Optimum number of minimal repairs for a system under increasing failure rate shock model with cumulative repair-cost limit

2013 ◽  
Vol 7 (2) ◽  
pp. 95 ◽  
Author(s):  
Min Tsai Lai
Keyword(s):  
Failure Rate ◽  
Optimum Number ◽  
Shock Model ◽  
Repair Cost ◽  
Increasing Failure Rate ◽  
Cost Limit

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

REPLACEMENT MODEL WITH CUMULATIVE REPAIR COST LIMIT FOR A TWO-UNIT SYSTEM UNDER FAILURE RATE INTERACTION BETWEEN UNITS

2012 ◽  
Vol 19 (05) ◽  
pp. 1250023 ◽  
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.

Failure distributions of shock models

1980 ◽  
Vol 17 (3) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

ACKNOWLEDGMENT OF PRIORITY: “On the conditions for mixtures of increasing failure rate distributions to have an increasing failure rate”

2003 ◽  
Vol 17 (1) ◽  
pp. 153-153
Author(s):  
James Lynch
Keyword(s):  
Failure Rate ◽  
Applied Probability ◽  
Increasing Failure Rate

The above-mentioned article by James Lynch was published in Probability in the Engineering and Informational Sciences (1999), 13: 33–36.It has recently been brought to the author's attention that the results in that paper were preceded and superseded by the results in Thomas H. Savits' paper, “A multivariate IFR class,” which appeared in the Journal of Applied Probability (1985), 22: 197–204. This acknowledgment is to correct this contretemps.

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