The Evaluation on the Process Capability Index CL for Exponentiated Frech’et Lifetime Product under Progressive Type I Interval Censoring

Shu-Fei Wu,Wei-Tsung Chang

doi:10.3390/sym13061032

Abstract

We present the likelihood inferences on the lifetime performance index CL to evaluate the performance of lifetimes of products following the skewed Exponentiated Frech’et distribution in many manufacturing industries. This research is related to the topic of skewed Probability Distributions and Applications across Disciplines. Exponentiated Frech’et distribution is a generalization of some lifetime distributions. The maximum likelihood estimator for CL for lifetimes with exponentiated Frech’et distribution is derived to develop a computational testing procedure so that experimenters can implement it to test whether the lifetime performance reached the pre-assigned level of significance with a given lower specification limit under progressive type I interval censoring. At the end, two examples are provided to demonstrate the implementation on the algorithm for our proposed computational testing procedure.

Highlights

In this artificial intelligence era, the constantly changing of technology makes production techniques become sophisticated and complicated
It’s very crucial to upgrade the quality of products in the competitive emerging markets and the lifetime performance index is an effective measurement on the quality of products in terms of lifetime
The attractive property of progressive type I interval censoring is the convenient collection of data for a quality engineer

Summary

Introduction

In this artificial intelligence era, the constantly changing of technology makes production techniques become sophisticated and complicated. =1 R j , pi ), 0 ≤ pi ≤ 1 and pm = 1 For this type of interval censoring, Utilize the maximum likelihood estimator (MLE) for CL to propose a hypothesis testing procedure for various kinds of lifetime distributions can be referred to Wu and Lin [4] for one-parameter exponential distribution; Wu and. −δ L = − ln 1 − e− LU ) is the new lower specification limit for new lifetime variable Y Observe that this index is a non-increasing function of scale parameter and so is the hazard function. The conforming rate is defined as the proportion of products with lifetime exceeding the given lower specification limit and it is calculated in Equation (9): Pr = P(U ≥ LU ) = P(Y ≥ L) = exp(−θL) = exp(CL − 1), −∞ < CL < 1. Pr to be greater than 0.8187308, CL must be greater than 0.80 to attain the desired conforming rate

Results

Example

Conclusions