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Article

Inference on the lifetime performance index of gamma distribution: point and interval estimation

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Pages 1368-1386 | Received 22 Mar 2021, Accepted 18 Feb 2022, Published online: 02 Mar 2022

References

  • Ahmadi, M. V., J. Ahmadi, and M. Abdi. 2019. Evaluating the lifetime performance index of products based on generalized order statistics from two-parameter exponential model. International Journal of System Assurance Engineering and Management 10 (2):251–75. doi:10.1007/s13198-019-00780-2.
  • Ahmadi, M. V., and M. Doostparast. 2021. Evaluating the lifetime performance index of products based on progressively Type-II censored Pareto samples: A new bayesian approach. Quality and Reliability Engineering International. doi:10.1002/qre.3040.
  • Ahmadi, M. V., M. Doostparast, and J. Ahmadi. 2013. Estimating the lifetime performance index with Weibull distribution based on progressive first-failure censoring scheme. Journal of Computational and Applied Mathematics 239:93–102. doi:10.1016/j.cam.2012.09.006.
  • Ahmadi, M. V., M. Doostparast, and J. Ahmadi. 2015. Statistical inference for the lifetime performance index based on generalised order statistics from exponential distribution. International Journal of Systems Science 46 (6):1094–107. doi:10.1080/00207721.2013.809611.
  • Alzer, H. 1997. On some inequalities for the gamma and psi functions. Mathematics of Computation 66 (217):373–89. doi:10.1090/S0025-5718-97-00807-7.
  • Askitis, D. 2016. Asymptotic expansions of the inverse of the beta distribution. arXiv preprint arXiv:1611.03573.
  • Bain, L. J., and M. Engelhardt. 1975. A two-moment chi-square approximation for the statistic log (x¯/x˜). Journal of the American Statistical Association 70 (352):948–50.
  • Caroni, C. 2002. The correct “ball bearings” data. Lifetime Data Analysis 8 (4):395–9. doi:10.1023/A:1020523006142.
  • Chen, P., and Z.-S. Ye. 2017. Approximate statistical limits for a gamma distribution. Journal of Quality Technology 49 (1):64–77. doi:10.1080/00224065.2017.11918185.
  • Cheng, R., and N. Amin. 1979. Maximum product-of-spacings estimation with applications to the lognormal distribution. University of Wales IST, Math Report 79-1.
  • Dey, S., and M. Saha. 2018. Bootstrap confidence intervals of the difference between two generalized process capability indices for inverse Lindley distribution. Life Cycle Reliability and Safety Engineering 7 (2):89–96. doi:10.1007/s41872-018-0045-9.
  • Dey, S., and M. Saha. 2019. Bootstrap confidence intervals of generalized process capability index Cpyk using different methods of estimation. Journal of Applied Statistics 46 (10):1843–69.
  • Dey, S., and M. Saha. 2020. Bootstrap confidence intervals of process capability index Spmk using different methods of estimation. Journal of Statistical Computation and Simulation 90 (1):28–50. doi:10.1080/00949655.2019.1671980.
  • Dey, S., M. Saha, and S. Kumar. 2021a. Parametric confidence intervals of Spmk for generalized exponential distribution. American Journal of Mathematical and Management Sciences :1–22. doi:10.1080/01966324.2021.1949412.
  • Dey, S., M. Saha, S. S. Maiti, and C.-H. Jun. 2018. Bootstrap confidence intervals of generalized process capability index Cpyk for Lindley and power Lindley distributions. Communications in Statistics-Simulation and Computation 47 (1):249–62.
  • Dey, S., C. Zhang, and M. Saha. 2021b. Classical and Bayesian estimation of the index Cpmk and its confidence intervals for normally distributed quality characteristic. Journal of Statistical Computation and Simulation 91 (10):1911–34.
  • Franklin, L. A., and G. Wasserman. 1991. Bootstrap confidence interval estimates of cpk: An introduction. Communications in Statistics - Simulation and Computation 20 (1):231–42. doi:10.1080/03610919108812950.
  • Glaser, R. E. 1976. The ratio of the geometric mean to the arithmetic mean for a random sample from a gamma distribution. Journal of the American Statistical Association 71 (354):480–7. doi:10.1080/01621459.1976.10480373.
  • Hannig, J., H. Iyer, and P. Patterson. 2006. Fiducial generalized confidence intervals. Journal of the American Statistical Association 101 (473):254–69. doi:10.1198/016214505000000736.
  • Hong, C.-W., J.-W. Wu, and C.-H. Cheng. 2007. Computational procedure of performance assessment of lifetime index of businesses for the Pareto lifetime model with the right type II censored sample. Applied Mathematics and Computation 184 (2):336–50. doi:10.1016/j.amc.2006.05.199.
  • Jafari, A., and S. Bafekri. 2021. Inferences on the performance index of Weibull distribution based on k-record values. Journal of Computational and Applied Mathematics 382:113060. doi:10.1016/j.cam.2020.113060.
  • Kao, J. H. 1958. Computer methods for estimating Weibull parameters in reliability studies. IRE Transactions on Reliability and Quality Control, PGRQC 13:15–22.
  • Krishnamoorthy, K., and X. Wang. 2016. Fiducial confidence limits and prediction limits for a gamma distribution: Censored and uncensored cases. Environmetrics 27 (8):479–93. doi:10.1002/env.2408.
  • Kumar, S., A. S. Yadav, S. Dey, and M. Saha. 2021. Parametric inference of generalized process capability index cpyk for the power Lindley distribution. Quality Technology & Quantitative Management :1–34. doi:10.1080/16843703.2021.1944966.
  • Lee, W.-C. 2010. Assessing the lifetime performance index of gamma lifetime products in the manufacturing industry. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 224 (10):1571–9. doi:10.1243/09544054JEM1783.
  • Lee, W.-C. 2011. Inferences on the lifetime performance index for Weibull distribution based on censored observations using the max p-value method. International Journal of Systems Science 42 (6):931–7. doi:10.1080/00207720903260168.
  • Lee, W.-C., J.-W. Wu, and C.-W. Hong. 2009. Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model. Mathematics and Computers in Simulation 79 (7):2167–79. doi:10.1016/j.matcom.2008.12.001.
  • Lee, A. H., C.-W. Wu, S.-W. Liu, and C.-H. Liu. 2021. Designing acceptance sampling plans based on the lifetime performance index under gamma distribution. The International Journal of Advanced Manufacturing Technology 115 (11–12):3409–22. doi:10.1007/s00170-021-07299-6.
  • Louzada, F., P. L. Ramos, and E. Ramos. 2019. A note on bias of closed-form estimators for the gamma distribution derived from likelihood equations. The American Statistician 73 (2):195–9. doi:10.1080/00031305.2018.1513376.
  • Macdonald, P. D. M. 1971. Comments and queries comment on “An estimation procedure for mixtures of distributions” by Choi and Bulgren. Journal of the Royal Statistical Society: Series B (Methodological) 33 (2):326–9.
  • Montgomery, D. C. 1985. Introduction to statistical quality control. New York: John Wiley & Sons.
  • Ranneby, B. 1984. The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics 11 (2):93–112.
  • Saha, M., S. Dey, and S. Nadarajah. 2021a. Parametric inference of the process capability index Cpc for exponentiated exponential distribution. Journal of Applied Statistics:1–25. doi:10.1080/02664763.2021.1971632.
  • Saha, M., S. Dey, A. S. Yadav, and S. Ali. 2021b. 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):138–57.
  • Saha, M., S. Kumar, S. S. Maiti, A. Singh Yadav, and S. Dey. 2020. 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.
  • Swain, J. J., S. Venkatraman, and J. R. Wilson. 1988. Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation 29 (4):271–97. doi:10.1080/00949658808811068.
  • Tong, L.-I., K. S. Chen, and H. T. Chen. 2002. Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution. International Journal of Quality & Reliability Management 19 (7):812–24. doi:10.1108/02656710210434757.
  • Tsui, K. W., and S. Weerahandi. 1989. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. Journal of the American Statistical Association 84 (406):602–7. doi:10.2307/2289949.
  • Wang, B. X., and F. Wu. 2018. Inference on the gamma distribution. Technometrics 60 (2):235–44. doi:10.1080/00401706.2017.1328377.
  • Weerahandi, S. 1993. Generalized confidence intervals. Journal of the American Statistical Association 88 (423):899–905. doi:10.1080/01621459.1993.10476355.
  • Wu, S.-F., and W.-T. Chang. 2021. Power comparison of the testing on the lifetime performance index for Rayleigh lifetime products under progressive type I interval censoring. Communications in Statistics - Simulation and Computation :1–14. doi:10.1080/03610918.2021.1884716.
  • Wu, S.-F., and Y.-T. Hsieh. 2019. The assessment on the lifetime performance index of products with Gompertz distribution based on the progressive type I interval censored sample. Journal of Computational and Applied Mathematics 351:66–76. doi:10.1016/j.cam.2018.10.044.
  • Wu, S.-F., J.-J. Jheng, and W.-T. Chang. 2021. Sampling design for the lifetime performance index of exponential lifetime distribution under progressive type I interval censoring. Communications in Statistics - Theory and Methods :1–17. doi:10.1080/03610926.2021.1959933.
  • Wu, S.-F., and J.-Y. Lu. 2017. Computational testing algorithmic procedure of assessment for lifetime performance index of Pareto products under progressive type I interval censoring. Computational Statistics 32 (2):647–66. doi:10.1007/s00180-017-0717-3.
  • Ye, Z.-S., and N. Chen. 2017. Closed-form estimators for the gamma distribution derived from likelihood equations. The American Statistician 71 (2):177–81. doi:10.1080/00031305.2016.1209129.
  • Zhang, Y., and W. Gui. 2021. Statistical inference for the lifetime performance index of products with Pareto distribution on basis of general progressive type II censored sample. Communications in Statistics - Theory and Methods 50 (16):3790–808. doi:10.1080/03610926.2020.1801735.
  • Zhu, J., H. Xin, C. Zheng, and T.-R. Tsai. 2022. Inference for the process performance index of products on the basis of power-normal distribution. Mathematics 10 (1):35. doi:10.3390/math10010035.

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