Optimal replacement model with age-dependent failure type based on a cumulative repair-cost limit policy

In this note, a pseudodynamic cost limit replacement policy presented by Park1 is considered. Park1 showed that the pseudodynamic policy is inferior to constant repair cost limit policy. In this note, the correct mean cost rate under the same assumption in the Park's model is obtained and the pseudodynamic policy is shown to be better than the constant repair cost limit policy2 through the same numerical examples of Park.1

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A bivariate optimal replacement policy with cumulative repair cost limit for a two-unit system under shock damage interaction

Brazilian Journal of Probability and Statistics ◽

10.1214/16-bjps317 ◽

2017 ◽

Vol 31 (2) ◽

pp. 353-372

Author(s):

Min-Tsai Lai ◽

Chung-Ho Chen ◽

Taqwa Hariguna

Keyword(s):

Replacement Policy ◽

Repair Cost ◽

Unit System ◽

Optimal Replacement ◽

Optimal Replacement Policy ◽

Cost Limit

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Optimal replacement period with cumulative repair cost limit under a cumulative damage model

International Journal of Industrial and Systems Engineering ◽

10.1504/ijise.2017.10003897 ◽

2017 ◽

Vol 26 (1) ◽

pp. 133

Author(s):

Chung Ho Chen ◽

Min Tsai Lai

Keyword(s):

Damage Model ◽

Cumulative Damage ◽

Repair Cost ◽

Optimal Replacement ◽

Cumulative Damage Model ◽

Cost Limit

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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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