Abstract
One important application of statistical models in the industry is statistical process control. Many control charts have been developed and used in the industry. They are easy to use but have been developed based on statistical principles. However, for today’s high-quality processes, traditional control-charting techniques are not applicable in many situations. Research has been going on in the last few decades, and new methods have been proposed. This chapter summarizes some of these techniques.
High-quality processes are generally defined as those with very low defective rate or defect-occurrence rate, which is achieved in six sigma environment and in the advanced manufacturing environment. 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-events 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Shewhart, W.A.: Economic Control of Quality of Manufactured Product. ASQ Quality Press (1931)
Xie, M., Goh, T.N.: Some procedures for decision making in controlling high yield processes. Qual. Reliab. Eng. Int. 8(4), 355–360 (1992)
Calvin, T.: Quality control techniques for ``zero defects”. IEEE Trans. Compon. Hybrids Manuf. Technol. 6(3), 323–328 (1983)
Goh, T.N.: A charting technique for control of low-defective production. Int. J. Qual. Reliab. Manage. 4(1), 53–62 (1987)
Goh, T.N.: Statistical monitoring and control of a low defect process. Qual. Reliab. Eng. Int. 7(6), 479–483 (1991)
Xie, M., Goh, T.N.: Improvement detection by control charts for high yield processes. Int. J. Qual. Reliab. Manage. 10(7) (1993)
Xie, M., Goh, T.N.: The use of probability limits for process control based on geometric distribution. Int. J. Qual. Reliab. Manage. 14(1), 64–73 (1997)
Bourke, P.D.: Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection. J. Qual. Technol. 23(3), 225–238 (1991)
Chang, T.C., Gan, F.F.: Charting techniques for monitoring a random shock process. Qual. Reliab. Eng. Int. 15(4), 295–301 (1999)
Glushkovsky, E.A.: On-line g-control chart for attribute data. Qual. Reliab. Eng. Int. 10(3), 217–227 (1994)
Kaminsky, F.C., Benneyan, J.C., Davis, R.D., Burke, R.J.: Statistical control charts based on a geometric distribution. J. Qual. Technol. 24(2), 63–69 (1992)
Quesenberry, C.P.: Geometric Q charts for high quality processes. J. Qual. Technol. 27(4), 304–315 (1995)
Wu, Z., Yeo, S.H., Fan, H.T.: A comparative study of the CRL-type control charts. Qual. Reliab. Eng. Int. 16(4), 269–279 (2000)
Xie, W., Xie, M., Goh, T.N.: Control charts for processes subject to random shocks. Qual. Reliab. Eng. Int. 11(5), 355–360 (1995)
Xie, M., Goh, T.N., Ranjan, P.: Some effective control chart procedures for reliability monitoring. Reliab. Eng. Syst. Saf. 77(2), 143–150 (2002)
Riaz, M., Abbas, N., Mahmood, T.: A communicative property with its industrial applications. Qual. Reliab. Eng. Int. 33(8), 2761–2763 (2017)
Chang, T.C., Gan, F.F.: Cumulative sum charts for high yield processes. Stat. Sin. 11(3), 791–806 (2001)
Yeh, A.B., Mcgrath, R.N., Sembower, M.A., Shen, Q.: EWMA control charts for monitoring high-yield processes based on non-transformed observations. Int. J. Prod. Res. 46(20), 5679–5699 (2008)
Mavroudis, E., Nicolas, F.: EWMA control charts for monitoring high yield processes. Commun. Stat. Theory Methods. 42(20), 3639–3654 (2013)
Chan, L.Y., Xie, M., Goh, T.N.: Two-stage control charts for high yield processes. Int. J. Reliab. Qual. Saf. Eng. 4(2), 149–165 (1997)
Bersimis, S., Koutras, M.V., Maravelakis, P.E.: A compound control chart for monitoring and controlling high quality processes. Eur. J. Oper. Res. 233(3), 595–603 (2014)
Xie, M., Lu, X.S., Goh, T.N., Chan, L.Y.: A quality monitoring and decision-making scheme for automated production processes. Int. J. Qual. Reliab. Manage. 16(2), 148–157 (1999)
Ohta, H., Kusukawa, E., Rahim, A.: A CCC-r chart for high-yield processes. Qual. Reliab. Eng. Int. 17(6), 439–446 (2001)
Albers, W.: The optimal choice of negative binomial charts for monitoring high-quality processes. J. Statist. Plann. Inference. 140(1), 214–225 (2010)
Kotani, T., Kusukawa, E., Ohta, H.: Exponentially weighted moving average chart for high-yield processes. Ind. Eng. Manag. Syst. 4(1), 75–81 (2005)
Kusukawa, E., Kotani, T., Ohta, H.: A synthetic exponentially weighted moving average chart for high-yield processes. Ind. Eng. Manag. Syst. 7(2), 101–112 (2008)
He, B., Xie, M., Goh, T.N., Ranjan, P.: On the estimation error in zero-inflated Poisson model for process control. Int. J. Reliab. Qual. Saf. Eng. 10(02), 159–169 (2003)
Böhning, D.: Zero-inflated Poisson models and CA MAN: a tutorial collection of evidence. Biom. J. 40(7), 833–843 (1998)
Yang, J., Xie, M., Goh, T.N.: Outlier identification and robust parameter estimation in a zero-inflated Poisson model. J. Appl. Stat. 38(2), 421–430 (2011)
Li, D.Y., Yang, J., Li, M., Zhang, X.: Control chart based on middle mean for fine manufacturing process. Adv. Mater. Res. 339, 406–410 (2011)
Rakitzis, A.C., Castagliola, P.: The effect of parameter estimation on the performance of one-sided Shewhart control charts for zero-inflated processes. Commun. Stat. Theory Methods. 45(14), 4194–4214 (2016)
He, S., Huang, W., Woodall, W.H.: CUSUM charts for monitoring a zero-inflated poisson process. Qual. Reliab. Eng. Int. 28(2), 181–192 (2012)
He, S., Li, S., He, Z.: A combination of CUSUM charts for monitoring a zero-inflated Poisson process. Commun. Stat. Simul. Comput. 43(10), 2482–2497 (2014)
Fatahi, A.A., Noorossana, R., Dokouhaki, P., Moghaddam, B.F.: Zero inflated Poisson EWMA control chart for monitoring rare health-related events. J Mech Med Biol. 12(04), 1250065 (2012).
Leong, R.N.F., Tan, D.S.Y.: Some zero inflated Poisson-based combined exponentially weighted moving average control charts for disease surveillance. The Philipp. Stat. 64(2), 17–28 (2015)
Consul, P.C.: Generalized Poisson Distributions: Properties and Applications. Marcel Dekker, New York (1989)
Chen, N., Zhou, S., Chang, T.S., Huang, H.: Attribute control charts using generalized zero-inflated Poisson distribution. Qual. Reliab. Eng. Int. 24(7), 793–806 (2008)
Yang, J., Xie, M., Goh, T.N.: Control limits based on the narrowest confidence interval. Commun. Stat. Theory Methods. 40(12), 2172–2181 (2011)
Mahmood, T., Xie, M.: Models and monitoring of zero-inflated processes: the past and current trends. Qual. Reliab. Eng. Int. 35(8), 2540–2557 (2019).
Chan, L.Y., Xie, M., Goh, T.N.: Cumulative quantity control charts for monitoring production processes. Int. J. Prod. Res. 38(2), 397–408 (2000)
Gan, F.: Design of optimal exponential CUSUM control charts. J. Qual. Technol. 26(2), 109–124 (1994)
Gan, F.: Designs of one-and two-sided exponential EWMA charts. J. Qual. Technol. 30(1), 55–69 (1998)
Gan, F., Chang, T.: Computing average run lengths of exponential EWMA charts. J. Qual. Technol. 32(2), 183–187 (2000)
Liu, J., Xie, M., Goh, T., Sharma, P.: A comparative study of exponential time between events charts. Qual. Technol. Quant. Manag. 3(3), 347–359 (2006)
Borror, C.M., Keats, J.B., Montgomery, D.C.: Robustness of the time between events CUSUM. Int. J. Prod. Res. 41(15), 3435–3444 (2003)
Pehlivan, C., Testik, M.C.: Impact of model misspecification on the exponential EWMA charts: a robustness study when the time-between-events are not exponential. Qual. Reliab. Eng. Int. 26(2), 177–190 (2010)
Ozsan, G., Testik, M.C., Weiß, C.H.: Properties of the exponential EWMA chart with parameter estimation. Qual. Reliab. Eng. Int. 26(6), 555–569 (2010)
Zhang, M., Megahed, F.M., Woodall, W.H.: Exponential CUSUM charts with estimated control limits. Qual. Reliab. Eng. Int. 30(2), 275–286 (2014)
Yen, F.Y., Chong, K.M.B., Ha, L.M.: Synthetic-type control charts for time-between-events monitoring. PLoS One. 8(6), e65440 (2013).
Ali, S.: Time-between-events control charts for an exponentiated class of distributions of the renewal process. Qual. Reliab. Eng. Int. 33(8), 2625–2651 (2017)
Murthy, D.N.P., Xie, M., Jiang, R.: Weibull Models. Wiley, New York (2003)
Xie, M., Goh, T.N., Kuralmani, V.: Statistical Models and Control Charts for High Quality Processes. Kluwer Academic, Boston (2002)
Shafae, M.S., Dickinson, R.M., Woodall, W.H., Camelio, J.A.: Cumulative sum control charts for monitoring Weibull-distributed time between events. Qual. Reliab. Eng. Int. 31(5), 839–849 (2015)
Aslam, M.: A mixed EWMA–CUSUM control chart for Weibull-distributed quality characteristics. Qual. Reliab. Eng. Int. 32(8), 2987–2994 (2016)
Wang, F.K., Bizuneh, B., Abebe, T.H.: A comparison study of control charts for Weibull distributed time between events. Qual. Reliab. Eng. Int. 33(8), 2747–2759 (2017)
Chong, K.M.B., Xie, M.: A study of time-between-events control chart for the monitoring of regularly maintained systems. Qual. Reliab. Eng. Int. 25(7), 805–819 (2009)
Aslam, M., Arif, O.H., Jun, C.-H.: An attribute control chart for a Weibull distribution under accelerated hybrid censoring. PLoS One. 12(3), e0173406 (2017).
Aslam, M., Azam, M., Jun, C.-H.: A HEWMA-CUSUM control chart for the Weibull distribution. Commun. Stat. Theory Methods. 47(24), 5973–5985 (2018)
Sparks, R., Jin, B., Karimi, S., Paris, C., MacIntyre, C.: Real-time monitoring of events applied to syndromic surveillance. Qual. Eng. 31(1), 73–90 (2019)
Megahed, F.M.: Discussion on ``Real-time monitoring of events applied to syndromic surveillance”. Qual. Eng. 31(1), 97–104 (2019)
Wilson, J.D.: Discussion on ``Real-time monitoring of events applied to syndromic surveillance''. Qual. Eng. 31(1), 91--96 (2019)
Wu, Z., Jiao, J., He, Z.: A control scheme for monitoring the frequency and magnitude of an event. Int. J. Prod. Res. 47(11), 2887--2902 (2009)
Wu, Z., Jiao, J., He, Z.: A single control chart for monitoring the frequency and magnitude of an event. Int. J. Prod. Econ. 119(1), 24--33 (2009)
Rahali, D., Castagliola, P., Taleb, H., Khoo, M.B.: Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions. Qual. Eng. 31(2), 240--254 (2019)
Cheng, Y., Mukherjee, A., Xie, M.: Simultaneously monitoring frequency and magnitude of events based on bivariate gamma distribution. J. Stat. Comput. Simul. 87(9), 1723--1741 (2017)
Sanusi, R.A., Mukherjee, A.: A combination of max-type and distance based schemes for simultaneous monitoring of time between events and event magnitudes. Qual. Reliab. Eng. Int. 35(1), 368--384 (2019)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 Springer-Verlag London Ltd., part of Springer Nature
About this chapter
Cite this chapter
Xie, M., Goh, T.N., Mahmood, T. (2023). Statistical Models for Monitoring the High-Quality Processes. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-4471-7503-2_14
Download citation
DOI: https://doi.org/10.1007/978-1-4471-7503-2_14
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-7502-5
Online ISBN: 978-1-4471-7503-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)