315
Views
23
CrossRef citations to date
0
Altmetric
Articles

Bootstrap confidence intervals of generalized process capability index Cpyk using different methods of estimation

&
Pages 1843-1869 | Received 23 Apr 2018, Accepted 10 Jan 2019, Published online: 31 Jan 2019

References

  • L.K. Chan, S.W. Cheng and F.A Spiring, A new measure of process capability: Cpm, J. Qual. Technol. 20 (1988), pp. 162–175. doi: 10.1080/00224065.1988.11979102
  • R.C.H. Cheng and N.A.K. Amin, Maximum product-of-spacings estimation with applications to the log-normal distribution. Math Report, Department of Mathematics, UWIST, Cardi1979.
  • 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.
  • I.S. Choi and D.S. Bai, Process capability indices for skewed distributions. Proceedings of 20th International Conference on Computer and Industrial Engineering, Kyongju, Korea, 1996, pp. 1211–1214.
  • S. Chatterjee and J.B Singh, A NHPP based software reliability model and optimal release policy with logistic-exponential test coverage under imperfect debugging, Int. J. Syst. Assur. Eng. Manage. 5 (2014), pp. 399–406. doi: 10.1007/s13198-013-0181-6
  • S. Dey, M. Saha, S.S. Maiti and H.C. Jun, Bootstrap confidence intervals of generalized process capability index cpyk for Lindley and power Lindley distributions, Commun. Stat. -Simul. Comput. 27 (2017), pp. 249–262.
  • S. Dey and M. Saha, Bootstrap confidence intervals of the difference between two generalized probability indices for inverse Lindley distribution, Life C. Reliab. Saf. Eng. 7 (2018), pp. 89–96. doi: 10.1007/s41872-018-0045-9
  • J.J. Flaig, Process capability sensitivity analysis, Qual. Eng. 11 (1999), pp. 587–592. doi: 10.1080/08982119908919279
  • A.F. Franklin and G.S Wasserman, Bootstrap confidence interval estimation of Cpk: An introduction, Commun. Stat. - Simul. Comput. 20 (1991), pp. 231–242. doi: 10.1080/03610919108812950
  • B.S. Gildeh, A. Iziy and B Ghasempour, Estimation of Cpmk process capability index based on bootstrap method for Weibull distribution, Int. J. Qual. Res. 8 (2014), pp. 255–264.
  • B.H Gunter, The use and abuse of Cpk, Qual. Progress 22 (1989), pp. 108–109.
  • T.C. Hsiang and G. Taguchi, A tutorial on quality control and assurance – the Taguchi methods. ASA Annual Meeting, Las Vegas, Nevada, 188, 1985.
  • R. Ihaka and R. Gentleman, R: A language for data analysis and graphics, J. Comput. Graph. Stat. 5 (1996), pp. 299–314.
  • J.M. Juran, Juran's Quality Control Handbook, 3rd ed, McGraw-Hill, New York, 1974.
  • Institute. Juran, The tools of quality, Part IV: Histograms, Qual. Progress 9 (1990), pp. 75–78.
  • M. Kashif, M. Aslam, A.H. Al-Marshadi and C.H. Jun, Capability indices for non-normal distribution using Gini's mean difference as measure of variability. IEEE Access 4 (2010), pp. 7322–7330. doi: 10.1109/ACCESS.2016.2620241
  • 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, Arabian J. Sci. Eng. 42 (2017), pp. 4565–4573. doi:10.1007/s13369-017-2562-7.
  • M. Kashif, M. Aslam, C.H. Jun, A.H. Al-Marshadi and G.S Rao, The efficacy of process capability indices using median absolute deviation and their bootstrap confidence intervals, Arabian J. Sci. Eng. 42 (2017), pp. 4941–4955. doi: 10.1007/s13369-017-2699-4
  • V.E. Kane, Process capability indices, J. Qual. Technol. 18 (1986), pp. 41–52. doi: 10.1080/00224065.1986.11978984
  • J.H.K. Kao, Computer methods for estimating Weibull parameters in reliability studies, Trans. IRE Reliab. Qual. Control 13 (1958), pp. 15–22. doi: 10.1109/IRE-PGRQC.1958.5007164
  • J.H.K. Kao, A graphical estimation of mixed Weibull parameters in life testing electron tube, Technometrics 1 (1959), pp. 389–407. doi: 10.1080/00401706.1959.10489870
  • V. Leiva, C. Marchant, H. Saulo, 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. doi: 10.1080/02664763.2014.897690
  • Y. Lan and L.M Leemis, The logistic-exponential distributions, Naval Res. Logistics 55 (2008), pp. 252–264. doi: 10.1002/nav.20279
  • S.S. Maiti, M. Saha and A.K Nanda, On generalizing process capability indices, J. Qual. Technol. Quant. Manage. 7 (2010), pp. 279–300. doi: 10.1080/16843703.2010.11673233
  • N.R. Mann, N.D. Singpurwalla and R.E. Schafer, Methods for Statistical Analysis of Reliability and Life Data, Wiley, New York, 1974.
  • P.D.M. MacDonald, Comment on an estimation procedure for mixtures of distributions by Choi and Bulgren, J. R. Stat. Soc.: Ser. B 33 (1971), pp. 326–329.
  • M.H. Myers, B.F. Hankey and N. Mantel, A logistic-exponential model for use with response-time data involving regressor variables, Biometrics 29 (1973), pp. 257–269. doi: 10.2307/2529390
  • K.K. Ng and K.L. Tsui, Expressing variability and yield with a focus on the customer, Qual. Eng. 5 (1992), pp. 255–267. doi: 10.1080/08982119208918967
  • A.K Peng, Parametric lower confidence limits of quantile-based process capability indices, J. Qual. Technol. Quant. Manage. 7 (2010), pp. 199–214. doi: 10.1080/16843703.2010.11673228
  • W.L. Pearn and K.S. Chen, Capability indices for non-normal distributions with an application in electrolytic capacitor manufacturing, Microelectron. Reliab. 37 (1997), pp. 1853–1858. doi: 10.1016/S0026-2714(97)00023-1
  • W.L. Pearn, S. Kotz and N.L. Johnson, Distributional and inferential properties of process capability indices, J. Qual. Technol. 24 (1992), pp. 216–231. doi: 10.1080/00224065.1992.11979403
  • 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.
  • 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. doi: 10.1520/JTE20150357
  • C. Peng, Parametric lower confidence limits of quantile-based process capability indices, J. Qual. Technol. Quant. Manage. 7 (2010a), pp. 199–214. doi: 10.1080/16843703.2010.11673228
  • C. Peng, Estimating and testing quantile-based process capability indices for processes with skewed distributions, J. Data. Sci. 8 (2010b), pp. 253–268.
  • M.R. Pina-Monarrez, J.F. Ortiz-Yañez, and M.I Rodríguez-Borbón, Non-normal capability indices for the weibull and log-normal distributions, Qual. Reliab. Eng. Int. 32 (2016), pp. 1321–1329. doi: 10.1002/qre.1832
  • B. Ranneby, The maximum spacing method. An estimation method related to the maximum likelihood Method, Scandinavian J. Stat. 11 (1984), pp. 93–112.
  • 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. doi: 10.1080/00949655.2015.1040799
  • G.S. Rao, K. Rosaiah and S.B. Mothukuri, Bootstrap Confidence Intervals of CNpk for exponentiated Frèchet distribution, Life Cycle Reliab. Safety Eng. (2018), pp. 1–9. doi:10.1007/s41872-018-0069-1.
  • Mohammad Z. Raqab, Shafiqah A. Al-Awadhi and D Kundu, Discriminating among Weibull, log-normal and log-logistic distributions, Commun. Statist. - Simul. Comput. 47 (2017), pp. 1397–1419. doi:10.1080/03610918.2017.1315729.
  • M. Saha, S. Dey and S.S. Maiti, Parametric and non-parametric bootstrap confidence intervals of CNpk for exponential power distribution, J. Ind. Prod. Eng. 35 (2018), pp. 160–169. doi:10.1080/21681015.2018.1437793.
  • M. Saha, S. Kumar, S.S. Maiti and A.S. Yadav, Asymptotic and bootstrap confidence intervals of generalized process capability index Cpy for exponentially distributed quality characteristic, Life Cycle Reliab. Safety Eng. 7 (2018), pp. 235–243. doi:10.1007/s41872-018-0050-z.
  • 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. doi: 10.1177/00131640121971392
  • P.J. Staden and R.A.R King, Kurtosis of the logistic exponential survival distribution, Commun. Stat. - Theory Methods 45 (2016), pp. 6891–6899. doi: 10.1080/03610926.2014.972566
  • J.H. Steiger, Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis, Psychol. Methods. 9 (2004), pp. 164–182. doi: 10.1037/1082-989X.9.2.164
  • 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. doi: 10.1080/00949658808811068
  • G. Taguchi, Introduction to quality engineering: Designing quality ito products and processes, 1st Edn, Asian Productivity Organization, Tokyo, ISBN: 9283310837, 1986.
  • K.L. Tsui, Interpretation of process capability indices and some alternatives, Qual. Eng. 9 (1997), pp. 587–596. doi: 10.1080/08982119708919080
  • B. Thompson, What future quantitative social science research could look like: Confidence intervals for effect sizes, Educ. Res. 31 (2002), pp. 25–32. doi: 10.3102/0013189X031003025
  • S. Weber, T. Ressurreição and C. Duarte, Yield prediction with a new generalized process capability index applicable to non-normal data, IEEE Trans. Computer-Aided Design Int. Circuits Syst. 35 (2016), pp. 931–942. doi: 10.1109/TCAD.2015.2481865

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.