A graphical method to repair-cost limit replacement policies with imperfect repair

This paper addresses statistical estimation problems of the optimal repair-cost limits minimizing the long-run average costs per unit time in discrete seting. Two discrete repair-cost limit replacement models with/without imperfect repair are considered. We derive the optimal repair-cost limits analytically and develop the statistical non-parametric procedures to estimate them from the complete sample of repair cost. Then the discrete total time on test (DTTT) concept is introduced and applied to propose the resulting estimators. Numerical experiments through Monte Carlo simulation are provided to show their asymptotic convergence properties as the number of repair-cost data increases. A comprehensive bibliography in this research topic is also provided.

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The Lorenz Transform approach to the Optimal Repair-Cost limit remplacement Policy with Imperfect Repair

RAIRO - Operations Research ◽

10.1051/ro:2001101 ◽

2001 ◽

Vol 35 (1) ◽

pp. 21-36 ◽

Cited By ~ 2

Author(s):

T. Dohi ◽

F. S. Othman ◽

N. Kaio ◽

Sunji Osaki

Keyword(s):

Repair Cost ◽

Imperfect Repair ◽

Cost Limit

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Geometrical Interpretations of Repair-Cost Limit Replacement Policies

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539397000217 ◽

1997 ◽

Vol 04 (03) ◽

pp. 309-333 ◽

Cited By ~ 6

Author(s):

T. Dohi ◽

H. Koshimae ◽

N. Kaio ◽

S. Osaki

Keyword(s):

Graphical Method ◽

Computer Software ◽

Algebraic Method ◽

Repair Cost ◽

Numerical Examples ◽

Optimal Policies ◽

Solution Methods ◽

Age Replacement ◽

Replacement Problem ◽

Cost Limit

The 'total time on test' (TTT) concept has proven to be a very useful tool in many reliability applications. The graphical method based on this concept gives geometrical interpretations to solutions of stochastic maintenance problems as well as estimates of the optimal policies directly from empirical failure or repair data. In fact, some renewal type of maintenance models such as age replacement and burn-in problems have been analyzed by applying the TTT concept. In this paper, we discuss a repair limit replacement problem with a cost constraint for determining the optimal cost–limit to stop repairing a unit after it fails. Two solution methods for the problem are proposed: one is a straightforward/algebraic method and the other is a geometrical one based on the TTT concept. Also, we develop a computer software to calculate numerically the optimal repair-cost limit policies or its estimates by using the function of computer graphics, and refer to its educational effect throughout numerical examples.

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Optimal repair/replacement policy for a general repair model

Advances in Applied Probability ◽

10.1017/s0001867800010703 ◽

2001 ◽

Vol 33 (1) ◽

pp. 206-222 ◽

Cited By ~ 5

Author(s):

Xiaoyue Jiang ◽

Viliam Makis ◽

Andrew K. S. Jardine

Keyword(s):

Average Cost ◽

Failure Time ◽

Operating Time ◽

Replacement Policy ◽

Repair Cost ◽

Virtual Age ◽

Preventive Replacement ◽

Long Run ◽

Special Cases ◽

Cost Limit

In this paper, we study a maintenance model with general repair and two types of replacement: failure and preventive replacement. When the system fails a decision is made whether to replace or repair it. The repair degree that affects the virtual age of the system is assumed to be a random function of the repair-cost and the virtual age at failure time. The system can be preventively replaced at any time before failure. The objective is to find the repair/replacement policy minimizing the long-run expected average cost per unit time. It is shown that a generalized repair-cost-limit policy is optimal and the preventive replacement time depends on the virtual age of the system and on the length of the operating time since the last repair. Computational procedures for finding the optimal repair-cost limit and the optimal average cost are developed. This model includes many well-known models as special cases and the approach provides a unified treatment of a wide class of maintenance models.

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