Chin-Chih Chang

An Extended Periodic Imperfect Preventive Maintenance Model With Age-Dependent Failure Type

This paper presents a generalized periodic imperfect preventive maintenance (PM) model for a system with age-dependent failure type. The imperfect PM model proposed in this study incorporates improvement factors vis-a-vis the hazard-rate function, and effective age. As failures occur, the system experiences one of the two types of failure: type-I failure (minor), and type-II failure (catastrophic). Type-I failures are rectified with minimal repair. In a PM period, the system is preventively maintained following the occurrence of a type-II failure, or at age T, whichever takes place first. At the N th PM, the system is replaced. An approach that generalizes the existing studies on the periodic PM policy is proposed. Taking age-dependent failure type into consideration, the objective consists of determining the optimal PM & replacement schedule that minimize the expected cost per unit of time, over an infinite horizon.

Optimal age-replacement time with minimal repair based on cumulative repair cost limit and random lead time

In this study, we consider an age-replacement model with minimal repair based on a cumulative repair cost limit and random lead time for replacement delivery. A cumulative repair cost limit policy uses information about a systems entire repair cost history to decide whether the system is repaired or replaced; a random lead time models delay in delivery of a replacement once it is ordered. A general cost model is developed for the average cost per unit time based on the stochastic behavior of the assumed system, reflecting the costs of both storing a spare and of system downtime. The minimum-cost policy time is derived, its existence and uniqueness is shown, and structural properties are presented.

Optimal preventive maintenance and repair policies for multi-state systems

This paper studies the optimal preventive maintenance (PM) policies for multi-state systems. The scheduled PMs can be either imperfect or perfect type. The improved effective age is utilized to model the effect of an imperfect PM. The system is considered as in a failure state (unacceptable state) once its performance level falls below a given customer demand level. If the system fails before a scheduled PM, it is repaired and becomes operational again. We consider three types of major, minimal, and imperfect repair actions, respectively. The deterioration of the system is assumed to follow a non-homogeneous continuous time Markov process (NHCTMP) with finite state space. A recursive approach is proposed to efficiently compute the time-dependent distribution of the multi-state system. For each repair type, we find the optimal PM schedule that minimizes the average cost rate. The main implication of our results is that in determining the optimal scheduled PM, choosing the right repair type will significantly improve the efficiency of the system maintenance. Thus PM and repair decisions must be made jointly to achieve the best performance.

A generalised maintenance policy with age-dependent minimal repair cost for a system subject to shocks under periodic overhaul

A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur, the system has two types of failures: type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by overhaul or replacement. The cost of minimal repair depends on age. A system is overhauled when the occurrence of a type 2 failure or at age T, whichever occurs first. At the N-th overhaul, the system is replaced rather than overhauled. A maintenance policy for determining optimal number of overhauls and optimal interval between overhauls which incorporate minimal repairs, overhauls and replacement is proposed. Under such a policy, an approach which using the concept of virtual age is adopted. It is shown that there exists a unique optimal policy which minimises the expected cost rate under certain conditions. Various cases are considered.

A Bivariate Optimal Replacement Policy for a System With Age-dependent Minimal Repair and Cumulative Repair-cost Limit

In this article, a repairable system with age-dependent failure type and minimal repair based on a cumulative repair-cost limit policy is studied, where the information of entire repair-cost history is adopted to decide whether the system is repaired or replaced. As the failures occur, the system has two failure types: (i) a Type-I failure (minor) type that is rectified by a minimal repair, and (ii) a Type-II failure (catastrophic) type that calls for a replacement. We consider a bivariate replacement policy, denoted by (n,T), in which the system is replaced at life age T, or at the n-th Type-I failure, or at the kth Type-I failure (k < n and due to a minor failure at which the accumulated repair cost exceeds the pre-determined limit), or at the first Type-II failure, whichever occurs first. The optimal minimum-cost replacement policy (n,T)* is derived analytically in terms of its existence and uniqueness. Several classical models in maintenance literature could be regard as special cases of the presented model. Finally, a numerical example is given to illustrate the theoretical results.

A Generalized Periodic Preventive Maintenance Model With Virtual Age for a System Subjected to Shocks

This article presents a periodic preventive maintenance (PM) model for a system subjected to random shocks. A system is subject to shocks that arrive according to a non homogeneous Poisson process. As shocks occur, the system experiences one of two types of failures: Type-I failure (minor) and Type-II failure (catastrophic). Type-I failures are rectified by a minimal repair. In a PM period, the system is preventively maintained following the occurrence of a Type-II failure or at age T, whichever takes place first. At the Nth PM, the system is replaced. An approach that generalizes the existing studies on the periodic PM policy is proposed. Taking the shock number-dependent failure type and the virtual age into consideration, the object consists of determining the optimal PM and replacement schedules that minimize the expected cost per unit of time, over an infinite time horizon.

Optimum random and age replacement policies for customer-demand multi-state system reliability under imperfect maintenance

This paper proposes the generalised random and age replacement policies for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system is evaluated via the combination of the stochastic process and the Lz-transform method. The concept of customer-centred reliability measure is developed based on the system performance and the customer demand. We develop the random and age replacement policies for an aging multi-state system subject to imperfect maintenance in a failure (or unacceptable) state. For each policy, the optimum replacement schedule which minimises the mean cost rate is derived analytically and discussed numerically.

Optimal preventive policies for imperfect maintenance models with replacement first and last

ABSTRACT This paper proposes preventive replacement policies for an operating system which may continuously works for N jobs with random working times and is imperfectly maintained upon failure. As a failure occurs, the system suffers one of the two types of failures based on some random mechanism: type-I (repairable or minor) failure is rectified by a minimal repair, or type-II (non repairable or catastrophic) failure is removed by a corrective replacement. A notation of preventive replacement last model is considered in which the system is replaced before any type-II failure at an operating time T or at number N of working times, whichever occurs last. Comparisons between such a preventive replacement last and the conventional replacement first are discussed in detail. For each model, the optimal schedule of preventive replacement that minimizes the mean cost rate is presented theoretically and determined numerically. Because the framework and analysis are general, the proposed models extend several existing results.

Optimisation of preventive maintenance policies with replacement first and last for systems subject to shocks

This paper addresses preventive replacement policies for operating systems subject to non-homogeneous Poisson process shocks. A shock causes two types of system failures with number-dependent probability: type-I (repairable or minor) failures can be rectified by minimal repair; type-II (non-repairable or catastrophic) failures must be removed by corrective replacement. A preventive replacement model is designed to replace the system before a type-II failure occurs. Similar to conventional replacement models, our model bases replacement on type-II failures at age T or number of working times N; however, contrary to conventional models, our model replaces the system at the last occurring age or working time. Thus, we refer to our model as a preventive replacement last model and existing methods as conventional replacement first models. Comparisons between these models are discussed in detail. The optimal schedule that minimises the mean cost rate of each preventive replacement model is derived analytically ...

Optimal Trivariate Replacement Policies for a Deteriorating System

Abstract HeIn this paper, three replacement policies for a deteriorating system are studied. Assume that the system after repair is not as good as new. This paper proposes two basic replacement policies and one co-policy in extending the general bivariate replacement policy for such a deteriorating system. The objective of our study is to determine the optimal replacement policies such that the expected cost rates are minimized. The explicit expressions of the expected cost rates are derived, and the corresponding optimal policies can be studied and determined numerically. Our model is a generalization of several traditional models in bivariate replacement literature. Finally, a numerical example is presented for illustrating the theoretical results.