Repair Cost Limit Research Articles

Some replacement policies with minimal repairs and repair cost limit

Some extended replacement policies based on the number of failures, incorporating the concept of repair cost limit are discussed. Three models are considered as follows: (a) a unit is replaced at the nth failure, or when the estimated minimal repair cost exceeds a particular limit c; (b) a unit has two types of failures and is replaced at the nth type 1 failure, or type 2 failure, or when the estimated repair cost of type 1 failures exceeds a predetermined limit c—type 1 failures are minimal; failures, type 2 failures are catastrophic failures and both occur with constant probability; (c) a unit has two types of failures and the type 1 and type 2 failures are age dependent—the unit is replaced at the nth type 1 failure, type 2 failure, or when the estimated repair cost due to type 1 failures exceeds a predetermined limit c. Introducing costs due to replacements, inspections, and minimal repairs, an optimal number of minimal repairs before replacement is obtained, which minimizes the expected cost rate. Some particular cases are also derived. Finally, the application of these models to computer science is discussed.

Optimal number of minimal repairs before replacement with repair cost limit

Abstract There are two well-known classical replacement policies with minimal repairs. Policy I: A unit is replaced at time T and undergoes only minimal repairs at failures between replacements. Policy II: A unit is replaced on nth failure and failures between replacements are removed by minimal repairs. Several extensions of policy I have been proposed in recent times. However, policy II has attracted attention only sparingly. This paper proposes a general policy based on policies I and II, which includes several other replacement policies as particular cases. Optimal policies minimising the expected cost rate are also discussed. A numerical example is presented at the end.

Repair cost limit replacement policy under imperfect inspection

A replacement policy with minimal repair cost limit is discussed. When a system fails, the repair cost is estimated by inspection and minimal repair is the undertaken if the estimated cost is less than a predetermined limit L ; otherwise, the system is replaced. It is assumed that repair cost can not be estimated exactly because of imperfect inspection. When the failure time follows a Weibull distribution and repair cost a normal distribution, the value of repair cost limit minimizing the expected cost rate is shown to be finite and unique.

An optimal repair cost limit policy for servicing warranty

In this paper we study a policy involving repair cost limit as a decision variable for minimizing the cost of servicing items sold under warranty.

Cost limit replacement policy under imperfect repair

A repair cost limit policy is studied for a system whose repair cost can be estimated by inspection. When a system fails, the repair cost is estimated and repair is undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. After repair, the system is as good as new with ( 1−p) or is minimally repaired with p. The s-expected cost rate is used as a criterion for optimization. The existence and uniqueness of optimum L are studied for the case of Weibull time-to-failure distribution and negative exponential repair cost distribution.

An age replacement policy with minimal repair cost limit : D. S. Bai and W. Y. Yun. IEEE Trans. Reliab.R-35 (4), 452 (1986)

An age replacement policy with minimal repair cost limit : D. S. Bai and W. Y. Yun. IEEE Trans. Reliab.R-35 (4), 452 (1986)

Optimal number of minor failures before replacement

This paper extends a replacement model based on failure number to include a repair-cost limit for general failure distributions. The stochastic behaviour of failures and repair costs are modelled by a non-homogeneous Poisson process. An efficient marginal analysis algorithm is presented for finding the optimal failure number for replacement that minimizes the average cost rate.

An Age Replacement Policy with Minimal Repair Cost Limit

A generalized replacement policy based both on the system age and the minimal repair cost limit is proposed. The system is replaced when it fails for the first time after age T. If it fails before age T, the repair cost is estimated and minimal repair is then undertaken if the estimated cost is less than a predetermined limit L; otherwise, the system is replaced. The mean cost rate is obtained, its behavior is examined, and ways of obtaining optimal T and L are explored.

Optimal number of major failures before replacement

When the repair cost of a failed system is random, it is no longer meaningful to expend more than the replacement cost on a catastrophic failure. This paper presents a mathematical model that uses two cost limits to combine and extend the replacement models based on minor-failure number[8] and constant repair cost limit[5] for general time-to-failure distributions. 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 minor repair-cost limit; or if the estimated cost is less than the replacement cost and the predetermined major-failure number is not reached. An example with a Weibull time-to-failure distribution and a negative exponential distribution of estimated repair cost is given to illustrate the computational results.

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.

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.