The Optimal Experimental Design for Exponentiated Frech’et Lifetime Products

Abstract

In many manufacturing industries, the lifetime performance index CL is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to achieve a specified level of significance and test power for products with lifetimes following the Exponentiated Frech’et distribution. Since lifetime distribution is an asymmetrical probability distribution, this investigation is related to the topic of asymmetrical probability distributions and applications in various fields. When the termination time is fixed but the number of intervals is variable, the optimal number of inspection intervals and sample sizes yielding the minimized total experimental costs are determined and tabulated. When the termination time is varying, the optimal number of inspection intervals, sample sizes, and equal interval lengths achieving the minimum total experimental costs are determined and tabulated. Optimal parameter values are displayed in tabular form for feasible applications for users. Additionally, a practical example is provided to illustrate how this sampling design can be used to collect data by using the optimal setup of parameters, followed by a testing procedure to assess the capability of the production process.

Keywords

• progressive type I interval censored sample
• exponentiated Frech’et distribution
• maximum likelihood estimator
• lifetime performance index
• testing algorithmic procedure
• reliability sampling design