Signal Probabilities of Runs Rules Supplementing a Shewhart Control Chart
Communication in Statistics: Simulation and Computation
Supplementary runs rules have often been suggested for use with Shewhart control charts. For a given set of runs rules supplementing a control chart, a method is given for calculating the probability any subset of these rules will cause the out-of-control signal. A Markov chain approach is used to represent the chart. Some closed form expressions are given.
Champ, Charles W., William H. Woodall.
"Signal Probabilities of Runs Rules Supplementing a Shewhart Control Chart."
Communication in Statistics: Simulation and Computation, 26 (4): 1347-1360.