，在故障系统不能“修复如新”的前提下，我们利用几何过程，以系统年龄Ｔ为策略，选择最优的Ｔ使得系统经长期运行单位时间的期望效益达到最大．本文还在一定的条件下证明了最优更换策略Ｔ的唯一存在，且求出了系统经长期运行单位时间的最大期望效益的明显表达式．     

Two-stage generalized age maintenance of a queue-like production system

In general, the initiation of preventive maintenance should be based on the technical state as well as the operating state of a production system. Since the operating state of a production system is often subject to fluctuations in time, the planning of preventive maintenance at preset points in time (e.g. age/block replacement) cannot be optimal. Therefore, we propose a so-called two-stage maintenance policy, which - in a first stage - uses the technical state of the production system to determine a finite interval [t, t + At] during which preventive maintenance must be carried out, and - in a second stage - uses the operating state of the production system to determine the optimal starting time t̂ for preventive maintenance within that interval. A generalized age maintenance policy optimizing both t and At is formulated in the first stage. To this end, the actual starting time of preventive maintenance is modelled in terms of a uniform distribution over the maintenance interval. Moreover, the expected costs of preventive maintenance are modelled as a decreasing function of the interval size. An efficient algorithm is developed to demonstrate the optimal strategy for a queue-like production system, via numerical results that offer useful insights.     

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.     

有限可修备件条件下系统计划更换策略

在现有的计划更换模型的基础上 ,研究了一种备件有限及部件可修的更换策略问题。利用在更换周期点上具有的马尔可夫性质 ,以系统首次故障前平均工作时间最大为目标建立了确定最佳更换周期的模型。     

Optimal maintenance scheduling for a complex manufacturing system subject to deterioration

We address the problem of determining inspection strategy and replacement policy for a deteriorating complex multi-component manufacturing system whose state is partially observable. We develop inspection and replacement scheduling models and other simple maintenance scheduling models via employing an imperfect repair model coupled with a damage process induced by operational conditions. The system state in performance of the imperfectly repaired system is modelled using a proportional intensity model incorporating a damage process and a virtual age process caused by repair. The system is monitored at periodic times and maintenance actions are carried out in response to the observed system state. Decisions to perform imperfect repair and replacement are based on the system state and crossing of a replacement threshold. The model proposed here aims at joint determination of a cost-optimal inspection and replacement policy along with an optimal level of maintenance which result in low maintenance cost and high operational performance and reliability of the system. To demonstrate the use of the model in practical applications a numerical example is provided. Solutions to optimal system parameters are obtained and the response of the model to these parameters is examined. Finally some features of the model are demonstrated. The approach presented provides a framework so that different scenario can be explored.     

An information‐based burn‐in procedure for minimally repaired items from mixed population

Burn‐in is a method used to eliminate the initial failures in field use. In this paper, we will consider an information‐based burn‐in procedure for repairable items, which is completely new type of burn‐in procedure. By this procedure, based on the operational (failure and repair) history of the items observed during burn‐in procedure, those with poor reliability performance are eliminated. From a probabilistic point of view, this burn‐in procedure utilizes the information contained in the ‘random paths’ of the corresponding point processes. A general formulation of the model will be suggested, and under the suggested framework, two‐stage optimization procedure for determining optimal burn‐in procedures will be studied in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

The average optimality of a repair-limit replacement policy

We consider a minimal-repair and replacement problem of a reliability system whose state at a failure is described by a pair of two attributes, i.e., the total number of its past failures and the current failure level. It is assumed that the system is bothered by more frequent and more costly failures as time passes. Our problem is to find and/or characterize a minimal-repair and replacement policy of minimizing the long-run average expected maintenance cost per unit time over the infinite time horizon. Formulating the problem as a semi-Markov decision process, we show that a repairlimit replacement policy is average optimal. That is, for each total number of past system failures, there exists a threshold, called a repair limit, such that it is optimal to repair minimally if the current failure level is lower than the repair limit, and to replace otherwise. Furthermore, the repair limit is decreasing in the total number of past system failures.     

A graphical method to repair-cost limit replacement policies with imperfect repair

In this paper, we consider a different type of repair-cost limit replacement problem with imperfect repair from earlier models. We focus on the problem of determining the timing to stop repairing a unit after it fails, and propose a nonparametric method to estimate the optimal repair-cost limit which minimizes the total expected cost per unit time in the steady-state, by applying the total time on test (TTT) concept. Through a numerical example, the optimal policy is calculated from the repair-cost data directly, and the benefit of the proposed method is shown.     

A deteriorating cold standby repairable system with priority in use

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. In this system, it is assumed that the working time distributions and the repair time distributions of the two components are both exponential and component 1 is given priority in use. After repair, component 2 is “as good as new” while component 1 follows a geometric process repair. Under these assumptions, using the geometric process and a supplementary variable technique, some important reliability indices such as the system availability, reliability, mean time to first failure (MTTFF), rate of occurrence of failure (ROCOF) and the idle probability of the repairman are derived. A numerical example for the system reliability R(t) is given. And it is considered that a repair-replacement policy based on the working age T of component 1 under which the system is replaced when the working age of component 1 reaches T. Our problem is to determine an optimal policy T^∗ such that the long-run average cost per unit time of the system is minimized. The explicit expression for the long-run average cost per unit time of the system is evaluated, and the corresponding optimal replacement policy T^∗ can be found analytically or numerically. Another numerical example for replacement model is also given.     

The persistent‐access‐caching algorithm

Caching is widely recognized as an effective mechanism for improving the performance of the World Wide Web. One of the key components in engineering the Web caching systems is designing document placement/replacement algorithms for updating the collection of cached documents. The main design objectives of such a policy are the high cache hit ratio, ease of implementation, low complexity and adaptability to the fluctuations in access patterns. These objectives are essentially satisfied by the widely used heuristic called the least‐recently‐used (LRU) cache replacement rule. However, in the context of the independent reference model, the LRU policy can significantly underperform the optimal least‐frequently‐used (LFU) algorithm that, on the other hand, has higher implementation complexity and lower adaptability to changes in access frequencies. To alleviate this problem, we introduce a new LRU‐based rule, termed the persistent‐access‐caching (PAC), which essentially preserves all of the desirable attributes of the LRU scheme. For this new heuristic, under the independent reference model and generalized Zipf's law request probabilities, we prove that, for large cache sizes, its performance is arbitrarily close to the optimal LFU algorithm. Furthermore, this near‐optimality of the PAC algorithm is achieved at the expense of a negligible additional complexity for large cache sizes when compared to the ordinary LRU policy, since the PAC algorithm makes the replacement decisions based on the references collected during the preceding interval of fixed length. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Inventory policy for products with price and time-dependent demands

This paper investigates the problem of jointly determining the order size and optimal prices for a perishable inventory system under the condition that demand is time and price dependent. It is assumed that a decision-maker has the opportunity to adjust prices before the end of the sales season to influence demand and to improve revenues. A mathematical model is developed to find the optimal number of prices, the optimal prices and the order quantity. Analytical results show that a stationary solution to the Kuhn–Tucker necessary conditions can be found and it is shown to be the optimal solution. The analytical results lead us to derive a solution procedure for determining the optimal order size and prices.     

An optimal replacement policy for a multistate degenerative simple system

In this paper, a degenerative simple system (i.e. a degenerative one-component system with one repairman) with k + 1 states, including k failure states and one working state, is studied. Assume that the system after repair is not “as good as new”, and the degeneration of the system is stochastic. Under these assumptions, we consider a new replacement policy T based on the system age. Our problem is to determine an optimal replacement policy T^∗ such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimized. The explicit expression of the average cost rate is derived, the corresponding optimal replacement policy can be determined, the explicit expression of the minimum of the average cost rate can be found and under some mild conditions the existence and uniqueness of the optimal policy T^∗ can be proved, too. Further, we can show that the repair model for the multistate system in this paper forms a general monotone process repair model which includes the geometric process repair model as a special case. We can also show that the repair model in the paper is equivalent to a geometric process repair model for a two-state degenerative simple system in the sense that they have the same average cost rate and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results of this model.     

修理工单重定期休假可修系统更换模型研究

针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性.     

Component redundancy allocation in optimal cost preventive maintenance scheduling

This work presents a methodology to assist maintenance teams in defining the maintenance schedule and redundancy allocation that minimise the life-cycle average cost of a system. The minimal data required are three average costs and one reliability function. This methodology is useful in a system design phase, since in this situation data is usually scarce or inaccurate, but can also be applied in the exploration phase. It consists of an adaptation of the classical optimal age replacement method, combined with a redundancy allocation problem. A set of simple illustrative examples covering a variety of operating conditions is presented, demonstrating quantitatively the applicability of the methodology to a range of maintenance optimisation decisions.     

Experience with a Stochastic Replacement Model

This paper reports on a study initiated to check the validity of an existing six-monthly block replacement policy for a set of filling valves in a canning line. After dealing with inadequacies in the data and changing to a production-based time measure, the paper shows how a renewal function measure of the expected number of valve replacements was obtained and led to the conclusion that the current block replacement policy could not be justified.The possibility of an age-based replacement policy being of value remained. In order to model such a policy, it was necessary to reverse the usual analysis of renewal-type processes in that an estimate was required of the distribution function of time between renewals, given the renewal function.A finite optimal replacement age was found which depended upon the objective being to minimize a measure of downtime due to replacements, or operating costs attributable to replacements. Calculations were further complicated by part of the plant having a finite remaining life before being upgraded.