Periodic Replacement Policy Research Articles

Optimal periodic condition inspection and replacement policy for a binary monotone system using a counting process approach

This paper considers a binary monotone system consisting of n components. The system failure process is given by a counting process whose intensity at all times is adapted to information about the system state and at periodic inspection times it is adapted also to information about the component states and their underlying conditions. A parametric policy is introduced prescribing replacement of the entire system either when it enters the failed state, which is observed immediately, or when upon an inspection the intensity is found to have reached a predefined threshold. Costs are associated with inspections, replacements, and system failures, and the periodic inspection interval and intensity threshold that jointly minimize the expected long run cost per unit of time are determined. A numerical example is also included.

A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events

This paper deals with the condition-based maintenance of single-unit systems which are subject to the competing and dependent failures due deterioration and traumatic shock events. The main aim is to provide a model to assess the value of condition monitoring information for the maintenance decision-making. A condition-based periodic inspection/replacement policy is developed and compared with a benchmark time-based block replacement policy. Numerical results show that it is indeed useful to follow closely the actual evolution of the system to adapt the maintenance decisions to the true system state to improve the performance of maintenance policies. The analysis of the maintenance costs savings can be used to justify or not the choice to implement a policy based on condition monitoring information and to invest in condition monitoring devices.

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers’ chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179–188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678–1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.

Replacement and inspection policies for products with random life cycle

In this paper, we consider maintenance policies for products in which the economical life cycle of products is a random variable. First, we study a periodic replacement policy with minimal repair. The system is minimally repaired at failure and is replaced by new one at age T (periodic replacement policy with minimal repair of Barlow and Hunter [1]). The expected present value of total maintenance cost of products with random life cycle is obtained and the optimal replacement interval minimizing the cost is found. Second, we consider an inspection policy for products with random life cycle to detect the system failure. The expected total cost is obtained and the optimal inspection interval is found. Numerical examples are also included.

Optimal periodic replacement policy for repairable products under free-repair warranty

This paper investigates the effects of a free-repair warranty on the periodic replacement policy for a repairable product. Cost models are developed for both a warranted and a non-warranted product, and the corresponding optimal periodic replacement policies are derived such that the long-run expected cost rate is minimized. For a product with an increasing failure rate function, structural properties of these optimal policies are obtained. By comparing these optimal policies, we show that the optimal replacement period for a warranted product should be adjusted toward the end of the warranty period. Finally, examples are given to numerically illustrate the impact of a product warranty on the optimal periodic replacement policy.

Periodic cache replacement policy for dynamic content at application server

Web caching has been widely adopted to improve server responsiveness without resorting to costly infrastructure overhauls. However, due to the need to support real-time transactions and content customization, an increasing proportion of web pages contain fragments that are dynamically generated, typically results of database queries, rendering whole-page caching at browser or proxy level inappropriate. A promising approach has been to place dynamic fragments in a web application server cache for multiple web requests. In this paper, we propose a periodic cache replacement policy for dynamic web content at application server. Since the content of a dynamically generated web fragment could become stale, the value of a cached copy of the fragment will likely decrease as updates accumulate at the back-end database. Constantly replacing the cached copy of the fragment will increase its freshness and value, yet will also incur a high cache replacement cost. In addition, not all fragments are equally important to various applications and it is preferable to cache mission-critical fragments. The decision problem then consists of what fragments should be selected to cache and how frequently the cache should be replaced so that the total cache benefits per unit time is maximized. Numerical and simulation experiments show that the periodic cache replacement policy is robust and effective in handling dynamic content.

Optimal periodic replacement policy for a two-unit system with failure rate interaction

In this paper, an economic periodic replacement model for a two-unit system with failure rate interaction between units is presented. In this model, whenever unit 1 fails, it causes a certain amount of damage to unit 2 by increasing the failure rate of unit 2 by a certain degree, while each unit 2 failure induces unit 1 into instantaneous failure. Without failure interaction between units, the failure rates of two units also increase with through an ageing process. The two-unit system is all replaced at age T, or on failure, whichever occurs first. The aim of this paper is to derive the long-run expected cost per unit time by introducing relative costs as a criterion of optimality. The optimal period T* that minimizes that cost is also discussed. A numerical example is given to illustrate the method.

OPTIMAL PERIODIC REPLACEMENT POLICY WITH CHECKING TIME

This investigation considers a generalized inspection policy for a deteriorating production system with general random minimal repair costs. The inspection times for the inspection strategy are assumed to be non-negligible. Additionally, uncertainty probabilities associated with inspections are introduced. Using a dynamic programming formulation, the optimal inspection time for maximizing profit per unit time for a given overhaul/replacement time is determined. Next, the procedure is extended to determine the optimal periodic overhaul/replacement time, as well as the optimal number of inspections and their schedule.

Optimal maintenance decisions under imperfect inspection

The process industry is increasingly making use of Risk Based Inspection (RBI) techniques to develop cost and/or safety optimal inspection plans. This paper proposes an adaptive Bayesian decision model to determine these optimal inspection plans under uncertain deterioration. It uses the gamma stochastic process to model the corrosion damage mechanism and Bayes’ theorem to update prior knowledge over the corrosion rate with imperfect wall thickness measurements. This is very important in the process industry as current non-destructive inspection techniques are not capable of measuring the exact material thickness, nor can these inspections cover the total surface area of the component. The decision model finds a periodic inspection and replacement policy, which minimizes the expected average costs per year. The failure condition is assumed to be random and depends on uncertain operation conditions and material properties. The combined deterioration and decision model is illustrated by an example using actual plant data of a pressurized steel vessel.

Renewal analysis of a replacement process

We consider a unit with a random lifetime which is replaced at renewal times by a new identical one regardless of whether it has failed before or not. For this random periodic replacement policy, we derive exact formulas for the cycle length, defined as the time between the replacements of two successive failed units, the stationary probability of the current unit to have failed, and the stationary and the transient distributions of the residual lifetime of the current unit.

Continuous-time predictive-maintenance scheduling for a deteriorating 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.

Replacement strategies with mixed corrective actions at failure

In this paper we consider periodic replacement policies where the operating unit is preventively replaced by a new one at times kT, k = 1, 2,…, independently of failure history. At failure the item is either replaced by a new one or minimally repaired or remains inactive until the next planned replacement. The mathematical model is defined and general analytical results are obtained. Computations are carried out in some particular cases for the gamma and Weibull distributions.

Optimal Periodic Replacement of Multicomponent Reliability Systems

A complex device, like a jet engine or an electronic computer, is composed of hundreds of major components that require maintenance. The determination of the reliability and the optimal maintenance policy for such systems is further complicated by the dependence among interacting components. Component lifetimes are generally stochastically dependent due to the fact that they all function under the same environmental conditions like temperature, humidity, and vibrations. Moreover, they are also economically dependent since it is possible to do preventive maintenance to functioning components at marginal, additional cost, while failed components are being maintained. We discuss the effects of these dependencies on periodic replacement policies, and provide useful characterizations of the optimal replacement policy. The formulation involves a sample path analysis of the reliability system which leads to the utilization of Markov decision theory. Interesting intuitive and counterintuitive results are presented.

A summary of discrete replacement policies

This paper summarizes replacement models with discrete variables: (i) Three standard age, block and periodic replacement policies are rewritten as discrete time models. (ii) Four models are considered where the unit is replaced after a specified number of failures, shocks, repairs and preventive maintenances have occurred. Optimal policies to minimize the expected cost rates are also discussed. (iii) Two discrete problems of a parallel redundant system which determine the total number of failed units and the number of all units are considered. Finally, extended models with two variables are introduced.

小修理を伴う定期取替のまとめ

Several periodic replacement policies with minimal repair at failures are summarized: 1) A policy for a unit with random and wearout failures. 2) Two modified policies where if a failure occurs just before the replacement time, then (i) a unit remains failed, (ii) a unit is replaced by a new one. 3) Three imperfect preventive maintenance (pm) policies where (i) a unit after pm has the same failure rate as before pm with a certain probability, (ii) the age of a unit becomes x units of time younger at pm, (iii) the age of a unit after pm reduces to at at pm. Expected cost rates for each model are obtained and optimum policies are discussed. Some examples for the above models are presented. and the (k - 1) previous failures are corrected with minimal repair. Fur- ther, Tilquin and Cl~roux (17) introduced the adjustment costs which increase with the age of a unit. Tahara and Nishida (15) also introduced the break-· down cost suffered for a failed unit which is replaced at the first failurE~ after some age. In this paper, we summarize the knovm results of the policy, and consider extended and modified models which could be applicable to practical fields. For instance, we consider the policy for a used unit of age x and for a unit

中古ユニットに対する最適取替方策

In many situations, it may be more economical to use a used unit than to do a new one. This paper considers an age replacement policy and a periodic replacement policy with minimal repair at failure for a used unit of age x. We discuss optimum replacement policies which minimize the expected cost rates for a specified age x. Further, we obtain an upper bound of an optimum time for an age replacement model and an optimum age of a used unit for a periodic replacement model when the replacement time is previously specified.

A Periodic Inspeciton and Replacement Policy for both the Early Detection and prevention of Equipment Failures

A Periodic Inspeciton and Replacement Policy for both the Early Detection and prevention of Equipment Failures

A Periodic Replacement Policy for Equipment with Posterior Inspections

A Periodic Replacement Policy for Equipment with Posterior Inspections

Periodic replacement with minimal repair at failure and adjustment costs

AbstractWe investigate periodic replacement policies with minimal repair at failure, thereby, minimizing the average expected cost per unit time over an infinite time span. The standard cost structure is modified by the introduction of a term which takes adjustment costs into account.