Assessing the Lifetime Performance Index Using Exponentiated Frechet Distribution with the Progressive First-Failure-Censoring Scheme

Abstract

Process capability analysis has been widely used to monitor the performance of industrial processes. In practice, lifetime performance index C is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. This study constructs the maximum likelihood (ML) and the Bayesian estimators of C for the exponentiated Frechet (EF) model with progressive first-failure-censoring scheme. These estimates are then used for constructing a confidence interval for C . The MLE and the Bayesian estimators of C are then utilized to develop a new hypothesis testing procedure in the condition of known L. Finally, we give a practical example and the Monte Carlo simulation study to illustrate the use of the testing procedure under given significance level.

Assessing the Lifetime Performance Index with Digital Inferences of Power Hazard Function Distribution Using Progressive Type-II Censoring Scheme

“…A lot of papers were studied on the statistical inference for C L X based on various types of censored and progressive censored data for different models of which [ 3 – 17 ] dealt with progressive censoring from various points of view considering several lifetime distributions and its applications. Soliman et al [ 18 , 19 ] discussed assessing the life time performance index for exponentiated Frechet distribution using Prog-Type-II-C and progressive first failure censoring scheme. Recently, Wu et al [ 20 ] introduced the reliability sampling design for C L X of Gompertz lifetime distribution under progressive type-I interval censoring, Zhang and Gui [ 21 ] studied the statistical inference for C L X with Pareto distribution on the basis of general progressive type-II censored sample, Wu et al [ 22 ] proposed experimental design for C L X of Weibull products based on the progressive type-I interval censored sample, and Hassan and Assar [ 23 ] discussed assessing C L X of Burr type-III distribution under progressive type-II censoring.…”

Inferences for Generalized Pareto Distribution Based on Progressive First‐Failure Censoring Scheme

“…For this reason, Wu and Kus ¸ [30] introduced a life testing scheme, which combines first-failure censoring with a progressive type-II censoring called a progressive first-failure censoring (Pro-F-F-C) scheme. Many previous studies have discussed inference under a Pro-F-F-C scheme for different lifetime distributions, for example, Weibull by Wu and Kus ¸ [30], Burr Type XII by Soliman et al [31,32], Gompertz by Soliman et al [33], Lomax by Mahmoud et al [34], Compound Rayleigh by Abushal [35], Generalized Inverted Exponential by Ahmed [36], the Mixture of Weibull and Lomax by Mahmoud et al [37], and exponentiated Frechet by Soliman et al [38]. Recently, Cai and Gui [39] discussed the classical and Bayesian inference for a Pro-F-F-C lefttruncated normal distribution.…”

Estimation for the generalized Fréchet distribution under progressive censoring scheme

“…Mubarak (2011b) considered Fre ´chet distribution associated with scale, shape and location parameters and obtained MLEs based on progressive type-II censored data with binomial removals. Soliman et al (2014) proposed various estimates of the unknown parameters for lifetime performance index of a two parameter exponentiated Fre…”