Classical and the Bayesian estimation of process capability index Cpy: A comparative study

  • Sumit Kumar Department of Mathematics, Chandigarh University, Mohali, Punjab, India
Keywords: Bootstrap confidence interval, process capability index, Lindley distribution, Xgamma distribution, Akash distribution


In this study, to estimate the process capability index Cpy when the process follows different distributions (Lindley, Xgamma, and Akash distribution), we have used five methods of estimation, namely, the maximum likelihood method of estimation, least and weighted least squares method of estimation, maximum product of spacings method of estimation and Bayesian method of estimation. The Bayesian estimation is studied for symmetric loss function with the help of the Metropolis-Hastings algorithm method. The confidence intervals for the index Cpy are constructed based on four bootstrap methods and Bayesian methods. We studied the performances of these estimators based on their corresponding MSEs/risks for the point estimates of Cpy, and average widths AW for interval estimates. To assess the accuracy of the various approaches, Monte Carlo simulations are conducted. It is found that the Bayes estimates performed better than the considered classical estimates in terms of their corresponding risks. To illustrate the performance of the proposed methods, two real data sets are analyzed.


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Author Biography

Sumit Kumar, Department of Mathematics, Chandigarh University, Mohali, Punjab, India

Sumit Kumar is currently working as an Assistant Professor in the Department of Mathematics at Chandigarh University, Mohali, Punjab. He did his M.Sc. in Statistics from the Department of Statistics at Chaudhary Charan Singh University, Meerut, and his Ph.D. from the Department of Statistics at the Central University of Rajasthan. He has made good contributions in the areas of statistical quality control, classical and Bayesian inference, and distribution theory. He has also reviewed several papers for different reputed journals. He has published 11 research articles and 1 edited book chapter in reputed national/international journals. He has presented his research work at various national and international conferences and attended several seminars and FDP’s on statistics and related areas


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