A combination of max‐type and distance based schemes for simultaneous monitoring of time between events and event magnitudes. (29th October 2018) - Sanusi, Ridwan A.; Mukherjee, Amitava
Abstract: Traditionally, two isolated sequential stopping rules are employed for monitoring the time of occurrence of an event ( T ) and the magnitude of an event ( X ). Recently, several researchers recommend monitoring T and X together using some unified approach. A unified approach based on combinations of two statistics, one for monitoring T and the other for X, is often more efficient. Likewise, a new approach of simultaneous monitoring of location and scale parameters of a process, combining a max and a distance based statistics, is recently introduced in literature. Motivated by such emerging concepts, we design a new scheme combining a Max‐type and a Distance‐type schemes, referred to as the MT scheme, to monitor T and X simultaneously and efficiently. It retains the advantages of both the Max‐type and the Distance‐type schemes for joint inference. The proposed scheme is very competent in detecting a shift in the process distribution of T or X or both. Moreover, it is computationally simpler. It has nice exact expressions for design parameters. Therefore, it is easier to implement. It has a distinct advantage over its traditional counterparts in detecting moderate to large shifts. Finally, we illustrate the implementation of the proposed scheme with a real dataset of damage caused by outbreak of fire disaster.