Properties and performance of one-sided cumulative count of conforming chart with parameter estimation in high-quality processes

Jing-Er Chiu · Chih‐Hsin Tsai

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

The one-sided cumulative count of conforming (CCC) chart is a useful method to monitor nonconforming fraction in high-quality manufacturing processes. The nonconforming fraction parameter is assumed to be known when implementing a one-sided CCC chart. In this study, we investigated the impact of estimated nonconforming fraction, [pcirc] 0, in a one-sided CCC chart. The run length distribution is derived as well as the conditional probability of a false alarm rate (CFAR), conditional average run length (CARL) and its standard deviation (CSDRL). Simulation results are conducted to evaluate the effect of [pcirc] 0 in a one-sided CCC chart. The results show that values of CFAR, CARL and CSDRL are close to the nominal values for a large sample. The impact of estimation errors was also studied. We find that CFAR decreases for large [pcirc] 0. Thus, a large value of [pcirc] 0 is suggested for fewer false alarms.

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References

1999Research Issues and Ideas in Statistical Process Control 2006Effects of Parameter Estimation on Control Chart Properties: A Literature Review 1997Control Charts Based on Attribute Data: Bibliography and Review 1983Quality Control Techniques for "Zero Defects"1992Statistical Control Charts Based on a Geometric Distribution 2002Statistical Models and Control Charts for High-Quality Processes 2004The Run Length Distribution of the CUSUM with Estimated Parameters 1984Quality control techniques for “Zero Defects”

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