Average run lengths and run length probability distributions for cuscore charts to control normal mean

Cuscore charts have recently been proposed as a statistical process monitoring tool designed to cope with situations in which special kinds of signals are feared a priori because they are known to affect the particular system being monitored. This paper provides algorithms to compute average run lengths and corresponding run length probability distributions for cuscore charts to control a process mean. Paralleling standard cusum techniques, a handicap may be used to define the cuscore statistic. Three schemes are described depending on whether or not the signals and handicap are reinitialized every time the cuscore statistic reaches its zero limit. Hypothetical situations in which the signal that is being searched for might be different from the true signal may be easily dealt with by the algorithms. Similarly, although the handicap should usually be chosen proportional to the signal to be detected to improve chart performance, the algorithms may easily cope with more general handicaps.