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Testing capability indices for manufacturing processes with asymmetric tolerance limits and measurement errors

Published online by Cambridge University Press:  29 June 2011

D. Grau
D. Grau*
Affiliation:
Laboratory of Applied Mathematics, CNRS UMR 5142, IUT de Bayonne, Université de Pau et des Pays de l’Adour, 17 Place Paul Bert, 64100 Bayonne, France
*
⋆ Correspondence: daniel.grau@univ-pau.fr
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Abstract

Most research works related to process capability indices assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when advanced measuring instruments are employed. If we do not take into account these errors, conclusions drawn from process capability are therefore unreliable. In this paper we study the sampling distribution of capability indices Cp''(u,v) in the presence of measurements errors, and when small subsamples data are collected from past “in-control”. We show that using a critical value without taking into account these errors, severely underestimates the α-risk which causes a less accurate testing capacity. To improve the results we suggest the use of an adjusted critical value, and we give a Maple program to get it. An example in a nougat manufactory is presented to illustrate this approach.

Keywords

Process capability indicesgauge measurement errorasymmetric tolerancescritical valuepower test
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 2 , Issue 1 , 2011 , pp. 61 - 73
Copyright
© EDP Sciences 2011

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References

S. Kotz, N.L. Johnson, Process capability indices (Chapman and Hall, London, 1993)
D.R. Bothe, Measuring process capability (MC Graw Hill, New York, 1997)
S. Kotz, C.R. Lovelace, Process capability indices in theory and practice (Arnold, London, 1998)
W.L. Pearn, S. Kotz, Encyclopedia and handbook of process capability indices (World Scientific Publishing, Singapore, 2006), Vol. 12
Kane, V.E., Process capability indices, J. Qual. Tech. 18, 41–52 (1986)Google Scholar
Chan, L.K., Cheng, S.W., Spiring, F.A., A new measure of process capability: Cpm, J. Qual. Tech. 20, 162–175 (1988) Google Scholar
Pearn, W.L., Kotz, S., Johnson, N.L., Distributional and inferential properties of process capability indices, J. Qual. Tech. 24, 216–231 (1992)Google Scholar
Vännman, K., A unified approach to capability indices, Stat. Sinica 5, 805–820 (1995)Google Scholar
Boyles, R.A., Process capability with asymmetric tolerances, Comm. Stat. Sim. Comp. 23, 615–643 (1994)CrossRefGoogle Scholar
Chen, K.S., Pearn, W.L., Capability indices for processes with asymmetric tolerances, J. Chin. Inst. Eng. 24, 559–568 (2001)CrossRefGoogle Scholar
Grau, D., Process yield and capability indices, Commun. Stat. Theory. Methods 40, 2751–2771 (2011) CrossRefGoogle Scholar
Montgomery, D.C., Runger, G.C., Gauge capability and designed experiments. Part I: basic methods, Qual. Eng. 6, 115–135 (1993)CrossRefGoogle Scholar
Montgomery, D.C., Runger, G.C., Gauge capability and designed experiments. Part II: experimental design models and variance component estimation, Qual. Eng. 6, 289–305 (1993)CrossRefGoogle Scholar
Levinson, W.A., How good is gauge? Semicond. Int. 165–168 (1995)Google Scholar
Mittag, H.J., Measurement error effects on the performance of process capability indices, Front. Stat. Qual. Control 5, 195–206 (1997)CrossRefGoogle Scholar
Bordignon, S., Scagliarini, M., Statistical analysis of process capability indices with measurement errors, Qual. Rel. Eng. Int. 18, 321–332 (2002) CrossRefGoogle Scholar
Bordignon, S., Scagliarini, M., Statistical analysis of process capability indices with measurement errors: the case of Cp, Stat. Meth. Appl. 10, 273–285 (2001) CrossRefGoogle Scholar
Bordignon, S., Scagliarini, M., Estimation of Cpm when measurement errors is present, Qual. Rel. Eng. Int. 22, 787–801 (2006) CrossRefGoogle Scholar
Pearn, W.L., Liao, M.Y., Measuring process capability based on Cpk with gauge measurement errors, Microelec. Rel. 45, 739–751 (2005) CrossRefGoogle Scholar
Pearn, W.L., Liao, M.Y., One-sided process capability assessment in the presence of measurement errors, Qual. Rel. Eng. Int. 22, 771–785 (2006) CrossRefGoogle Scholar
Pearn, W.L., Liao, M.Y., Estimating and testing process precision with presence of gauge measurement errors, Qual. Quant. 41, 757–777 (2007) CrossRefGoogle Scholar
Pearn, W.L., Shu, M.H., Hsu, B.M., Testing process capability based on Cpm in the presence of random measurement errors, J. Appl. Stat. 32, 1003–1024 (2005) CrossRefGoogle Scholar
Hsu, B.M., Shu, M.H., Pearn, W.L., Measuring process capability based on Cpmk with gauge measurement errors, Qual. Rel. Eng. Int. 23, 597–614 (2007) CrossRefGoogle Scholar
Grau, D., Moments of the unbalanced non-central chi-square distribution, Stat. Prob. Lett. 79, 361–367 (2009) CrossRefGoogle Scholar
Pearn, W.L., Lin, P.C., Chen, K.S., Estimating process capability index Cpmk'' for asymmetric tolerances: Distributional properties, Metrika 54, 261–279 (2001) CrossRefGoogle Scholar
Pearn, W.L., Lin, P.C., Testing process performance based on capability index Cpk with critical values, Comp. Ind. Eng. 47, 351–369 (2004) CrossRefGoogle Scholar
Lin, P.C., Pearn, W.L., Testing process performance based on the capability index Cpm, Int. J. Adv. Manuf. Tech. 27, 351–358 (2005) CrossRefGoogle Scholar