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.     

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.     

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.     

Optimal stocking for replacement with minimal repair

Joint stocking and replacement model with minimal repair at failure is considered. A recursive relationship among the optimal replacement intervals is obtained, which shows that replacement intervals are an increasing sequence due to the inventory carrying cost. Using the relationship, a procedure is given for determining how many units to purchase on each order and when to replace each unit after it has begun operating so as to minimize the total cost per unit time over an infinite time span. The problem can be simplified if equal replacement intervals are assumed, and the solution is very close to that of the unconstrained problem.     

Optimal continuous-wear limit replacement under periodicinspections

An item breaks down when it wears continuously beyond a certain threshold. The item is preventively replaced as the wear at periodic inspections exceeds a certain wear limit; on failure, it is replaced immediately. The optimal wear limit for preventive replacement that minimizes the long-run total average-cost rate is derived. A numerical example demonstrates its computability     

Multi-standby system with repair and replacement policy

This paper investigates the mathematical model of a system composed of (m + 1) non-identical units—one functioning and m standbys. Each unit of the system has four possible states—normal, partial failure, total failure and repair facility—the last one meaning that the totally failed unit is being attended to at the repair facility where it might be either repaired or eventually rejected and replaced. The normal and partial failure states are up states while the other two are down states. The system breaks down when the (m + 1)th unit after total failure is finally rejected and no standby remains to replace it. Several reliability characteristics of interest to system designers as well as operations managers have been computed. Results obtained earlier are verified as particular cases.     

An ordering policy with age-dependent minimal repair and age-dependent random repair costs

In this paper we consider an ordering policy for a one-unit system with age-dependent minimal repair and age-dependent random repair costs. We derive the expected cost per unit time in the steady-state as a criterion of optimality and seek the optimum policy by minimizing that cost. We show that, under certain conditions, there exists a finite and unique optimum policy. Various special cases are discussed.     

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.     

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.     

Improvement, deterioration, and optimal replacement underage-replacement with minimal repair

Improvement and deterioration for a repairable system are studied, in particular in terms of the effect of ageing on the distribution of the time to first failure under a nonhomogeneous Poisson process. For a repairable system undergoing minimal repair, the optimal replacement time under the age replacement policy is discussed     

A multi-standby multi-failure mode system with repair and replacement policy

This paper investigates the mathematical model of a system composed of (m + 1) non identical units—one functioning and m standby. Each unit of the system has three possible states—normal, degraded and failed. We consider two types of repair facilities—overhaul and minor repair. The system breaks down when the (m + 1)th unit after total failure is finally rejected and no standby remains to replace it. Several reliability characteristics of interest to system designers as well as operations managers have been computed. Results obtained earlier are verified as particular cases.     

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.     

An economic discrete replacement policy for a shock damage model with minimal repairs

A discrete replacement model for a repairable system which is subject to shocks and minimal repairs is discussed. Such shocks can be classified, depending on its effect to the system, into two types: Type I and Type II shocks. Whenever a type II shock occurs causes the system to go into failure, such a failure is called type II failure and can be corrected by a minimal repair. A type I shock does damage to the system in the sense that it increases the failure rate by a certain amount and the failure rate also increases with age due to aging process without external shocks; furthermore, the failure occurred in this condition is called type I failure. The system is replaced at the time of the first type I failure or the n-th type Il failure, whichever occurs first. Introducing costs due to replacement and mininal repairs, the long-run expected cost per unit time is derived as a criterion of optimality and the optimal number n∗ found by minimizing that cost. It is shown that, under certain conditions, there exists a finite and unique optimal number n∗.     

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.     

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.     

A note on minimal repair

The cumulative function for the number of failures for a unit which is subjected to minimal repair after each failure is a nonstationary Poisson process. In this note, a simple method for obtaining this result is presented. A conditional probability approach is used for the derivation     

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.     

All opportunity-triggered replacement policy for multiple-unitsystems

A model is presented for a system which consists of n i.i.d units. Hazard rates of these units are increasing in time. A unit is replaced at failure or when the age of a unit exceeds T, whichever occurs first. When a unit is replaced, all the operating units with their age in the interval (T-w,T) are replaced. Both failure replacement and active replacement create the opportunities to replace other units preventively. This policy allows joint replacements and avoids the disadvantages resulting from replacement of new units, down time, and unrealistic assumptions for distributions of unit life. An algorithm is developed to compute the steady-state cost rate. Optimal T&W are obtained to minimize the mean total replacement cost rate. Application and analysis of results are illustrated through a numerical example     

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.     

Optimal replacement policy for induced draft fans

This paper derives the optimal block replacement policies for four different operating configurations of induced draft fans. Under the usual assumption of higher cost of repair or replacement on failure compared to preventive replacement, the optimal preventive replacement interval is found by minimising the total relevant cost per unit time. Specifically, this paper finds optimal preventive maintenance strategies for the following two situations.

1. (i)|Both the time to failure and time to carry out minimal repair or replacement are exponentially distributed.

2. (ii)|The time to failure follows the Weibull distribution and there is no possibility of on-line repair or replacement.

For both situations closed form expressions are derived whose solutions give optimum preventive maintenance intervals.