The Effect of Gauge Measurement Capability and Dependency Measure of Process Variables on the MCp

Document Type : Research Paper

Authors

Department of Industrial Engineering; Isfahan University of Technology; Iran

Abstract

It has been proved that process capability indices provide very efficient measures of the capability of processes from many different perspectives. These indices have been widely used in the manufacturing industry for measuring process reproduction capability according to manufacturing specifications. In the past few years, univariate capability indices have been introduced and used to characterize process performance, but are comparatively neglected for multivariate processes where multiple dependent characteristics are involved in quality measurement. Also, most of researches related to process capability indices have assumed no gauge measurement errors. Unfortunately, such an assumption does not reflect real situations accurately even with highly sophisticated advanced measuring instruments. Conclusions drawn from process capability analysis are hence unreliable. In this paper, we consider the effect of process variables correlation coefficient on the multivariate process capability index (MCp) for different gauge measurement capabilities. Also, with respect to correlation coefficient and measurement capability we investigate the statistical properties of the estimated MCp. The results indicate that gauge measurement capability has an important role in determining process capability. This factor would increase the effect of correlation coefficient on estimating the process capability, such that for different gauge measurement capabilities, correlation coefficients will change the results of estimating and testing the process capability.

Keywords

Main Subjects


[1] Boyles R.A. (1996), Exploratory Capability Analysis; Journal of Quality Technology 28; 91–98.
[2] Chan L.K., Cheng S.W.; Spiring F.A. (1991), A Multivariate Measure of Process Capability; Journal
of Modeling and Simulation 11; 1–6.
[3] Chang Y.C, Wei Wu, Chien. (2008), Assessing process capability based on the lower confidence
bound of Cpk for asymmetric tolerances; European Journal of Operational Research 190; 205-227.
[4] Chen H. (1994), A multivariate process capability index over a rectangular solid tolerance zone;
Statistica Sinica 4; 749–758.
[5] Karl D.P., Morisette J.; Taam W. (1994), Some Applications of a Multivariate Capability Index in
Geometric Dimensioning and Tolerancing; Quality Engineering 6; 649–665.
[6] Kotz S., Johnson N.L. (2002), Process capability indices – a review, 1992-2000; Journal of Quality
Technology 34(1); 1-19.
[7] Montgomery D.C. (1996), Introduction to Statistical Quality Control; 3rd ed, John Wiley & Sons;
NewYork, NY.
[8] Montgomery D.C., Runger G.C. (1993), Gauge Capability and Designed Experiments, Part I: Basic
Methods; Quality Engineering 6(1); 115-135.
[9] Pearn W.L., Kotz S., Johnson N.L. (1992), Distributional and inferential properties of process
capability indices; Journal of Quality Technology 24; 216–231.
[10] Pearn W.L., Liao M.Y. (2005), Measuring process capability based on Cpk with gauge measurement
errors; Microelectronics Reliability 45; 739–751.
[11] Pearn W.L., Kotz S. (2006), Encyclopedia and Handbook of Process Capability Indices. Series on
Quality, Reliability and Engineering Statistics, Vol. 12; World Scientific publishing Co, Pte. Ltd.
[12] Pearn W.L., Liao M.Y. (2007), Estimating and testing process precision with presence of gauge
measurement errors; Quality and Quantity; Forthcoming.
[13] Pearn W.L., Wang F.K., Chen (2007), Multivariate Capability Indices: Distributional and Inferential
Properties; Journal of Applied Statistics 34(8); 941–962.
[14] Shahriari H., Hubele N.F., Lawrence F.P. (1995), A Multivariate Process Capability Vector;
Proceedings of the 4th Industrial Engineering Research Conference, Institute of Industrial Engineers;
pp 304–309.
[15] Shishebori D., Hamadani A.Z. (2008), The Effect of Gauge Measurement Errors on Multivariate
Process Capability, Proceedings of the 3th World Conference on Production and Operations
Management (POM), Tokyo, 5-8 August 2008, Chapter 17; pp.2425-2432.
[16] Taam W., Subbaiah P., Liddy J.W. (1993), A Note on Multivariate Process Capability Indices; Journal
of Applied Statistics 20(3); 339-351.
[17] Vannman K., Hubele N.F. (2003), Distributional Properties of Estimated Capability Indices Based on
Subsamples; Quality and Reliability Engineering International 19; 111–128.
[18] Wang F.K., Du T.C.T. (2000), Using Principal Component Analysis in Process Performance for
Multivariate Data; OMEGA, the International Journal of Management Science 28; 185-194.
[19] Wang F.K.; Miskulin J.D, Shahriari H. (2000), Comparison of Three Multivariate Process Capability
Indices; Journal of Quality Technology 32(3l); 263-275.
[20] Wang F.K., Chen J. (1998), Capability index using principal component analysis; Quality Engineering
11; 21–27.