Equivalence of the tampered random variable and the tampered failure rate models in accelerated lifetesting for a class of life distributions having the 'setting the clock back to zero property'
Titel:
Equivalence of the tampered random variable and the tampered failure rate models in accelerated lifetesting for a class of life distributions having the 'setting the clock back to zero property'
Auteur:
Rao, B. Raja
Verschenen in:
Communications in statistics
Paginering:
Jaargang 21 (1992) nr. 3 pagina's 647-664
Jaar:
1992
Inhoud:
It is well-known that Nelson's (1980) Cumulative Exposure (CE) model in a step-stress accelerated life test is equivalent to the Tampered Random Variable (TRV) model of DeGroot and Goel (1979) if the life distributions under the two stresses belong to the same scale-parameter family. In the present paper, it is proved that if a step-stress accelerated life test is performed on a population of units whose life distribution belongs to a class of life distributions having the 'setting the clock back to zero' property, (see B.R. Rao and Talwaker 1989, 1990 and B.R. Rao 1990a), then the TRV is equivalent to the Tampered Failure Rate (TFR) model of Bhattacharyya and Soejoeti (1989). The proof of the necessity is simple. Simple examples of the family of life distributions with this property include the exponential, the linear hazard exponential and the Gompertz distributions. The Weibull distribution does not have this property and it is demonstrated that the TRV and the TFR models lead to different surival distributions. This paper, therefore, corrects a statement made by Bhattacharyya and Soejoeti (1989) that the TRV and TFR models coincide if, and only if, the life distribution is exponential. As a simple application of this result, it is shown, see B.R. Rao (1990a and 1990b), that a new survival model considered by Chiang and Conforti (1989) for the estimation of time to tumor has the setting the clock back to zero property. Thus it follows that if accelerated life tests are performed on such living organisms by increasing an individual's continuous exposure to toxic materials in the environment, then the TRV and the TFR models give equivalent results. The life expectancy of the organisms under these models is also derived.
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