A geometric-process repair-model with good-as-new preventive repair

This paper studies a deteriorating simple repairable system. In order to improve the availability or economize the operating costs of the system, the preventive repair is adopted before the system fails. Assume that the preventive repair of the system is as good as new, while the failure repair of the system is not, so that the successive working times form a stochastic decreasing geometric process while the consecutive failure repair times form a stochastic increasing geometric process. Under this assumption and others, by using geometric process we consider a replacement policy N based on the failure number of the system. Our problem is to determine an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. And the fixed-length interval time of the preventive repair in the system is also discussed. Finally, an appropriate numerical example is given. It is seen from that both the optimal policies N** and N* are unique. However, the optimal policy N** with preventive repair is better than the optimal policy N* without preventive repair     

Optimal periodic preventive repair and replacement policy assuming geometric process repair

In this paper, a simple deteriorating system with repair is studied. When failure occurs, the system is replaced at high cost. To extend the operating life, the system can be repaired preventively. However, preventive repair does not return the system to a "good as new" condition. Rather, the successive operating times of the system after preventive repair form a stochastically decreasing geometric process, while the consecutive preventive repair times of the system form a stochastically increasing geometric process. We consider a bivariate preventive repair policy to solve the efficiency for a deteriorating & valuable system. Thus, the objective of this paper is to determine an optimal bivariate replacement policy such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined numerically. An example is given where the operating time of the system is given by a Weibull distribution.     

Joint optimization of block-replacement and periodic-review spare-provisioning policy

This paper considers the problem of joint optimization of "preventive maintenance" and "spare-provisioning policy" for system components subject to wear-out failures. A stochastic mathematical model is developed to determine the jointly optimal "block replacement" and "periodic review spare-provisioning policy." The objective function of the model represents the s-expected total cost of system maintenance per unit time, while the preventive replacement interval and the maximal inventory level are chosen as the decision variables. The objective function of the model is in an analytic form with parameters easily obtainable from field data. The model has been tested using field data on electric locomotives in Slovenian Railways. The calculated optimal values of the model decision variables are realistic. "Sensitivity analysis of the model" shows that the model is relatively insensitive to moderate changes of the parameter values. The results of testing and of sensitivity analysis of the model prove that a trade-off exists between the replacement related cost and the inventory related cost. The jointly optimal preventive replacement interval defined by this model differs appreciably from the corresponding interval determined by the conventional model where only replacement related costs are considered. Also, the results of the sensitivity analysis show that even minor modification of the value of each model decision variable (without the appropriate adjustment of the value of the other decision variable) can lead to important increase of the s-expected total cost of system maintenance. This indicates that separate optimization of preventive maintenance policy and spare-provisioning policy does not ensure minimal total cost of system maintenance. This model can be readily applied to optimize maintenance procedures for a variety of industrial systems, and to upgrade maintenance policy in situations where block replacement preventive maintenance is already in use.     

Age replacement of components during IFR delay time

This paper proposes two alternative policies for preventive replacement of a component, which shows sign of occurrence of a fault, and operates for some random time with degraded performance, before its final failure. The time between fault occurrence and component failure is termed as delay time. The first policy, namely age replacement during delay time policy (ARDTP), recommends replacement of a faulty component on failure or preventive replacement of the same after a fixed time during its delay time. It considers the performance degradation during delay time to develop an age replacement policy. It is also shown that the policy is a feasible proposition for a component that has positive (nonnegative) performance degradation during its CFR (IFR) delay time. The second policy, OARDTP, extends ARDTP to opportunistic age replacement policy where a faulty component is replaced at the first available randomly occurring maintenance opportunity, after a fixed time from occurrence of fault, or on failure. The time between opportunities (TBO) is considered to be exponentially distributed. This policy reduces the number of forced shutdowns, which is essential to ARDTP. It is shown that the second policy is superior to the first policy if the cost of a preventive replacement with forced shutdown is more than the preventive replacement cost during an opportunity. The policies are appropriate for complex process plants, where the tracking of the entire service life of each component is difficult. Their implementation requires tracking of components' delay time only, and estimation of mean time to occurrence of faults. The policies are relatively insensitive to estimation error in failure replacement cost. As their implementation requires immediate capturing of fault occurrence information, they are particularly attractive to organizations where operators are involved in the maintenance of machines.     

Continuous-time predictive-maintenance scheduling for adeteriorating system

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system     

Optimal replacement policy (N, n) for a parallel system with common cause failure and geometric repair time

The purpose of this article is to present an improved replacement model for a parallel system of N identical units, by bringing in common cause failure (CCF), maintenance cost and repair cost per unit time additionally, and to develop a procedure to obtain the optimal redundant units N^* and optimal number of repairs n^* with the conditions that the system is allowed to undergo at most a prefixed number of repairs before to be replaced and the successive reapir times after failures constitute a non-decreasing Geometric process. Several conditions for the existence of the optimal N^* and n^* is stated and the results are illustrated by a numerical example.     

Optimal policies with decreasing probability of imperfect maintenance

This study applies periodic preventive maintenance to three repair models: major repaired, minimal repaired, or fixed until perfect preventive maintenance upon failure. Two types of preventive maintenance are performed, namely imperfect preventive maintenance, and perfect preventive maintenance. The probability that preventive maintenance is perfect depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas for the expected cost per unit time are obtained. For each model, the optimum preventive maintenance time T/sup */, which would minimize the cost rate, is discussed. Various special cases are considered. A numerical example is presented.     

One unit reliability system subject to random shocks and preventive maintenance

In this paper we consider two systems each consisting of one unit. The operating unit is subject to random shocks which occur at random times. Due to the shock the following may happen: (i) The unit is not at all affected by the shock; (ii) the failure rate of the unit increases from λ₀ to λ₁; (iii) the unit fails. The failure time of the unit is exponentially distributed. The repair, shock and preventive maintenance times follow general distributions. In System 2 there is provision of preventive maintenance, whereas in System 1 there is no provision of preventive maintenance. There is one repair man available in each system. In this paper the mean time to system failure, steady state availablities and the impact of shocks on these are studied. In System 2 the effect of the preventive maintenance on MTSF and steady-state availabilities is investigated.     

Optimal inspection when the system is repaired upon detection of failure

In Barlow and Proschan (Mathematical Theory of Reliability, 1965, Section 3.2) a cost model is presented for a system subject to random failure and whose state is known only by inspection. Upon detection of failure repair (or replacement) is performed and the system is then as good as new. A method of determining the inspection schedule which minimizes the long run average (expected) cost per unit time is proposed. In this present paper we look closer into the problem of finding an optimal inspection schedule for this model. Some new results, which are useful in connection with the computation of the optimal inspection schedule, are given.     

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-À-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.      

Cost limit replacement policy under minimal repair

This paper presents a policy for either repairing or replacing a system that has failed. When a system requires repair, it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the “repair cost limit”. However, the repair cannot return the system to “as new” condition but instead returns it to the average condition for a working system of its age. Examples include complex systems where the repair or replacement of one component does not materially affect the condition of the whole system. A Weibull distribution of time to failure and a negative exponential distribution of estimated repair cost are assumed for analytic amenability. An optimal “repair cost limit” policy is developed that minimizes the average cost per unit time for repairs and replacement. It is shown that the optimal policy is finite and unique.     

Optimal maintenance-policies for deteriorating systems undervarious maintenance strategies

This paper presents algorithms for deriving optimal maintenance policies to minimize the mean long-run cost-rate for continuous-time Markov deteriorating systems. The degree of deterioration (except failure) of the system is known only through inspection. The time durations of inspection and replacement are nonnegligible. The costs are for inspection, replacement, operation, and downtime (idle). In particular, the replacement time, replacement cost, and operating cost-rate increase as the system deteriorates. Five maintenance strategies are considered-failure replacement, age replacement, sequential inspection, periodic inspection, and continuous inspection. Iterative algorithms are developed to derive the optimal maintenance policy and the corresponding cost rate for each strategy. Under sufficient conditions, structural optimal policies are obtained     

Maintenance-policy cost-analysis for a series system withhighly-censored data

This paper considers the problem of estimating the optimal age-replacement time for a series arrangement of functional subsystems when data are subject to high levels of random censoring on the right. The system does not have redundant components. Simulation is used to compare the performance of the Kaplan-Meier Estimator (KME), the Piecewise Exponential Estimator (PEXE) and the Maximum Likelihood Estimator (MLE) in estimating the optimal replacement time for the system, as well as for each component, under high levels of random censorship. Monte Carlo analysis is used to estimate `average optimal age replacement times' determined using total time on test (TTT) transforms based on the KME, PEXE, and MLE methods. The optimal replacement time is used to calculate a value which is used to compare the relative long-run cost per unit-time for each method. The differences between using system-level data vs. component-level data to construct a maintenance policy are examined. With respect to cost effectiveness, the results identify the crucial factor in determining whether to perform system-level maintenance or component-level maintenance; that factor is the ratio of the `cost of performing preventive maintenance' and the `penalty cost of experiencing a system failure'. For the ratios used in this study (0.1 to 0.5) a `component-level maintenance policy' is more cost effective than a `system-level maintenance policy'. The results also show that for a correctly specified model and for large sample sizes, the age replacement times provided by the MLE are more accurate than those provided by the KME and PEXE, especially under high levels of censoring     

Optimal replacement policy for a warrantied system with imperfect preventive maintenance operations

This paper determines the optimal replacement time for a system with imperfect preventive maintenance operations under the modified warranty policy. The hazard rate after preventive maintenance lies between the states as good as new and as bad as old. After minimal repair, the hazard rate remains unchanged. Modified warranty policy is a mixed type of free and pro-rata warranty policy. Numerical examples using the Weibull case are presented.     

The reliability function and the availability of a duplication redundant system with a single service facility for preventive maintenance and repair

This paper concerns a two-unit system with a cold standby and a single service facility for the performance of preventive maintenance and repair. Explicit expressions for the Laplace transforms of the availability of the system, the reliability, the mean down time during (0, t) and for the mean time to system failure have been obtained under the assumption that the failure times, the inspection times, the repair times and the preventive maintenance times of the two units are governed by distinct arbitrary general distributions. The results obtained by Srinivasan and Gopalan and by Gopalan and d'Souza are derived from the present results as special cases.     

An age replacement policy with minimal repair and general random repair cost

An age replacement policy is introduced which incorporates minimal repair, replacement, and general random repair costs. If an operating unit fails at age y<T, it is either replaced by a new unit with probability p(y) at a cost c₀, or it undergoes minimal repair with probability q(y) = 1−p(y). Otherwise, a unit is replaced when it fails for the first time after age T. The cost of the i-th minimal repair of an unit at age y depends on the random part C(y) and the deterministic part c_i(y). The aim of the paper is to find the optimal T which minimizes the long run expected cost per unit time of the policy. Various special cases are considered.     

Periodic replacement when minimal repair costs depend on the age and the number of minimal repairs for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for a multi-unit system which has a specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed for any intervening component failure. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repairs. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. The necessary and sufficient conditions for the existence of an optimal replacement interval are found.     

Cost-benefit analysis of a n-unit two-server system with preventive maintenance

This paper deals with the cost-benefit analysis of a 1 out of n:G system with two servers, one for preventive maintenance (PM) and one for repair. All standby units are cold. An operating unit is taken off for repair when it fails or for PM when a PM action is due. If a unit that needs service (PM or repair) finds the corresponding server busy it enters a first-come-first-served queue. When a unit is taken off for service and no standby is available, the system goes down. Expressions for steady-state expected up-time, time spent on PM and time spent on repair are obtained. These, along with linearity assumptions on the revenue and costs, are used to obtain an expression for the steady-state expected net revenue per unit time. A special case with age replacement is taken up for study and numerical results are presented.     

Maintenance strategies following the expiration of warranty

The authors study two types of replacement policies, following the expiration of warranty, for a unit with an IFR failure-time distribution: (1) the user applies minimal repair for a fixed length of time and replaces the unit by a new one at the end of this period; and (2) the unit is replaced by the user at first failure following the minimal repair period. In addition to stationary strategies that minimize the long-run mean cost to the user, the authors also consider nonstationary strategies that arise following the expiration of a nonrenewing warranty. Following renewing warranties, they prove that the cost rate function is pseudo-convex under a fixed maintenance period policy. The same result holds under nonrenewing repair warranties, and nonrenewing replacement warranties when the optimal maintenance period of each cycle is determined as a function of the age of the item in use at the end of the warranty period