Fk. Hwang et D. Trietsch, A SIMPLE RELATION BETWEEN THE PATTERN PROBABILITY AND THE RATE OF FALSE SIGNALS IN CONTROL CHARTS, Probability in the engineering and informational sciences, 10(3), 1996, pp. 315-323
Citations number
12
Categorie Soggetti
Operatione Research & Management Science","Engineering, Industrial","Statistic & Probability","Operatione Research & Management Science
A special pattern of consecutive points on a control chart often sugge
sts that the process is out of control due to a special cause. Usually
, the probability of such a pattern is not difficult to calculate, but
its relation to the rate of a false signal in a control chart is uncl
ear. In this paper we give such a relation for a wide class of pattern
s that includes six of the eight patterns of special cause discussed i
n the AT&T Statistical Qualify Control Handbook (1958). We derive a su
rprisingly simple formula for the rate of a false signal in terms of t
he pattern probability and use this result to improve on the test prop
osed in the handbook. We also use this formula to give a simple proof
of a result of Wolfowitz (1944, Annals of Mathematical Statistics 15:
163-172) and Olmstead (1945, Annals of Mathematical Statistics 17: 24-
33) on the monotone sequence. Finally, we give an approximation of the
rate of a false signal for another wide class of patterns that covers
the two remaining patterns of special cause in the AT&T handbook.