CONSTANT PREDICTIVE VALUE OF AN ALARM

Abstract

One main purpose of statistical surveillance is to detect a change in a process, often expressed as a shift from one level to another. When a sequence of decisions is made, measures, like the number of decisions that have to be taken before an alarm are of interest. In many situations a shift might occur any time after the surveillance was initiated. Prior knowledge of the probability of a change, the incidence, can become crucial when a method is selected and the parameter values of the method are set. The predictive value of an alarm is a measure of performance that takes this information into consideration and is an important tool for evaluating methods. Mostly an alarm is useful only if its predictive value is large. The predictive value of an alarm is the probability that a change has occurred given an alarm. In this paper it is demonstrated that the incidence in the first point has to be relatively high, or the alarm limits very wide, in order to achieve a predictive value greater than, say 0.5. The interpretation of an alarm is difficult to make if the predictive value of an alarm varies with time. For the ordinary Shewhart method and a selection of Moving Average Methods it is demonstrated how the predictive value increases with time if the incidence is constant. The incidence which would give the methods a constant predictive value are determined. The methods are thus demonstrated to give easily interpreted alarms only if the values of the incidence are strongly decreasing with time. Since in most applications a constant incidence is assumed a modification of the ordinary Shewhart method is suggested. With this modification it is possible to obtain a constant predictive value in the whole range of observations or in some interesting interval.