Estimation of a Modified Capability Index for Non-Normal Distributions

Abstract

Process capability indices (PCIs), which are very important in quality control have been one of a numerical measure index in manufacturing processes. Index Cpk is the most popular one used in the manufacturing industry. It is applied under the assumption that the processes are normally distributed. In real-world applications, non-normal processes may occur in industries, and the index CNpk has been proposed for non-normal processes in which its exact sampling distribution is mathematically intractable. Quality practitioners commonly use the existing NCPPM (non-conformities in parts per million) table of Cpk to obtain process yields. However, the table could not be applied directly via the value of index CNpk. For the consistency of NCPPM mapping, we propose procedures to obtain the modified index C*Npk and its approximately unbiased estimator C˜*Npk for three non-normal distributions, involving Log-normal, Gamma, and Weibull distributions. The values of modified index C*Npk could be used to inquire the existing popular NCPPM table of Cpk. In addition, four bootstrap methods were used to construct the lower confidence bounds of the index C*Npk, which are useful to the practitioners for making reliable decisions regarding process performance based on process yield.

Fuzzy Evaluation of Process Quality with Process Yield Index

“…Wisnowski, Simpson, and Montgomery [14] proposed an asymptotic distribution for an estimator of this index. This asymptotic distribution can assist statistical inferences of the process yield [15]. As the process yield index concurrently reflects process capability and yield [16,17], this study uses this index for the evaluation of process quality.…”

Estimation and Confidence Intervals of a New PCI CNpmc for Logistic‐Exponential Process Distribution

“…Pearn et al [5,6], Kashif et al [7,8], Weber et al [9], Rao et al [10], and Alomani et al [11], to name a few. Further, Saha et al [12] in their studies focussed on parametric estimation, bootstrap confidence interval, and highest posterior density credible interval of the index C pk using normal distribution.…”

Parametric inference of the loss based index Cpm for normal distribution

“…Since then, several researchers have developed numerous techniques for constructing CIs. In this regard, readers may refer to Peng 16,17 ; Leiva et al 18 ; Pearn et al 19,20 ; Kashif et al 21,22 ; Weber et al 23 ; Pina-Monarrez et al 24 ; Rao et al 25 ; Dey et al 26 ; Dey and Saha 27,28 ; Park et al 29 ; Saha et al [30][31][32] , Alomani et al 33 and the references cited therein.…”