Tampered random variable modeling for multiple step-stress life test.

In this paper, we introduce the tampered random variable (TRV) modeling in multiple step-stress life testing experiments. Here τ 1 < τ 2 < ... < τ k − 1 be (k − 1) prespecified time points and s 1 , s 2 , ... , s k be k prefixed stress levels with si being the stress level in force during the time interval [ τ i − 1 , τ i) for i = 1 , ... , k with τ 0 = 0 and τ k = ∞. We define the tampered random variable T TRV (k) in multiple step-stress scenario and calculate the PDF, CDF, and Hazard rate for the proposed tampered variable T TRV (k) . We derive a general expression for the expectation of T TRV (k) 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 s1) 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 T TRV (k) to include incorporation of the stress levels, discrete life time, bivariate or multivariate life times. [ABSTRACT FROM AUTHOR]