# Optimal strategies for some repair replacement models

@article{Stadje1990OptimalSF, title={Optimal strategies for some repair replacement models}, author={Wolfgang Stadje and Dror Zuckerman}, journal={Advances in Applied Probability}, year={1990}, volume={22}, pages={641-656} }

The problem of finding optimal replacement strategies for certain classes of failure systems is considered. These systems can be repaired upon failure, but are stochastically deteriorating, i.e., the lengths of the operating intervals decrease in some sense, whereas the durations of the repairs increase. For several models of this type optimal replacement strategies are derived under natural assumptions on the reward and the cost structure. This study deals with the problem of optimal…

## 98 Citations

Optimal repair-replacement policies for a system with two types of failures

- EngineeringEur. J. Oper. Res.
- 2013

An extended optimal replacement model for a deteriorating system with inspections

- BusinessReliab. Eng. Syst. Saf.
- 2015

An optimal age-replacement policy for a simple repairable system with delayed repair

- Mathematics
- 2017

ABSTRACT In this article, a simple repairable system (i.e., a repairable system consisting of one component and one repairman) with delayed repair is studied. Assume that the system after repair is…

Optimal periodic preventive repair and replacement policy assuming geometric process repair

- BusinessIEEE Transactions on Reliability
- 2006

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.

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

- EngineeringIEEE Trans. Reliab.
- 2002

This paper studies a deteriorating simple repairable system and determines an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized.

Extended optimal replacement model for deteriorating systems

- EngineeringEur. J. Oper. Res.
- 1999

An extended replacement policy for a deteriorating system with multi-failure modes

- EngineeringAppl. Math. Comput.
- 2011

A bivariate optimal replacement policy for a multistate repairable system

- MathematicsReliab. Eng. Syst. Saf.
- 2007

Optimal number of minimal repairs before replacement of a deteriorating system with inspections

- EngineeringInt. J. Syst. Sci.
- 2015

In this study, a generalised replacement model for a deteriorating system with failures that could only be detected through inspection work is proposed, and the expected net cost rate is obtained.

An optimal replacement policy for repairable cold standby system with priority in use

- EngineeringInt. J. Syst. Sci.
- 2007

A cold standby repairable system consisting of two nonidentical components and one repairman is studied and an optimal replacement policy N* is determined numerically so that the long-run average cost per unit time of the system is minimized.

## References

SHOWING 1-9 OF 9 REFERENCES

Optimal replacement under a minimal repair strategy—a general failure model

- MathematicsAdvances in Applied Probability
- 1983

In this paper we generalize the minimal repair replacement model introduced by Barlow and Hunter (1960). We assume that there is available information about the underlying condition of the system,…

A General Failure Model: Optimal Replacement with State Dependent Replacement and Failure Costs

- MathematicsMath. Oper. Res.
- 1980

There exists an optimal replacement rule, and that it is a threshold rule for the process γt = dct/dt + Ktrt, which means that there exists a* < ∞, such that an optimal replacements rule is to replace at the time when the process rt assumed to be nondecreasing reaches the level a*, or if failure occurs before this, to replacement at failure.

A note on the optimal replacement problem

- BusinessAdvances in Applied Probability
- 1988

In this note, we study a new repair replacement model for a deteriorating system, in which the successive survival times of the system form a geometric process and are stochastically non-increasing,…

SOME RESULTS FOR REPAIRABLE SYSTEMS WITH GENERAL REPAIR

- Mathematics
- 1989

In this paper, we develop general repair models for a repairable system by using the idea of the virtual age process of the system. If the system has the virtual age V, _ = y immediately after the (n…

Age Dependent Minimal Repair.

- Mathematics
- 1985

Abstract : The failure process studied in this paper models the following maintained system setting. A piece of equipment is put in operation at time t=0. Each time it fails, a maintenance action is…

Optimal replacement under a general failure model

- EconomicsAdvances in Applied Probability
- 1978

Replacement policies based on measurements of some increasing state variable, e.g. wear, accumulated damage or accumulated stress, are studied in this paper. It is assumed that the state measurements…

Applied Probability Models with Optimization Applications

- 1970