DISCRETE REPAIR-COST LIMIT REPLACEMENT POLICIES WITH/WITHOUT 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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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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REPLACEMENT MODEL WITH CUMULATIVE REPAIR COST LIMIT FOR A TWO-UNIT SYSTEM UNDER FAILURE RATE INTERACTION BETWEEN UNITS

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539312500234 ◽

2012 ◽

Vol 19 (05) ◽

pp. 1250023 ◽

Cited By ~ 2

Author(s):

MIN-TSAI LAI

Keyword(s):

Failure Rate ◽

Replacement Policy ◽

Repair Cost ◽

Unit System ◽

Model Combining ◽

Long Run ◽

Replacement Model ◽

Rate Interaction ◽

Failure Rate Interaction ◽

Cost Limit

In this paper, a periodical replacement model combining the concept of cumulative repair cost limit for a two-unit system with failure rate interaction is presented. In this model, whenever unit 1 fails, it causes a certain amount of damage to unit 2 by increasing the failure rate of unit 2 of a certain degree. Unit 2 failure whenever occurs causes unit 1 into failure at the same time and then the total failure of the system occurs. Without failure rate interaction between units, the failure rates of two units also increase with age. When unit 1 fails, the necessary repair cost is estimated and is added to the accumulated repair cost. If the accumulated repair cost is less than a pre-determined limit L, unit 1 is corrected by minimal repair. Otherwise, the system is preventively replaced by a new one. Under periodical replacement policy and cumulative repair cost limit, the long-run expected cost per unit time is derived by introducing relative costs as a criterion of optimality. The optimal period T* which minimizes that cost is discussed. A numerical example is given to illustrate the method.

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