A comparison of two major methods to design alarm deadbands for IID process variables

Deadbands are embedded functions of transducers frequently exploited to remove false alarms. In existing literature, there are two major methods to design alarm deadbands, either based on the estimated probability density function (PDF) of process variables or the estimated PDF of maximum amplitude deviations (MADs). The former method only applies to independently and identically distributed (IID) process variables, while the latter method does not have this restriction. A natural question is: which method should be used for IID process variables? The objective of this paper is to compare the two major methods to design alarm deadbands for IID process variables. In particular, two technical problems are addressed for the comparison. First, theoretical values of false alarm ratios (FARs) for both methods are derived. Second, confidence intervals of FARs for both methods are obtained. Based on these results, it is concluded that the former method performs better when data samples are limited, whereas the two methods are with similar performance when data samples are sufficient. Numerical and industrial examples are provided to support and illustrate the obtained results and conclusion.