Optimal design of simple step-stress accelerated life tests for one-shot devices under Weibull distributions

“One-shot” devices are widely used in many fields nowadays. All of these devices can be used only once and then they will be destroyed extensively, which is called “oneshot” devices. Weibull distribution presents a more flexible model than Exponential distribution, is adopted in this paper. Optimal deign for sample allocation with simple step-stress accelerated life test under a Weibull cumulative exposure distribution will be designed. In this paper we get the information matrix after obtaining derivatives of observed log-likelihood function, and asymptotic covariance matrix of the model parameters in order that optimal design that minimized the asymptotic variance of estimate of the reliability at a mission time of simple step-stress accelerated life test using maximum loglikelihood estimation under normal conditions in terms of one decided variable, sample allocation. Also, a procedure that determines the sample allocation with the termination time, inspection time, stress level and normal condition are given. Simulation studies are conducted to show the process of optimal design is reliable.