Tampered random variable modeling for multiple step-stress life test

Article Type

Research Article

Publication Title

Communications in Statistics - Theory and Methods


In this paper, we introduce the tampered random variable (TRV) modeling in multiple step-stress life testing experiments. Here (Formula presented.) be (Formula presented.) prespecified time points and (Formula presented.) be k prefixed stress levels with si being the stress level in force during the time interval (Formula presented.) for (Formula presented.) with (Formula presented.) and (Formula presented.) We define the tampered random variable (Formula presented.) in multiple step-stress scenario and calculate the PDF, CDF, and Hazard rate for the proposed tampered variable (Formula presented.) We derive a general expression for the expectation of (Formula presented.) under different number k of stress levels and also obtain some results on stochastic ordering for different k. All these results are obtained under arbitrary baseline (under normal stress condition with stress level s 1) life distribution. In particular, we consider exponential distribution with mean θ and Weibull distribution with scale parameter λ and shape parameter α for specific expressions. We also prove some results on equivalence of the TRV modeling with the two other existing models for step-stress life testing, namely, cumulative exposure and tampered failure rate. Finally, we consider some variations of the modeling approach for (Formula presented.) to include incorporation of the stress levels, discrete life time, bivariate or multivariate life times.



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