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Research Article

Process capability vector for multivariate nonlinear profiles

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Pages 1292-1321 | Received 08 Dec 2020, Accepted 07 Oct 2021, Published online: 15 Nov 2021

References

  • Montgomery DC. Introduction to statistical quality control. Hoboken (NJ): John Wiley & Sons; 2007.
  • Ryan TP. Statistical methods for quality improvement. Hoboken (NJ): John Wiley & Sons; 2011.
  • Juran JM. Juran's quality control handbook. Vol. 3, New York: McGraw-Hill; 1974.
  • Kane VE. Process capability indices. J Quality Technol. 1986;18(1):41–52.
  • Chan LK, Cheng SW, Spiring FA. A new measure of process capability: cpm. J Quality Technol. 1988;20(3):162–175.
  • Pearn WL, Kotz S, Johnson NL. Distributional and inferential properties of process capability indices. J Quality Technol. 1992;24(4):216–231.
  • Johnson NL. Systems of frequency curves generated by methods of translation. Biometrika. 1949;36(1/2):149–176.
  • Box GE, Cox DR. An analysis of transformations. J R Stat Soc: Ser B (Methodol). 1964;26(2):211–243.
  • Somerville SE, Montgomery DC. Process capability indices and non-normal distributions. Qual Eng. 1996;9(2):305–316.
  • Clements JA. Process capability calculations, for non-normal distributions. Quality Progress. 1989;22:95–100.
  • Pearn W, Kotz S. Application of clements' method for calculating second-and third-generation process capability indices for non-normal pearsonian populations. Qual Eng. 1994;7(1):139–145.
  • Ciupke K. Multivariate process capability index based on data depth concept. Quality Reliab Eng Int. 2016;32(7):2443–2453.
  • Taam W, Subbaiah P, Liddy JW. A note on multivariate capability indices. J Appl Stat. 1993;20(3):339–351.
  • Shahriari H, Hubele N, Lawrence F. A multivariate process capability vector. Proceedings of the 4th Industrial Engineering Research Conference; 1995.
  • Wang F, Hubele NF, Lawrence FP, et al. Comparison of three multivariate process capability indices. J Quality Technol. 2000;32(3):263–275.
  • Pan JN, Lee CY. New capability indices for evaluating the performance of multivariate manufacturing processes. Quality Reliab Eng Int. 2010;26(1):3–15.
  • Shahriari H, Abdollahzadeh M. A new multivariate process capability vector. Qual Eng. 2009;21(3):290–299.
  • Ciupke K. Multivariate process capability vector based on one-sided model. Quality Reliab Eng Int. 2015;31(2):313–327.
  • Wierda SJ. A multivariate process capability index. Commun Stat-Simul Comput. 1993;47:342–342.
  • Chen H. A multivariate process capability index over a rectangular solid tolerance zone. Stat Sin. 1994;:–.
  • Pal S. Performance evaluation of a bivariate normal process. Qual Eng. 1999;11(3):379–386.
  • Polansky AM. A smooth nonparametric approach to multivariate process capability. Technometrics. 2001;43(2):199–211.
  • Castagliola P, Castellanos JVG. Capability indices dedicated to the two quality characteristics case. Qual Technol Quant Manag. 2005;2(2):201–220.
  • Abbasi NSTA B. Estimating process capability indices of multivariate nonnormal processes. Int J Adv Manuf Technol. 2010;50(5-8):823–830.
  • Wang CH. Constructing multivariate process capability indices for short-run production. Int J Adv Manuf Technol. 2005;26(11-12):1306–1311.
  • Scagliarini M. Multivariate process capability using principal component analysis in the presence of measurement errors. AStA Adv Stat Anal. 2011;95(2):113–128.
  • Perakis M, Xekalaki E. On the implementation of the principal component analysis-based approach in measuring process capability. Quality Reliab Eng Int. 2012;28(4):467–480.
  • de Felipe D, Benedito E. A review of univariate and multivariate process capability indices. Int J Adv Manuf Technol. 2017;92(5-8):1687–1705.
  • González I, Sánchez I. Capability indices and nonconforming proportion in univariate and multivariate processes. The Int J Adv Manuf Technol. 2009;44(9-10):1036–1050.
  • Kakde D, Chaudhuri A, Shaw D. A new non-parametric process capability index. 2018 IEEE International Conference on Prognostics and Health Management (ICPHM); IEEE; 2018. p. 1–7.
  • Ganji ZA. Multivariate process incapability vector. Quality Reliab Eng Int. 2019;35(4):902–919.
  • Ganji ZA, Sadeghpour Gildeh B. A new multivariate process capability index. Total Qual Manag Bus Excell. 2019;30(5-6):525–536.
  • Chatterjee M. Impact of multivariate normality assumption on multivariate process capability indices. Commun Stat: Case Stud, Data Anal Appl. 2019;5(4):314–345.
  • Khadse KG, Khadse AK. On properties of probability-based multivariate process capability indices. Quality Reliab Eng Int. 2020;36(5):1768–1785.
  • Woodall WH. Current research on profile monitoring. Production. 2007;17(3):420–425.
  • Kang L, Albin SL. On-line monitoring when the process yields a linear profile. J Quality Technol. 2000;32(4):418–426.
  • Mahmoud MA, Woodall WH. Phase I analysis of linear profiles with calibration applications. Technometrics. 2004;46(4):380–391.
  • Kusiak A, Zheng H, Song Z. Models for monitoring wind farm power. Renew Energy. 2009;34(3):583–590.
  • Wang K, Tsung F. Using profile monitoring techniques for a data-rich environment with huge sample size. Quality Reliab Eng Int. 2005;21(7):677–688.
  • Woodall WH, Spitzner DJ, Montgomery DC, et al. Using control charts to monitor process and product quality profiles. J Quality Technol. 2004;36(3):309–320.
  • Noorossana R, Saghaei A, Amiri A. Statistical analysis of profile monitoring. Vol. 865. Hoboken (NJ): John Wiley & Sons; 2011.
  • Woodall WH, Montgomery DC. Some current directions in the theory and application of statistical process monitoring. J Quality Technol. 2014;46(1):78–94.
  • Maleki MR, Amiri A, Castagliola P. An overview on recent profile monitoring papers (2008–2018) based on conceptual classification scheme. Computers Indust Eng. 2018;126:705–728.
  • Pan JN, Li CI, Lu MZ. Detecting the process changes for multivariate nonlinear profile data. Quality Reliab Eng Int. 2019;35(6):1890–1910.
  • Kordestani M, Hassanvand F, Samimi Y, et al. Monitoring multivariate simple linear profiles using robust estimators. Commun Stat-Theor Meth. 2020;49(12):2964–2989.
  • Ghosh M, Li Y, Zeng L, et al. Modeling multivariate profiles using gaussian process-controlled B-splines. IISE Trans. 2020;53:1–12.
  • Zahra Hosseinifard S, Abbasi B. Evaluation of process capability indices of linear profiles. Int J Quality Reliab Manag. 2012;29(2):162–176.
  • Hosseinifard SZ, Abbasi B. Process capability analysis in non normal linear regression profiles. Commun Stat-Simul Comput. 2012;41(10):1761–1784.
  • Ebadi M, Shahriari H. A process capability index for simple linear profile. Int J Adv Manuf Technol. 2013;64(5–8):857–865.
  • Ebadi M, Amiri A. Evaluation of process capability in multivariate simple linear profiles. Scientia Iranica. 2012;19(6):1960–1968.
  • Wang FK, Guo YC. Measuring process yield for nonlinear profiles. Quality Reliab Eng Int. 2014;30(8):1333–1339.
  • Chiang JY, Lio Y, Tsai TR. Mewma control chart and process capability indices for simple linear profiles with within-profile autocorrelation. Quality Reliab Eng Int. 2017;33(5):1083–1094.
  • Alevizakos V, Koukouvinos C, Lappa A. Comparative study of the cp and spmk indices for logistic regression profile using different link functions. Qual Eng. 2019;31(3):453–462.
  • Alevizakos V, Koukouvinos C, Castagliola P. Process capability index for poisson regression profile based on the spmk index. Qual Eng. 2019;31(3):430–438.
  • Ganji ZA, Gildeh BS. Fuzzy process capability indices for simple linear profile. J Appl Stat. 2020;47(12):2136–2158. Available from: https://doi.org/https://doi.org/10.1080/02664763.2019.1704225.
  • Alevizakos V, Koukouvinos C. Evaluation of process capability in gamma regression profiles. Commun Stat-Simul Comput. 2020;1–16. DOI:https://doi.org/10.1080/03610918.2020.1758941.
  • Schabenberger O, Pierce FJ. Contemporary statistical models for the plant and soil sciences. Boca Raton (FL): CRC Press; 2001.
  • Nemati Keshteli R, Kazemzadeh RB, Amiri A, et al. Functional process capability indices for circular profile. Quality Reliab Eng Int. 2014;30(5):633–644.
  • Guevara RD, Vargas JA. Process capability analysis for nonlinear profiles using depth functions. Quality and Reliability Engineering International. 2015;31(3):465–487.
  • Guevara RD, Vargas JA, Castagliola P. Evaluation of process capability in non-linear profiles using hausdorff distance. Qual Technol Quant Manag. 2016;13(1):1–15.
  • Negash YT. Process yield index and variable sampling plans for autocorrelation between nonlinear profiles. IEEE Access. 2018;7:8931–8943.
  • Guevara RD, Vargas JA. Evaluation of process capability in multivariate nonlinear profiles. J Stat Comput Simul. 2016;86(12):2411–2428.
  • Lupo T. The new nino capability index for dynamic process capability analysis. Quality Reliab Eng Inte. 2015;31(2):305–312.
  • Niavarani MR, Noorossana R, Abbasi B. Three new multivariate process capability indices. Commun Stat-Theor Meth. 2012;41(2):341–356.
  • Ganji ZA, Gildeh BS. A modified multivariate process capability vector. Int J Adv Manuf Technol. 2016;83(5–8):1221–1229.
  • Zuo Y, Serfling R. General notions of statistical depth function. Ann Stat. 2000;28:461–482.
  • Rafalin E, Souvaine D. Data depth contours-a computational geometry perspective. Tufts University; 2004.
  • Zuo Y, He X. On the limiting distributions of multivariate depth-based rank sum statistics and related tests. Ann Stat. 2006;34(6):2879–2896.
  • Serfling R. Quantile functions for multivariate analysis: approaches and applications. Stat Neerl. 2002;56(2):214–232.
  • Mahalanobis P. On the generalized distance in statistics. National Institute of Sciences of India; Vol. 12, 1936. p. 49–55.
  • Tukey JW. Mathematics and the picturing of data. International Congress of Mathematicians; Vol. 2, Canadian Mathematical Congress; 1975. p. 523–531.
  • Barnett V. The ordering of multivariate data. J R Stat Soc Ser A. 1976;139:319–354.
  • Oja H. Descriptive statistics for multivariate distributions. Stat Probab Lett. 1983;1:327–332.
  • Liu RY. On a notion of data depth based on random simplices. Ann Stat. 1990;18:405–414.
  • Liu RY, Parelius JM, Singh K. Multivariate analysis by data depth: descriptive statistics, graphics and inference. Ann Stat. 1999;27:783–858.
  • Serfling R. Nonparametric multivariate descriptive measures based on spatial quantiles. J Stat Plan Inference. 2004;123:259–278.
  • Wang J, Serfling R. Data depth: robust multivariate analysis, computational geometry, and applications. Chapter on scale curves for nonparametric description of dispersion. Vol. 72, American Mathematical Society; 2006. p. 37–48.
  • Claeskens G, Hubert M, Slaets L, et al. Multivariate functional halfspace depth. J Am Stat Assoc. 2014;109(505):411–423.
  • Mosler K. Depth statistics. Robustness and complex data structures. Berlin, Heidelberg: Springer; 2013.
  • Liu RY, Singh K. A quality index based on data depth and multivariate rank tests. J Am Stat Assoc. 1993;88(421):252–260.
  • Liu RY. Control charts for multivariate processes. J Am Stat Assoc. 1995;90(432):1380–1387.
  • Stoumbos ZG, Jones LA, Woodall WH, et al. On nonparametric multivariate control charts based on data depth. Frontiers in statistical quality control. Vol. 6, Springer; 2001. p. 207–227.
  • Li J, Zhang X, Jeske DR. Nonparametric multivariate cusum control charts for location and scale changes. J Nonparametr Stat. 2013;25(1):1–20.
  • Li Z, Dai Y, Wang Z. Multivariate change point control chart based on data depth for phase I analysis. Commun Stat-Simul Comput. 2014;43(6):1490–1507.
  • Bell RC, Jones-Farmer LA, Billor N. A distribution-free multivariate phase I location control chart for subgrouped data from elliptical distributions. Technometrics. 2014;56(4):528–538.
  • Barale M, Shirke D. Nonparametric control charts based on data depth for location parameter. J Stat Theor Pract. 2019;13(3):41.
  • Fraiman R, Muniz G. Trimmed means for functional data. Test. 2001;10:419–440.
  • Cuevas A, Febrero M, Fraiman R. On the use of bootstrap for estimating functions with functional data. Comput Stat Data Anal. 2006;51:1063–1074.
  • Cuevas A, Febrero M, Fraiman R. Robust estimation and classification for functional data via projection-based depth notions. Comput Stat. 2007;22:481–496.
  • Febrero M, Galeano P, González-Manteiga W. Outlier detection in functional data by depth measures, with application to identify abnormal nox levels. Environmetrics. 2008;19:331–345.
  • López-Pintado S, Romo J. On the concept of depth for functional data. J Am Stat Assoc. 2009;104(486):718–734.
  • López-Pintado S, Romo J. A half-region depth for functional data. Comput Stat Data Anal. 2011;55:1679–1695.
  • Narisetty NN, Nair VN. Extremal depth for functional data and applications. J Am Stat Assoc. 2016;111(516):1705–1714.
  • Berrendero JR, Justel A, Svarc M. Principal components for multivariate functional data. Comput Stat Data Anal. 2011;55(9):2619–2634.
  • Ieva F, Paganoni AM. Depth measures for multivariate functional data. Commun Stat-Theor Meth. 2013;42(7):1265–1276.
  • Ramsay JO. Functional data analysis. Vol. 4. New York: Wiley Online Library; 2004.
  • Horváth L, Kokoszka P. Inference for functional data with applications. Vol. 200. New York: Springer Science & Business Media; 2012.
  • Kokoszka P, Reimherr M. Introduction to functional data analysis. Boca Raton, FL: CRC Press; 2017.
  • Magagnoli U, Zappa D. Parametric and non-parametric capability indices for multivariate processes. Università cattolica del Sacro Cuore, Dipartimento di scienze statistiche; 2007.
  • de Berg M, Cheong O, Van Kreveld M, et al. Computational geometry algorithms and applications. Berlin, Heidelberg: Springer; 2008.
  • Johnson NL, Kemp AW, Kotz S. Univariate discrete distributions. Vol. 444. Hoboken (NJ): John Wiley & Sons; 2005.
  • Kemp A, Kemp C. Distributional properties of a model for the spread or drug abuse. Commun Stat-Theor Meth. 1986;15(11):3287–3298.
  • Alevizakos V, Koukouvinos C. Monitoring of zero-inflated binomial processes with a dewma control chart. J Appl Stat. 2020;48:1–20.
  • R Core Team. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2018. Available from: https://www.R-project.org/.
  • Genest M, Masse JC, src/depthf contains eigen JFP, et al. Depth: Nonparametric depth functions for multivariate analysis; 2019. R package version 2.1-1.1; Available from: https://CRAN.R-project.org/package=depth.
  • Habel K, Grasman R, Gramacy RB, et al. Geometry: Mesh generation and surface tessellation; 2019. R package version 0.4.5. Available from: https://CRAN.R-project.org/package=geometry.
  • Munck L, Nørgaard L, Engelsen SB, et al. Chemometrics in food sciencea demonstration of the feasibility of a highly exploratory, inductive evaluation strategy of fundamental scientific significance. Chemometr Intell Lab Syst. 1998;44(1–2):31–60.
  • Bro R. Exploratory study of sugar production using fluorescence spectroscopy and multi-way analysis. Chemometr Intell Lab Syst. 1999;46(2):133–147.
  • Smilde A, Bro R, Geladi P. Multi-way analysis with applications in the chemical sciences. 2004.

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