Abstract
One important application of statistical models in industry is statistical process control. Many control charts have been developed and used in industry. They are easy to use, but have been developed based on statistical principles. However, for todayʼs high-quality processes, traditional control-charting techniques are not applicable in many situations. Research has been going on in the last two decades and new methods have been proposed. This chapter summarizes some of these techniques.
High-quality processes are those with very low defect-occurrence rates. Control charts based on the cumulative count of conforming items are recommended for such processes. The use of such charts has opened up new frontiers in the research and applications of statistical control charts in general. In this chapter, several extended or modified statistical models are described. They are useful when the simple and basic geometric distribution is not appropriate or is insufficient.
In particular, we present some extended Poisson distribution models that can be used for count data with large numbers of zero counts. We also extend the chart to the case of general time-between-event monitoring; such an extension can be useful in service or reliability monitoring. Traditionally, the exponential distribution is used for the modeling of time-between-events, although other distributions such as the Weibull or gamma distribution can also be used in this context.
Abbreviations
- EWMA:
-
exponentially weighted moving average
References
W. A. Shewhart: Economic Control of Quality of Manufacturing Product (Van Nostrand, New York 1931)
M. Xie, T. N. Goh: Some procedures for decision making in controlling high yield processes, Qual. Reliab. Eng. Int. 8, 355–360 (1992)
T. W. Calvin: Quality control techniques for “zero-defects”, IEEE Trans. Compon. Hybrids Manuf. Technol. 6, 323–328 (1983)
T. N. Goh: A charting technique for control of low-nonconformity production, Int. J. Qual. Reliab. Man. 4, 53–62 (1987)
T. N. Goh: Statistical monitoring, control of a low defect process, Qual. Reliab. Eng. Int. 7, 497–483 (1991)
M. Xie, T. N. Goh: Improvement detection by control charts for high yield processes, Int. J. Qual. Reliab. Man. 10, 24–31 (1993)
M. Xie, T. N. Goh: The use of probability limits for process control based on geometric distribution, Int. J. Qual. Reliab. Man. 14, 64–73 (1997)
P. D. Bourke: Detecting shift in fraction nonconforming using run-length control chart with 100 % inspection, J. Qual. Technol. 23, 225–238 (1991)
F. C. Kaminsky, R. D. Benneyan, R. D. Davis, R. J. Burke: Statistical control charts based on ageometric distribution, J. Qual. Technol. 24, 63–69 (1992)
E. A. Glushkovsky: On-line G-control chart for attribute data, Qual. Reliab. Eng. Int. 10, 217–227 (1994)
C. P. Quesenberry: Geometric Q charts for high quality processes, J. Qual. Technol. 27, 304–313 (1995)
W. Xie, M. Xie, T. N. Goh: Control charts for processes subject to random shocks, Qual. Reliab. Eng. Int. 11, 355–360 (1995)
T. C. Chang, F. F. Gan: Charting techniques for monitoring a random shock process, Qual. Reliab. Eng. Int. 15, 295–301 (1999)
Z. Wu, S. H. Yeo, H. T. Fan: A comparative study of the CRL-type control charts, Qual. Reliab. Eng. Int. 16, 269–279 (2000)
M. Xie, T. N. Goh, P. Ranjan: Some effective control chart procedures for reliability monitoring, Reliab. Eng. Sys. Saf. 77(2), 143–150 (2002)
L. Y. Chan, M. Xie, T. N. Goh: Two-stage control charts for high yield processes, Int. J. Reliab. Qual. Saf. Eng. 4, 149–165 (1997)
M. Xie, X. S. Lu, T. N. Goh, L. Y. Chan: A quality monitoring, decision-making scheme for automated production processes, Int. J. Qual. Reliab. Man. 16, 148–157 (1999)
H. Ohta, E. Kusukawa, A. Rahim: A CCC-r chart for high-yield processes, Qual. Reliab. Eng. Int. 17, 439–446 (2001)
B. He, M. Xie, T. N. Goh, P. Ranjan: On the estimation error in zero-inflated Poisson model for process control, Int. J. Reliab. Qual. Saf. Eng. 10, 159–169 (2003)
D. Bohning: Zero-inflated Poisson models, C.A.MAN: A tutorial collection of evidence, Biom. J. 40, 833–843 (1998)
P. C. Consul: Generalized Poisson Distributions: Properties and Applications (Marcel Dekker, New York 1989)
L. Y. Chan, M. Xie, T. N. Goh: Cumulative quantity control charts for monitoring production processes, Int. J. Prod. Res. 38(2), 397–408 (2000)
D. N. P. Murthy, M. Xie, R. Jiang: Weibull Models (Wiley, New York 2003)
M. Xie, T. N. Goh, V. Kuralmani: Statistical Models and Control Charts for High Quality Processes (Kluwer Academic, Boston 2002)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag
About this entry
Cite this entry
Xie, M., Goh, T. (2006). Some Statistical Models for the Monitoring of High-Quality Processes. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_16
Download citation
DOI: https://doi.org/10.1007/978-1-84628-288-1_16
Publisher Name: Springer, London
Print ISBN: 978-1-85233-806-0
Online ISBN: 978-1-84628-288-1
eBook Packages: EngineeringEngineering (R0)