Stress-strength reliability under partially accelerated life testing using Weibull model

The reliability of a system is the probability that its strength exceeds its stress. This reliability is called as the stress-strength reliability. The inferences of the stress-strength reliability R=P(X>Y), when: (1) the strength (X) and stress (Y) are independent random variables follow one-parameter exponential distributions; and (2) the strength variable is subjected to the step-stress partially accelerated life test (SSPALT) are discussed recently. Exponential distribution has limitation to describe the strength and stress due to its constant failure rate. In this paper, we consider the estimate of R, when: (1) X and Y are independent random variables that follow two-parameter Weibull distributions; and (2) the strength variable X is subjected to the SSPALT. The maximum likelihood estimator of R and its asymptotic distribution are not obtained analytically and therefore the asymptotic confidence interval of R is discussed. A real data set is analyzed using the proposed model for illustrative and comparison purposes. Based on the numerical results, we would conclude that the exponential distribution is rejected to fit the strength and stress, at any significant level that is greater than or equal to 2.58%, against the Weibull model.