References
- Ahmad, S., Abdollahian, M., & Zeephongsekul, P. (2008). Process capability estimation for non normal quality characteristics: A comparison of clements, burr and box-cox methods. Anziam Journal, 49, 642–665. https://doi.org/https://doi.org/10.21914/anziamj.v49i0.357
- Ali, S., & Riaz, M. (2014). On the generalized process capability under simple and mixture models. Journal of Applied Statistics, 41(4), 832–852. https://doi.org/https://doi.org/10.1080/02664763.2013.856386
- Chan, L. K., Spiring, F., & Xiao, H. (1988). An OC curve approach for analyzing the process capability index Cpyk. Technical Report, Department of Statistics, University of Manitoba, Canada.
- Chen, J. P., & Ding, C. G. (2001). A new process capability index for non-normal distributions. International Journal of Quality and Reliability Management, 18(7), 762–770. https://doi.org/https://doi.org/10.1108/02656710110396076
- Chen, K. S., & Pearn, W. L. (1997). An application of non-normal process capability indices. Quality and Reliability Engineering International, 13(6), 355–360. https://doi.org/https://doi.org/10.1002/(SICI)1099-1638(199711/12)13:6<355::AID-QRE125>3.0.CO;2-V
- Chen, M. H., & Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible and HPD intervals. Journal of Computational and Graphical Statistics, 8(1), 69–92. https://doi.org/http://doi.org/10.1080/10618600.1999.10474802
- Cheng, R. C. H., & Amin, N. A. K. (1979). Maximum product-of-spacings estimation with applications to the lognormal distribution. Math Report, 79-1. Department of Mathematics, UWIST, Cardiff.
- Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological), 45(3), 394–403. https://doi.org/https://doi.org/10.1111/j.2517-6161.1983.tb01268.x
- Cheng, S. W., & Spiring, F. A. (1989). Assessing process capability: A Bayesian approach. IEE Transactions, 21(1), 97–98. https://doi.org/https://doi.org/10.1080/07408178908966212
- Choi, B. C., & Owen, D. B. (1990). A study of a new capability index. Communications in Statistics: Theory and Methods, 19(4), 1231–1245. https://doi.org/https://doi.org/10.1080/03610929008830258
- Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge university press.
- Dennis, J. E., & Schnabel, R. B. (1983). Numerical methods for unconstrained optimization and non-linear equations. Prentice-Hall, Englewood Cliffs, (NJ).
- Dey, S., Ali, S., & Kumar, D. (2020). Weighted inverted Weibull distribution: Properties and estimation. Journal of Statistics & Management Systems, 23(5), 843–885. doi:https://doi.org/10.1080/09720510.2019.1669344
- Dey, S., Alzaatreh, A., Zhang, C., & Kumar, D. (2017b). A new extension of generalized exponential distribution with application to ozone data. Ozone Science and Engineering, 39(4), 273–285. https://doi.org/https://doi.org/10.1080/01919512.2017.1308817
- Dey, S., Kumar, D., Ramos, P. L., & Louzada, F. (2017a). Exponentiated Chen distribution: Properties and estimation. Communications in Statistics - Simulation and Computation, 46(10), 8118–8139. https://doi.org/https://doi.org/10.1080/03610918.2016.1267752
- Dey, S., Mazucheli, J., & Nadarajah, S. (2018b). Kumaraswamy distribution: Different methods of estimation. Computational and Applied Mathematics, 37(2), 2094–2111. https://doi.org/https://doi.org/10.1007/s40314-017-0441-1
- Dey, S., & Saha, M. (2018). Bootstrap confidence intervals of the difference between two generalized process capability indices for inverse Lindley distribution. Life Circle Reliability and Safety Engineering, 7(2), 89–96. https://doi.org/https://doi.org/10.1007/s41872-018-0045-9
- Dey, S., & Saha, M. (2019). Bootstrap confidence intervals of generalized process capability index Cpyk using different methods of estimation. Journal of Applied Statistics, 46 (10), 1843-1869. https://doi.org/https://doi.org/10.1080/02664763.2019.1572721
- Dey, S., & Saha, M. (2020). Bootstrap confidence intervals of process capability index Spmk using different methods of estimation. Journal of Statistical Computation and Simulation, 90(1), 28–50. https://doi.org/https://doi.org/10.1080/00949655.2019.1671980
- Dey, S., Saha, M., Maiti, S. S., & Jun, C. H. (2018a). Bootstrap confidence intervals of generalized process capability index Cpyk for Lindley and power Lindley distributions. Communications in Statistics-Simulation and Computation, 47(1), 249–262. https://doi.org/https://doi.org/10.1080/03610918.2017.1280166
- Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7(1), 1–26. https://doi.org/https://doi.org/10.1214/aos/1176344552
- Efron, B. (1982). The jackknife, the bootstrap, and other re-sampling plans (Vol. 38). Siam.
- Gelman, A., & Rubin, D. B. (1992). A single series from the Gibbs sampler provides a false sense of security. Bayesian Statistics, 4, 625–631.
- Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. Bayesian Statistics, 4, 641–649.
- Ghitany, M. E., Al-Mutairi, D. F., & Aboukhamseen, S. M. (2015). Estimation of the reliability of a stress-strength system from power Lindley distributions. Communications in Statistics- Simulation and Computation, 44(1), 118–136. https://doi.org/https://doi.org/10.1080/03610918.2013.767910
- Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., & Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference. Computational Statistics & Data Analysis, 64, 20–33. https://doi.org/https://doi.org/10.1016/j.csda.2013.02.026
- Gunter, B. H. (1989). The use and abuse of Cpk. Quality Progress, 22(3), 108–109.
- Hall, P. (2013). The bootstrap and edgeworth expansion. In Springer science and business media. New York: Springer-Verlag. https://doi.org/https://doi.org/10.1007/978-1-4612-4384-7
- Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109. https://doi.org/https://doi.org/10.1093/biomet/57.1.97
- Henningsen, A., & Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443–458. https://doi.org/https://doi.org/10.1007/s00180-010-0217-1
- Hsiang, T. C., & Taguchi, G. (1985). A tutorial on quality control and assurance - the Taguchi methods. In ASA annual meeting (pp. 188).
- Huiming, Z. Y., Jun, Y., & Liya, H. (2007). Bayesian evaluation approach for process capability based on sub samples. IEEE International Conference on Industrial Engineering and Engineering Management, Singapore, 1200–1203.
- Ikha, R., & Gentleman, R. (1996). R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5, 299–314.
- Joukar, A., Ramezani, M., & MirMostafaee, S. M. T. K. (2020). Estimation of P(X>Y) for the power Lindley distribution based on progressively type II right censored samples. Journal of Statistical Computation and Simulation, 90(2), 355–389. https://doi.org/https://doi.org/10.1080/00949655.2019.1685994
- Juran, J. M. (1974). Juran’s Quality Control Handbook (3rd ed.). McGraw-Hill.
- Kane, V. E. (1986). Process capability indices. Journal of Quality Technology, 18(1), 41–52. https://doi.org/https://doi.org/10.1080/00224065.1986.11978984
- Kargar, M., Mashinchi, M., & Parchami, A. (2014). A Bayesian approach to capability testing based on Cpk with multiple samples. Quality and Reliability Engineering International, 30(5), 615–621. https://doi.org/https://doi.org/10.1002/qre.1512
- Kashif, M., Aslam, M., Al-Marshadi, A. H., & Jun, C. H. (2016). Capability indices for non-normal distribution using Gini’s mean difference as measure of variability. IEEE Access, 4, 7322–7330. https://doi.org/https://doi.org/10.1109/ACCESS.2016.2620241
- Kashif, M., Aslam, M., Rao, G. S., AL-Marshadi, A. H., & Jun, C. H. (2017). Bootstrap confidence intervals of the modified process capability index for Weibull distribution. Arabian Journal for Science and Engineering, 42(11), 4565–4573. https://doi.org/https://doi.org/10.1007/s13369-017-2562-7
- Kotz, S., & Johnson, N. L. (2002). Process capability indices - a review, 1992-2000. Journal of Quality Technology, 34(1), 2–53. https://doi.org/https://doi.org/10.1080/00224065.2002.11980119
- Kotz, S., & Lovelace, C. R. (1998). Process capability indices in theory and practice. Arnold.
- Kumar, S., Dey, S., & Saha, M. (2019). Comparison between two generalized process capability indices for Burr XII distribution using bootstrap confidence intervals. Life Cycle Reliability and Safety Engineering, 8(4), 347–355. https://doi.org/https://doi.org/10.1007/s41872-019-00092-1
- Kundu, D., & Pradhan, B. (2009). Bayesian inference and life testing plans for generalized exponential distribution. Science in China Series A: Mathematics, 52 special volume dedicated to Professor Z. D. Bai (6), 1373–1388. https://doi.org/https://doi.org/10.1007/s11425-009-0085-8
- Leiva, V., Marchant, C., Saulo, H., Aslam, M., & Rojas, F. (2014). Capability indices for Birnbaum-Saunders processes applied to electronic and food industries. Journal of Applied Statistics, 41(9), 1881–1902. https://doi.org/https://doi.org/10.1080/02664763.2014.897690
- Maiti, S. S., & Saha, M. (2012). Bayesian estimation of generalized process capability indices. Journal of Probability and Statistics, 2012. https://doi.org/https://doi.org/10.1155/2012/819730
- Maiti, S. S., Saha, M., & Nanda, A. K. (2010). On generalizing process capability indices. Quality Technology & Quantitative Management, 7(3), 279–300. https://doi.org/https://doi.org/10.1080/16843703.2010.11673233
- Mazucheli, J., Ghitany, M. E., & Louzada, F. (2013). Power Lindley distribution: Different methods of estimations and their applications to survival times data. J. Ournal of Applied Statistical Science, 21(2), 135–144. https://doi.org/https://doi.org/10.5902/2179460X27500
- Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092. https://doi.org/https://doi.org/10.1063/1.1699114
- Miao, R., Zhang, X., Yang, D., Zhao, Y., & Jiang, Z. (2011). A conjugate Bayesian approach for calculating process capability indices. Expert Systems with Applications, 38(7), 8099–8104. https://doi.org/https://doi.org/10.1016/j.eswa.2010.12.151
- Pak, A., & Dey, S. (2019). Statistical Inference for the power Lindley model based on record values and inter-record times. Journal of Computational and Applied Mathematics, 347, 156–172. https://doi.org/https://doi.org/10.1016/j.cam.2018.08.012
- Pak, A., Ghitany, M. E., & Mahmoudi, M. R. (2019). Bayesian inference on power Lindley distribution based on different loss functions. Brazilian Journal of Probability and Statistics, 33(4), 894–914. https://doi.org/https://doi.org/10.1214/18-BJPS428
- Pearn, W. L., Kotz, S., & Johnson, N. L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24(4), 216–231. https://doi.org/https://doi.org/10.1080/00224065.1992.11979403
- Pearn, W. L., Lin, G. H., & Chen, K. S. (1998). Distributional and inferential properties of the process accuracy and process precision indices. Communications in Statistics: Theory and Methods, 27(4), 985–1000. https://doi.org/https://doi.org/10.1080/03610929808832139
- Pearn, W. L., Tai, Y. T., Hsiao, I. F., & Ao, Y. P. (2014). Approximately unbiased estimator for non-normal process capability index CNpk. Journal of Testing and Evaluation, 42(6), 1408–1417. https://doi.org/https://doi.org/10.1520/JTE20130125
- Pearn, W. L., Tai, Y. T., & Wang, H. T. Estimation of a modified capability index for non-normal distributions. (2016). Journal of Testing and Evaluation, 44(5), 1998–2009. Research, 165(3),685-695. https://doi.org/https://doi.org/10.1520/JTE20150357
- Pearn, W. L., Wu, C. C., & Wu, C. H. (2015). Estimating process capability index C pk: Classical approach versus Bayesian approach. Journal of Statistical Computation and Simulation, 85(10), 2007–2021. https://doi.org/https://doi.org/10.1080/00949655.2014.914211
- Peng, C. (2010a). Parametric lower confidence limits of quantile-based process capability indices. Journal of Quality Technology and Quantitative Management, 7(3), 199–214. https://doi.org/https://doi.org/10.1080/16843703.2010.11673228
- Peng, C. (2010b). Estimating and testing quantile-based process capability indices for processes with skewed distributions. Journal of Data Science, 8(2), 253–268. https://doi.org/https://doi.org/10.6339/JDS.2010.08(2).582
- Perakis, M., & Xekalaki, E. (2002). A process capability index that is based on the proportion of conformance. Journal of Statistical Computation and Simulation, 72(9), 707–718. https://doi.org/https://doi.org/10.1080/00949650214270
- Pina-Monarrez, M. R., Ortiz-Yañez, J. F., & Rodríguez-Borbón, M. I. (2016). Non-normal capability indices for the weibull and log-normal distributions. Quality and Relaibility Engineering International, 32(4), 1321–1329. https://doi.org/https://doi.org/10.1002/qre.1832
- Ranneby, B. (1984). The maximum spacing method. an estimation method related to the maximum likelihood Method. Scandinavian Journal of Statistics, 11(2), 93–112.
- Rao, G. S., Aslam, M., & Kantam, R. R. L. (2016). Bootstrap confidence intervals of CNpk for inverse Rayleigh and log-logistic distributions. Journal of Statistical Computation and Simulation, 86(5), 862–873. https://doi.org/https://doi.org/10.1080/00949655.2015.1040799
- Rastogi, M. K., & Tripathi, Y. M. (2013). Inference on unknown parameters of a Burr distribution under hybrid censoring. Statistical Papers, 54(3), 619–643. https://doi.org/https://doi.org/10.1007/s00362-012-0452-3
- Saha, M., Dey, S., Yadav, A. S., & Kumar, S. (2019). Classical and Bayesian inference of Cpy for generalized Lindley distributed quality characteristic. Quality and Reliability Engineering International, 35(8), 2593–2611. https://doi.org/https://doi.org/10.1002/qre.2544
- Saha, M., Dey, S., Yadav, Y. S., & Ali, S. (2021). Confidence intervals of the index Cpk for normally distributed quality characteristics using classical and Bayesian methods of estimation. Brazilian Journal of Probability and Statistics, 35(1), 138–157. https://doi.org/https://doi.org/10.1214/20-BJPS469
- Saha, M., Kumar, S., Maiti, S. S., Singh Yadav, A., & Dey, S. (2020a). Asymptotic and bootstrap confidence intervals for the process capability index Cpy based on Lindley distributed quality characteristic. American Journal of Mathematical and Management Sciences, 39(1), 75–89. https://doi.org/https://doi.org/10.1080/01966324.2019.1580644
- Saha, M., Kumar, S., Maiti, S. S., & Yadav, A. S. (2018). Asymptotic and bootstrap confidence intervals of generalized process capability index Cpy for exponentially distributed quality characteristic. Life Cycle Reliability and Safety Engineering, 7(4), 235–243. https://doi.org/https://doi.org/10.1007/s41872-018-0050-z
- Saha, M., Kumar, S., & Sahu, R. (2020b). Comparison of two generalized process capability indices by using Bootstrap Confidence Intervals. International Journal of Statistics and Reliability Engineering, 7(1), 187–195.
- Saxena, S., & Singh, H. P. (2006). A Bayesian estimator of process capability index. Journal of Statistics and Management Systems, 9(2), 269–283. https://doi.org/https://doi.org/10.1080/09720510.2006.10701206
- Seifi, S., & Nezhad, M. S. F. (2017). Variable sampling plan for resubmitted lots based on process capability index and Bayesian approach. The International Journal of Advanced Manufacturing Technology, 88(9–12), 2547–2555. https://doi.org/https://doi.org/10.1007/s00170-016-8958-9
- Sharma, V. K., Singh, S. K., & Singh, U. (2017). Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data. Communications for Statistical Applications and Methods, 24(3), 193–209. https://doi.org/https://doi.org/10.5351/CSAM.2017.24.3.193
- Shiau, J. J. H., Chiang, C. T., & Hung, H. N. (1999a). A Bayesian procedure for process capability assessment. Quality and Reliability Engineering International, 15(5), 369–378. https://doi.org/https://doi.org/10.1002/(SICI)1099-1638(199909/10)15:5<369::AID-QRE262>3.0.CO;2-R
- Shiau, J. J. H., Hung, H. N., & Chiang, C. T. (1999b). A note on Bayesian estimation of process capability indices. Statistics & Probability Letters, 45(3), 215–224. https://doi.org/https://doi.org/10.1016/S0167-7152(99)00061-9
- Singh, B., Gupta, P. K., & Sharma, V. K. (2014). Parameter estimation of power Lindley distribution under hybrid censoring. Journal of Statistics Applications & Probability Letters, 1(3), 95–104. https://doi.org/https://doi.org/10.12785/jsapl/010306
- Smith, A. F., & Roberts, G. O. (1993). Bayesian computation via the gibbs sampler and related markov chain monte carlo methods. Journal of the Royal Statistical Society. Series B (Methodological), 55(1). https://www.jstor.org/stable/2346063
- Smithson, M. (2001). Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals. Educational and Psychological Measurement, 61(4), 605–632. https://doi.org/https://doi.org/10.1177/00131640121971392
- Swain, J. J., Venkatraman, S., & Wilson, J. R. (1988). Least-squares estimation of distribution functions in Johnson’s translation system. Journal of Statistical Computation and Simulation, 29(4), 271–297. https://doi.org/https://doi.org/10.1080/00949658808811068
- Upadhyay, S. K., Vasishta, N., & Smith, A. F. (2001). Bayes inference in life testing and reliability via Markov chain Monte Carlo simulation. Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), 63(1), 15–40. https://www.jstor.org/stable/25051337
- Valiollahi, R., Raqab, M. Z., Asgharzadeh, A., & Alqallaf, F. A. (2018). Estimation and prediction for power Lindley distribution under progressively type II right censored samples. Mathematics and Computers in Simulation, 149(C), 32–47. https://doi.org/https://doi.org/10.1016/j.matcom.2018.01.005
- Varian, H. R. (1975). A Bayesian approach to real estate assessment. In Studies in Bayesian econometric and statistics in honor of Leonard J. Savage (pp. 195–208). North-Holland, Amsterdam.
- Weber, S., Ressurreição, T., & Duarte, C. (2016). Yield prediction with a new generalized process capability index applicable to non-normal data. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 35(6), 931–942. https://doi.org/https://doi.org/10.1109/TCAD.2015.2481865