DISTRIBUTION OF RUNS IN A TWO-STAGE PROCESS MONITORING MODEL

Abstract

In statistical process control, procedures similar to double sampling technique can be used to incorporate information from two observations. This leads to the study of the distribution of runs. In this paper, a run is defined as the number of nonconformities observed until an alarm when the two stage procedure is used. The exact distribution of run and the average quantity inspected between alarms are derived and we also obtain some analytical results concerning the expected value of some interesting related quantities.

Keywords:

• Cumulative quantity
• Stastistical process control
• Two-stage control chart
• Nonconformity
• Run distribution

ACKNOWLEDGMENTS

Part of the research was done while the first author was visiting the University of Hong Kong as a William Mong Research Fellow in 1998. The third author's research is partly funded by a grant RP3981625 from National University of Singapore. We also wish to thank the referee for his helpful comments and suggestions.