Abstract
In this chapter the most recognized multivariate process capability indices are presented. The first section approaches the computation of these indices in R, and the next ones are dedicated to the indices based on ratios of the volume tolerance region to a process region such as Taam et al. (J Appl Stat 20:339–351, 1993), Shahriari et al. (Proceedings of the 4th Industrial Engineering Research Conference 1:304–309, 1995), and Pan and Lee (Qual Reliab Eng Int 26(1):3–15, 2010). While the last part of the chapter focuses on the indices derived of principal component analysis.
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References
Anderson, T.W.: Asymptotic theory for principal component analysis. Ann. Math. Stat. 34, 122–148 (1963)
Bartlett, M.S.: A note on the multiplying factors for various X2 approximations. J. R. Stat. Soc. Series B. 16, 296–298 (1954)
Bothe, D.R.: A capability study for an entire product. ASQC Quality Congress Transactions. 46, 172–178 (1992)
Castagliola, P., Castellanos, J.-V.G.: Capability indices dedicated to the two quality characteristics case. Qual. Technol. Quant. Manag. 2(2), 201–220 (2005)
Chan, L.K., Cheng, S.W., Spiring, F.A.: A multivariate measure of process capability. J. Model. Simulat. 1, 1–6 (1991)
Chen, H.: A multivariate process capability index over a rectangular solid zone. Statistica Sinica. 4, 749–758 (1994)
Chen, K.S., Pearn, W.L., Lin, P.C.: Capability measures for processes with multiple characteristics. Qual. Reliab. Eng. Int. 19, 101–110 (2003)
Hubele, N.F., Shahriari, H., Cheng, C.S.: A Bivariate Process Capability Vector, pp. 299–310. Marcel Dekker, New York (1991)
Montgomery, D.C.: Introduction to Statistical Quality Control, 5th edn. Wiley, New York (2004)
Nickerson, D.M.: Construction of a conservative confidence region from projections of an exact confidence region in multiple linear regression. The American Statistician. 48(2), 120–124 (1994)
Pan, J.-N., Lee, C.-Y.: New capability indices for evaluating the performance of multivariate manufacturing processes. Qual. Reliab. Eng. Int. 26(1), 3–15 (2010)
Pearn, W., Kotz, L.S., Johnson, N.L.: Distributional and inferential properties of process capability indices. J. Qual. Tech. 24, 216–231 (1992)
Pearn, W.L., Kotz, S.: Encyclopedia and Handbook of Process Capability Indices: A Comprehensive Exposition of Quality Control Measures. World Scientific Publishing Company, Singapore (2006)
Rencher, A.C.: Methods of Multivariate Analysis. Wiley, New York (2002)
Santos-Fernández, E., Scagliarini, M.: MPCI: an R package for computing multivariate process capability indices. J. Stat. Softw. 47(7), 1–15 (2012)
Scagliarini, M.: Multivariate process capability using principal component analysis in the presence of measurement errors. AStA Advances in Statistical Analysis. 95(2), 757–765 (2011)
Shahriari, H., Hubele, N.F., Lawrence, F.P.: A multivariate process capability vector. In: Proceedings of the 4th Industrial Engineering Research Conference, vol. 1, pp. 304–309. (1995)
Shinde, R.L., Khadse, K.G.: Multivariate process capability using principal component analysis. Qual. Reliab. Eng. Int. 25(1), 69–77 (2008)
Taam, W., Subbaiah, P., Liddy, W.J.: A note on multivariate capability indices. J. Appl. Stat. 20, 339–351 (1993)
Tano, I., Vännman, K.: Comparing confidence intervals for multivariate process capability indices. Qual. Reliab. Eng. Int. 28(4), 481–495 (2011)
Wang, C.H.: Constructing multivariate process capability indices for short-run production. Int. J. Adv. Manuf. Technol. 26, 1306–1311 (2005)
Wang, F.K., Chen, J.C.: Capability index using principal components analysis. Qual. Eng. 11, 21–27 (1998)
Wang, F.K., Hubele, N., Lawrence, F.P., Miskulin, J.D., Shahriari, H.: Comparison of three multivariate process capability indices. J. Qual. Tech. 32, 263–275 (2000)
Wierda, S.J.: A multivariate process capability index. In: ASQC Quality Congress Transactions, pp. 342–348. (1993)
Xekalaki, E., Perakis, M.: The use of principal component analysis in the assessment of process capability indices. In: Proceedings of the Joint Statistical Meetings of the American Statistical Association, The Institute of Mathematical Statistics, The Canadian Statistical Society. New York. Marcel Dekker, New York (2002)
Yum, B.-J., Kim, K.-W.: A bibliography of the literature on process capability indices: 2000–2009. Qual. Reliab. Eng. Int. 27(3), 251–268 (2012)
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Santos-Fernández, E. (2012). Multivariate Process Capability Indices (MPCI). In: Multivariate Statistical Quality Control Using R. SpringerBriefs in Statistics, vol 14. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5453-3_3
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