Design of delay timers based on estimated probability mass functions of alarm durations

Delay timers are widely used in practice to remove nuisance alarms. This paper proposes a method to design delay timers based on probability mass functions (PMFs) of alarm durations. The main rationale is that all nuisance alarms with alarm durations less than m samples are removed by a m-sample delay timer. The proposed method is composed of three steps. First, distribution change points of alarm durations are detected to separate consecutive samples of alarm durations into segments. Second, a reliable PMF estimate of alarm durations is obtained via the Bayesian estimation for each segment. Third, an optimal value of m is designed based on the estimated PMFs as the smallest one to make a designing index, being formulated as the percentage of false alarm occurrences to be unremoved, less than an upper bound. Contemporary methods are confined to analog process variables, which are usually assumed to be independently and identically distributed (IID) and whose probability density functions are exploited to design delay timers. In contrast, the proposed method does not require the IID assumption, and is equally applicable to both analog and digital process variables. Numerical and industrial examples are provided to support the proposed method.