Yield Prediction With a New Generalized Process Capability Index Applicable to Non-Normal Data

2022

Journal of Mathematics

The process capability index has been introduced as an effective tool used in industries to aid in the assessment of process performance as well as to measure how much the product meets the costumer expectations. We are aware that classical process capability indices provide better results when the quality characteristic of the processes follows normal distribution. However, these classical indices may not provide accurate results for evaluating nonnormally distributed process which in turn may hinder the decision-making. In this article, we consider a new process capability index C N p m c which is based on cost function and is applicable both for normally and nonnormally distributed processes. In order to estimate the process capability index C N p m c when the process follows logistic-exponential distribution, we have used ten classical methods of estimation, and the performances of these classical estimates of the index C N p m c are compared in terms of their mean squared errors through a simulation study. Next, we construct five bootstrap confidence intervals of the process capability index C N p m c and compare them in terms of their average width and coverage probabilities. Finally, two data sets related to electronic industries are reanalyzed to show the applicabilities of the proposed methods.

Section: Introductionmentioning

confidence: 99%

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

Alotaibi

Dey²,

2022

Journal of Mathematics

“…). For more information on CIs, readers may refer to the works of Peng, 14 Leiva et al., 15 Pearn et al., 16 Kashif et al., 17 Weber et al., 18 Rao et al., 19 Dey et al., 20 Wu, 21 , Dey and Saha, 22,23 Saha et al., 24–29 Alomani et al., 30 and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Modified estimation and confidence intervals of an asymmetric loss‐based process capability index Cpm′$\mathcal {C}^{\prime }_{pm}$

Dey¹,

Wang

Quality & Reliability Eng

2022

In this article, we are interested to estimate a new capability index scriptCpm′$\mathcal {C}^{\prime }_{pm}$, which is based on asymmetric loss function (linear‐exponential) when the underlying process follows normal distribution. We estimate the parameters of the model using maximum likelihood method, bias‐corrected maximum likelihood method and bootstrap bias‐corrected maximum likelihood method and subsequently the process capability index (PCI) scriptCpm′$\mathcal {C}^{\prime }_{pm}$ using the cited methods. Through extensive simulation studies, we compare the performances of the aforementioned methods of estimation for the PCI scriptCpm′$\mathcal {C}^{\prime }_{pm}$ in terms of their absolute bias (AB) and MSEs. Besides, four bootstrap methods are employed for constructing the confidence intervals for the index scriptCpm′$\mathcal {C}^{\prime }_{pm}$ by using the considered methods of estimation. The performances of the bootstrap confidence intervals (BCIs) are also compared in terms of average widths (AWs) and coverage probabilities (CPs) using Monte Carlo simulation. Finally, for illustrating the effectiveness of the proposed methods of estimation and BCIs, two real data sets from electronic industries are analyzed. All these data sets show that width of bias‐corrected accelerated bootstrap interval is minimum among all other considered BCIs.

“…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.…”

Section: Introductionmentioning

confidence: 99%

Parametric inference of the loss based index Cpm for normal distribution

Quality & Reliability Eng

Dey²,

Wang

2021

The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance and most of the traditional PCIs performed well when process follows the normal behavior. In this article, we consider a PCI,  𝑝𝑚 for normal random variables. The objective of this article is five fold: First, six different methods of estimation of the PCI  𝑝𝑚 are addressed from frequentist approaches and compare them in terms of their mean squared errors using extensive numerical simulations. Second, we compare three bootstrap confidence intervals (BCIs) of the PCI  𝑝𝑚 including standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap. Third, Bayesian estimation is considered under four loss functions (symmetric as well as asymmetric) using normal prior for location parameter and inverse gamma prior for the scale parameter for the considered model. Also, we obtain highest posterior density (HPD) credible intervals of the PCI  𝑝𝑚 . Fourth, a new cost effective PCI, namely,  𝑝𝑚𝑐 is introduced by incorporating tolerance cost function in the index  𝑝𝑚 . Fifth, the power of the test is obtained, and Monte Carlo simulation study has been carried out to compare the performances of the classical BCIs and HPD credible intervals of PCIs  𝑝𝑚 and  𝑝𝑚𝑐 in terms of average widths and coverage probabilities. Finally, two real data sets have been analyzed for illustrative purposes.