Single and Multiple Ramp Progressive Stress with Binomial Removal: Practical Application for Industry

The objective of this article is to conduct a full study on the failure times of items when subjected to a progressive-stress accelerated life test. These failure times follow the Modified Kies exponential distribution. We performed the experiments under a type-II censoring scheme with binomial removal. The stress design has two ways to be applied either the simple ramp-stress test or the multiple ramp-stress level design of acceleration. We made a comparison between these two designs to decide which design is better. When the lifetime of test units follows the Modified Kies distributions, the cumulative exposure model has been used to apply the acceleration on the failure times to produce early failures. The simulation study was done to compare two types of progressive-stress designs. Different estimation techniques such as maximum likelihood estimation and Bayes estimation are employed to estimate the model parameters. The Metropolis Hasting method is used to derive the Bayesian estimates under symmetric and asymmetric loss functions. We also developed interval estimation as well as point estimation, and we estimated the asymptotic confidence intervals, bootstrap, and credible for the distribution parameters. We made a comparison between different estimation methods. We used real data from a practical experiment as a real data set example to assess the performance of the estimations methods. These data are analyzed to demonstrate the adequacy and superiority of the distribution to fit accelerated failure times. Also, we studied the existence and uniqueness of the roots and we used graphs to assure that the estimates used are unique and global maximum. Finally, some noteworthy conclusions are reached.