Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T19:49:12.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Testing capability indices for one-sided processeswith measurement errors

Published online by Cambridge University Press:  07 November 2013

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: [email protected]
Get access

Abstract

In the manufacturing industry, many product characteristics are of one-sided tolerances. The process capability indices Cpu (u, v) and Cpl (u, v) can be used to measure process performance. Most research work related to capability indices assumes no gauge measurement errors. This assumption insufficiently reflects real situations even when advanced measuring instruments are used. In this paper 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. In order 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 polymer granulates manufactory is presented to illustrate this approach.

Keywords

Process capability indicesgauge measurement errorone-sided tolerance processcritical valuepower test
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 4 , Issue 2 , 2013 , pp. 71 - 80
Copyright
© EDP Sciences 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chan, L.K., Cheng, S.W., Spiring, F.A., A New Measure of Process Capability: Cpm, J. Qual. Technol. 20, 162–175 (1998) Google Scholar
Pearn, W.L., Kotz, S., Johnson, N.L., Distributional and inferential properties of process capability indices, J. Qual. Technol. 24, 216–231 (1992) Google Scholar
Vännman, K., A unified approach to capability indices, Stat. Sin. 5, 805–820 (1995) Google 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 Meth. 40, 2751–2771 (2011) CrossRefGoogle Scholar
Grau, D., New Process capability indices for one-sided tolerances, Qual. Technol. Quant. Manag. 6, 107–124 (2009) CrossRefGoogle Scholar
Grau, D., Process yield, process centering, and capability indices for one-sided tolerance processes, Qual. Technol. Quant. Manag. 9, 153–170 (2012) CrossRefGoogle Scholar
Mittag, H.J., Measurement error effects on the performance of process capability indices, Front. Stat. Qual. Control 5, 195–206 (1997) 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., Liao, M.Y., Measuring process capability based on Cpk with gauge measurement errors, Microelectron. Reliab. 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., 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., Lower confidence bound for capability indices with asymmetric tolerances and gauge measurement errors, Int. J. Qual. Eng. Technol. 2, 212–228 (2011) CrossRefGoogle Scholar
Grau, D., Testing capability indices for manufacturing processes with asymmetric tolerance limits and measurement errors, Int. J. Metrol. Qual. Eng. 2, 61–73 (2011) CrossRefGoogle Scholar