Optimal age-replacement policy with age-dependent minimal-repairand random-leadtime

A generalized age-replacement policy with age-dependent minimal repair and random leadtime is considered. A model is developed for the average cost per unit time and is based on the stochastic behavior of the assumed system and reflects the cost of storing a spare as well as the cost of system downtime. Determination of the minimum-cost policy time is described and illustrated with a numerical example. Because the model and its analysis are general, several existing results are shown to be subsumed by this model     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. 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. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

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.     

Optimum repair limit policies with a cost constraint

In this paper, we discuss the optimum repair limit policies with a cost constraint for continuous and discrete distributions, respectively. We apply the expected total discounted cost with a discount rate as a criterion, and obtain the optimum policies which minimize it. We show that, under certain conditions, there exist finite and unique optimum policies for continuous and discrete distributions, respectively.     

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.     

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     

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 repair for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening component failures. The cost of a minimal repair to the component is assumed to be a function of its age and the number of minimal repair. 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. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.     

On some minimal repair model

This paper deals with a one-unit system under the new maintenance policy subject to a minimal repair and a preventive maintenance. Under this policy, the Laplace transform of the point-wise availability and the stationary availability of the system are obtained using the supplementary variable method. The special cases of the results obtained here coincide with earlier results given by R.E.Barlow and L.Huter etc.,. Further, the optimum policy in the sense of the availability is discussed.     

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.     

An age replacement policy with increasing minimal repair cost

A replacement policy for a system in which minimal repair cost increases in system age is considered. If a system fails before age T, it is minimally repaired. Otherwise, the system is replaced when if fails for the first time after age T. The mean cost rate is used as a criterion for optimization. It is shown that the optimal T minimizing the mean cost rate is finite and unique.     

On profit evaluation in a modular system with two types of failures

A single unit maintained system consisting of two types of modules has been discussed. Failure of the type I module brings the system to the failed state, whereas failure of the type II module brings the system to the less productive state. The system is identified by up and down states and the expected profit is obtained. Two cases are discussed. In the first case, earnings (cost) in the failed state are assumed to be a continuous function of the repair rate, and the optimum repair rate which maximizes expected profit is obtained. In the second case, earnings (cost) in the failed state are taken as a discrete function of the repair rate. A procedure is suggested which enables one to make an optimum choice of repair policy. Numerical examples are included to illustrate the results.     

Tradeoffs in multichip module yield and cost with known good die probability and repair

The influences of known good die (KGD) probability, repair, and module testing on multichip module (MCM) yield and cost have been modeled and systematically analyzed. The current work extends our previous efforts on MCMs with single (one KGD probability) and dual (two KGD probabilities) populations to modules containing complex, multiple chip populations. Most of the analysis is performed on modules with multiple populations in the range of three to five (i.e., three to five distinct chip types). In order to develop a total cost picture for an MCM versus the respective KGD probabilities of the underlying chip populations, it was necessary to develop new algorithms or modify previously developed algorithms for the following items: number of modules (necessary to ensure at least one MCM works), KGD chip cost, and chip repair/replacement costs. In order to visualize the results and simplify calculations, averages over the respective subpopulations have been employed. The combination of these models and algorithms produces cost values in multiple (KGD) probability space that contain optimum or minimal points. Associated with the cost minimums are specific KGD probabilities for each chip type in the module population. Thus, one only pays for improved KGD probability up to the values that minimize overall module cost. Repair has a direct and significant impact on overall module yield and cost, with the first repair providing the largest improvement in both yield and cost reduction.     

Optimum inspection-ordering policies with salvage cost

In this paper we consider an inspection-ordering policy for a single-unit system with two kind of lead times. Introducing the cost structures including salvage cost, we derive the cost effectiveness defined by (The steady-state availability)/(The expected cost per unit time in the steady-state). We show that under certain conditions there exists a finite and unique optimum policy maximizing that cost effectiveness. We also present the numerical examples for illustration.     

Pseudodynamic cost limit replacement model under minimal repair

This paper presents a mathematical model to evaluate pseudodynamic cost limit replacement policies for a system that follows a general time-to-failure distribution. When the failed system requires repair, it is first inspected and the repair cost is estimated. Minimal repair is only then undertaken if the estimated cost is less than the exponentially declining repair cost limit. A negative exponential distribution of estimated repair cost is assumed for analytic tractability. An example with a Weibull time-to-failure distribution is given to illustrate the computational results.     

On computing the repair cost of a maintained reliability system with known repair cost function and probability of repair

In this paper, a simplified analytic cost model for maintained reliability system under opportunistic repair scheme is discussed. Life cycle cost curves under various operating life cycle times and linear repair cost function is derived.     

Optimum policy of one-unit system with two types of maintenance and minimal repair

This paper deals with a one-unit system with minimal repair. Two policies (new Policy IV and Policy IV′) are considered. Under these policies, the Laplace transform of the point-wise availability and the stationary availability of the system are obtained using not the renewal theory but the supplementary variable method. And under new Policy IV, the optimum policy in the sense of the availability is discussed.     

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.      

Optimum ordering policies with random lead times and salvage cost

This paper deals with the optimum ordering policy for a one unit system with general lifetime, where the failed unit is not repairable. A spare can only be provided after a lead time. Two kinds of orders (regular and emergency) are possible, each having a different lead time. A sensing device is attached to the unit by which the operational status of the unit is monitored continuously. The device is repairable and its lifetime and repair time are assumed to be exponentially distributed, random variables. The costs considered include salvage, penalty, downtime, ordering and repair costs. The optimal policy discussed is the one which maximizes the cost effectiveness.     

Cost analysis of a two unit repairable system subject to on-line preventive maintenance and/or repair

The purpose of this paper is to carry out the cost analysis of a two-unit repairable system subject to on-line preventive maintenance(PM) and repair. The policy adopted here is that the on-line PM work of the operating unit is undertaken followed by repair work of the failed unit(if any). All the random variables that. arise in the analysis are assumed to be independently and arbitrarily distributed. A mathematical model is developed using semi-regenerative phenomena and system of integral equations satisfied by various state probabilities corresponding to various initial conditions are obtained. An iterative numerical method is used to solve the system of integral equations. A cost function is built based on the expected number of various jobs completed by the server in [0, t].