Assessing the Lifetime Performance Index of Burr Type III Distribution under Progressive Type II Censoring

Amal Hassan,Amany Selmy,Salwa Assar

doi:10.18187/pjsor.v17i3.3635

Amal Hassan, Amany Selmy + Show 1 more

Open Access

https://doi.org/10.18187/pjsor.v17i3.3635

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Abstract

Process capability analysis has been widely applied in the ﬁeld of quality control to monitor the performance of industrial processes. Hence, lifetime performance index CL is used to measure the potential and performance of a process. In the present study, we construct a maximum likelihood estimator of CL under Burr Type III distribution based on the progressive Type II censored sample. The maximum likelihood estimator of CL is then utilized to develop the hypothesis testing procedure in the condition of known L. Finally, one practical example and Monte Carlo simulation are given to assess the behavior of the lifetime performance index under given significance level.

Highlights

Burr (1942) has suggested twelve types of cumulative distribution functions, which yield a variety of density shapes
Lee et al (2009) proposed a hypothesis testing procedure based on the maximum likelihood (ML) estimator of CL to evaluate the product quality for two-parameter exponential under progressive type II censoring (PTIIC) samples
Gildeh and Nadi (2016) obtained the uniformly minimum variance unbiased estimator (UMVUE) of CL under the assumption of two-parameter exponential distribution based on a progressive first-failure censored sample

Summary

Introduction

Burr (1942) has suggested twelve types of cumulative distribution functions, which yield a variety of density shapes. Gamchi et al (2019) studied the estimation and prediction problems for the BIII distribution under progressive type II hybrid censored data They obtained the ML estimates of unknown parameters using stochastic expectation maximization algorithm. Lee et al (2009) proposed a hypothesis testing procedure based on the ML estimator of CL to evaluate the product quality for two-parameter exponential under PTIIC samples. Gildeh and Nadi (2016) obtained the uniformly minimum variance unbiased estimator (UMVUE) of CL under the assumption of two-parameter exponential distribution based on a progressive first-failure censored sample. Hassanein (2018) devoted to evaluate CL for the three- parameter power Lomax distribution under progressive first-failure censoring samples with respect to a lower specification limit L. Utilizing the one-to-one relationship between Pr and CL, so the lifetime performance index can be a flexible and effective tool, for evaluating product quality, and for estimating

ML Estimator of Lifetime Performance Index

5: The value of CL is calculated by using

Testing Procedure for the Lifetime Performance Index

Power Function of the Test

W ˆL 2m

Conclusions