Economic analysis for detection of out-of-control of process using 2 of 2 runs rules

This research investigates economic characteristics of 2 of 2 runs rules under the Shewhart control chart scheme. A Markov chain approach is employed in order to calculate the in-control average run length (ARL) and the average length of analysis cycle. States of the process are defined according to the process conditions at sampling time and transition probabilities are derived from the state definitions. A steady state cost function is constructed based on the Lorezen and Vans conditions at sampling time and transition probabilities are derived from the state definitions.