Optimal scheme and estimation for a bivariate step-stress accelerated life test with the inverse Weibull distribution under type-I progressive censored samples

In this paper, we provide an optimization design for a step-stress accelerated life test (ALT) with two stress variables when the lifespan of test units is assumed to follow the inverse Weibull (IW) distribution. We first utilize progressive type-I censoring and accelerated life testing to shorten the time and reduce cost of testing and then adopt a cumulative exposure (CE) model to look at the impact of varying stress levels. A log-linear relationship between the scale parameter of the IW distribution and stress has been postulated. We obtain the maximum likelihood estimators and Bayes estimators of the unknown model parameters. Under normal operating conditions, we design an optimal test plan via minimizing the asymptotic variance (AV) of the percentile life. We carry out simulation studies to illustrate the performance and optimality of the proposed model. Finally, a real-life data is analyzed for illustrative purposes.