Parametric inference of the process capability index for exponentiated exponential distribution

References

• A. Araveeporn, Comparing parameter estimation of random coefficient autoregressive model by frequentist method, Math. 8 (2020), pp. 62. doi:10.3390/math8010062
   Google Scholar
• O.H. Arif, M. Aslam, and C.H. Jun, Acceptance sampling plan for multiple manufacturing lines using EWMA process capability index, J. Adv. Mech. Design, Syst., Manuf. 11 (2017), pp. JAMDSM0004–JAMDSM0004.
   Web of Science ®Google Scholar
• M. Aslam, A new sampling plan using neutrosophic process loss consideration, Symmetry 10 (2018), pp. 132.
   Google Scholar
• M. Aslam and M. Albassam, Inspection plan based on the process capability index using the neutrosophic statistical method, Mathematics 7 (2019), pp. 631. doi:10.3390/math7070631
   Web of Science ®Google Scholar
• M. Aslam, G.S. Rao, N. Khan, and L. Ahmad, Two-stage sampling plan using process loss index under neutrosophic statistics, Commun. Stat. -Simul. Comput. (2020), pp.1–11. doi:10.1080/03610918.2019.1702212
   Web of Science ®Google Scholar
• M. Aslam, C.W. Wu, M. Azam, and C.H. Jun, Variable sampling inspection for resubmitted lots based on process capability index Cpk for normally distributed items, Appl. Math. Model. 37 (2013), pp. 667–675.
   Web of Science ®Google Scholar
• G.J. Babu and C.R. Rao, Goodness-of-fit tests when parameters are estimated, Sankhyā 66 (2004), pp. 63–74.
   Google Scholar
• S. Balamurali and M. Aslam, Determination of multiple dependent state repetitive group sampling plan based on the process capability index, Seq. Anal. 38 (2019), pp. 385–399.
   Web of Science ®Google Scholar
• J.P. Chen and C.G. Ding, A new process capability index for non-normal distributions, Int. J. Quality Reliab. Manag. 18 (2001), pp. 762–770.
   Google Scholar
• K.S. Chen and F.A. Pearn, An application of the non-normal process capability indices, Quality Reliab. Eng. Int. 11 (1997), pp. 1–6.
   Google Scholar
• R.C.H. Cheng and N.A.K. Amin, Estimating parameters in continuous univariate distributions with a shifted origin, J. R. Stat. Soc.: Ser. B Stat. Methodol. 3 (1983), pp. 394–403.
   Google Scholar
• J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Non-linear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
   Google Scholar
• S. Dey, S. Ali, and C. Park, Weighted exponential distribution: properties and different methods of estimation, J. Stat. Comput. Simul. 85 (2015), pp. 3641–3661.
   Web of Science ®Google Scholar
• S. Dey, A. Alzaatreh, C. Zhang, and D. Kumar, A new extension of generalized exponential distribution with application to ozone data, Ozone Sci. Eng. 39 (2017c), pp. 273–285.
   Web of Science ®Google Scholar
• S. Dey, T. Dey, and D. Kundu, Two-parameter Rayleigh distribution: different methods of estimation, Amer. J. Math. Manag. Sci. 33 (2014), pp. 55–74.
   Google Scholar
• S. Dey, M.J. Josmar, and S. Nadarajah, Kumaraswamy distribution: different methods of estimation, Comput. Appl. Math. 37 (2017d), pp. 2094–2111. doi:10.1007/s40314-017-0441-1
   Google Scholar
• S. Dey, D. Kumar, P.L. Ramos, and F. Louzada, Exponentiated Chen distribution: properties and estimation, Commun. Stat. Simul. Comput. 46 (2017b), pp. 8118–8139.
   Web of Science ®Google Scholar
• S. Dey, F.A. Moala, and D. Kumar, Statistical properties and different methods of estimation of Gompertz distribution with application, J. Stat. Manag. Syst. 21 (2018), pp. 839–876.
   Web of Science ®Google Scholar
• S. Dey and M. Saha, Bootstrap confidence intervals of the difference between two generalized process capability indices for inverse Lindley distribution, Life Cycle Reliab. Saf. Eng. 7 (2018), pp. 89–96.
   Google Scholar
• S. Dey and M. Saha, Bootstrap confidence intervals of generalized process capability index Cpyk using different methods of estimation, J. Appl. Stat. 46 (2019), pp. 1843–1869.
   Web of Science ®Google Scholar
• S. Dey and M. Saha, Bootstrap confidence intervals of process capability index spmk using different methods of estimation, J. Stat. Comput. Simul. 90 (2020), pp. 28–50.
   Web of Science ®Google Scholar
• S. Dey, M. Saha, S.S. Maiti, and H.C. Jun, Bootstrap confidence intervals of generalized process capability Cpyk for Lindley and power Lindley distributions, Commun. Stat. Simul. Comput. 47 (2018), pp. 249–262.
   Web of Science ®Google Scholar
• B. Efron and R. Tibshirani, Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Stat. Sci. 1 (1983), pp. 54–75.
   Google Scholar
• M Ekström, Maximum product of spacings estimation, Wiley StatsRef , (2014). doi:10.1002/9781118445112.stat01584
   Google Scholar
• J.J. Flaig, Process capability sensitivity analysis, Qual. Eng. 11 (1999), pp. 587–592.
   Google Scholar
• R.D. Gupta and D. Kundu, Generalized exponential distributions, Aust. N. Z. J. Stat. 41 (1999), pp. 173–188.
   Web of Science ®Google Scholar
• R. Ihaka and R. Gentleman, R: a language for data analysis and graphics, J. Comput. Graph. Stat. 5 (1996), pp. 299–314.
   Google Scholar
• J.M. JuranJuran's Quality Control Handbook, 3rd ed., McGraw-Hill, New York, NY, 1974.
   Google Scholar
• K. Karplus, R. Karchin, G. Shackelford, and R. Hughey, Calibrating E-values for hidden Markov models using reverse-sequence null models, Bioinformatics 21 (2005), pp. 4107–4115.
   PubMed Web of Science ®Google Scholar
• M. Kashif, M Aslam, G.S. Rao, A.H. Al-Marshadi, and C.H. Jun, Bootstrap confidence intervals of the modified process capability index for Weibull distribution, Arab. J. Sci. Eng. 42 (2017), pp. 4565–4573. doi:10.1007/s13369-017-2562-7
   Web of Science ®Google Scholar
• V. Leiva, C. Marchant, M. Aslam, and F. Rojas, Capability indices for Birnbaum–Saunders processes applied to electronic and food industries, J. Appl. Stat. 41 (2014), pp. 1881–1902.
   Web of Science ®Google Scholar
• V. Leiva, C. Marchant, and H. Saulo, Capability index for Birnbaum-Saunders process applied to electronic and food Industries, J. Appl. Stat. 41 (2014), pp. 1881–1902.
   Web of Science ®Google Scholar
• J. Lieblein and M. Zelen, Statistical investigation of the fatigue life of deep-groove ball bearings, J. Res. Natl. Bur. Stand. (1934) 57 (1956), pp. 273–316.
   Google Scholar
• S.S. Maiti, M. Saha, and A.K. Nanda, On generalizing process capability indices, J. Qual. Technol. Quant. Manag. 7 (2010), pp. 279–300.
   Web of Science ®Google Scholar
• J.C. Pan, Y.F. Huang, and J.T.G. Hwang, Estimation of selected parameters, Comput. Stat. Data Anal. 109 (2017), pp. 45–63.
   Web of Science ®Google Scholar
• C. Park, S. Dey, L. Ouyang, J-H. Jai-Hyun Byun, and M Leeds, Improved bootstrap confidence intervals for the process capability index Cpk, Commun. Stat. Simul. Comput. 49 (2018), pp. 2583–2603. doi:10.1080/03610918.2018.1520877
   Google Scholar
• W.L Pearn, Y.T. Tai, I.F. Hsiao, and Y.P. Ao, Approximately unbiased estimator for non-normal process capability index CNpk, J. Test. Eval. 42 (2014), pp. 1408–1417.
   Web of Science ®Google Scholar
• W.L. Pearn, Y.T. Tai, and H.T. Wang, Estimation of a modified capability index for non-normal distributions, J. Test. Eval. 44 (2016), pp. 1998–2009.
   Web of Science ®Google Scholar
• C. Peng, Parametric lower confidence limits of quantile-based process capability indices, J. Quality Technol. Quant. Manag. 7 (2010a), pp. 199–214.
   Web of Science ®Google Scholar
• C. Peng, Estimating and testing quantile-based process capability indices for processes with skewed distributions, J. Data. Sci. 8 (2010b), pp. 253–268.
   Google Scholar
• M. Perakis and E. Xekalaki, A process capability index that is based on the proportion of conformance, J. Stat. Comput. Simul. 72 (2002), pp. 707–718.
   Web of Science ®Google Scholar
• M.R. Pina-Monarrez, J.F. Ortiz-Yaez, and M.I. Rodrguez-Borbn, Non-normal capability indices for the Weibull and log-normal distributions, Qual. Reliab. Eng. Int. 32 (2016), pp. 1321–1329.
   Web of Science ®Google Scholar
• L.X. Qian, Z.X. Wang, H.R. Wang, and C.Y. Deng, An improved method for predicting water shortage risk in the case of insufficient data and its application in Tianjin, China, J. Earth Syst. Sci. 129 (2020), pp. 1–10. doi:10.1007/s12040-019-1299-y
   Web of Science ®Google Scholar
• G.S. Rao, M. Aslam, and R.R.L. Kantam, Bootstrap confidence intervals of CNpk for inverse Rayleigh and log-logistic distributions, J. Stat. Comput. Simul. 86 (2016), pp. 862–873.
   Web of Science ®Google Scholar
• M. Saha, S. Dey, and S.S. Maiti, Parametric and non-parametric bootstrap confidence intervals of CNpk for exponential power distribution, J. Indust. Prod. Eng. 35 (2018), pp. 160–169.
   Web of Science ®Google Scholar
• M. Saha, S. Dey, and S.S. Maiti, Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications, Int. J. Syst. Assur. Eng. Manag. 10 (2019b), pp. 623–631.
   Web of Science ®Google Scholar
• M. Saha, S. Dey, A.S. Yadav, and S. Kumar, Classical and Bayesian inference of Cpy for generalized Lindley distributed quality characteristic, Qual. Reliab. Eng. Int. 35 (2019a), pp. 2593–2611.
   Web of Science ®Google Scholar
• M. Saha, S. Kumar, S.S. Maiti, Y.S. Yadav, and S. Dey, Asymptotic and bootstrap confidence intervals for the process capability index Cpy based on Lindley distributed quality characteristic, Amer. J. Math. Manag. Sci.39 (2019c), pp. 75–89. doi:10.1080/01966324.2019.1580644
   Google Scholar
• M. Smithson, Correct confidence intervals for various regression effect sizes and parameters: the importance of non-central distributions in computing intervals, Educ. Psychol. Meas. 61 (2001), pp. 605–632.
   Web of Science ®Google Scholar
• J. Swain, S. Venkatraman, and J. Wilson, Least squares estimation of distribution function in Johnsons translation system, J. Stat. Comput. Simul. 29 (1988), pp. 271–297.
   Google Scholar
• S. Weber, T. Ressurreio, and C. Duarte, Yield prediction with a new generalized process capability index applicable to non-normal data, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 35 (2016), pp. 931–942.
   Web of Science ®Google Scholar
• C.W. Wu, M. Aslam, and C.H. Jun, Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk, Eur. J. Oper. Res. 27 (2012), pp. 56–566.
   Google Scholar
• Y. Zhang and W.H. Gui, Statistical inference for the lifetime performance index of products with Pareto distribution on basis of general progressive type II censored sample, Commun. Stat. Theor. Meth. 50 (2021), pp. 3790–3808. doi:10.1080/03610926.2020.1801735
   Web of Science ®Google Scholar
• W.J. Zimmer, J.B. Keats, and F.K. Wang, The Burr XII distribution in reliability analysis, J. Qual. Technol. 30 (1988), pp. 386–394.
   Google Scholar