Multistate Coherent Systems

Abstract

The present report represents an entry MULTISTATE COHERENT SYSTEMS which is to appear in the Encyclopedia of Statistical Sciences, Vol. 5 published by Wiley in 1984. It gives a summary of the present state of the art of multistate theory also aiming to standardize the terminology.

A multi-state warm standby system with preventive maintenance, loss of units and an indeterminate multiple number of repairpersons

“…This concept was first discussed by Murchland (1975), and the question of MSS reliability has since been developed extensively. Important early achievements (up to the mid-1980s) have been reviewed by Natvig (1985) and by El-Neweihi and Proschan (1984), and Lisnianski et al (2010) performed a comprehensive analysis of MSS. These systems can also be studied using Markov and semi-Markov models , Li et al (2017), Peng et al (2017)).…”

Statistical Inference for Multi-state Systems: The Weibull Case

“…Although the resulting estimator is of some interest, the estimation of the individual scale parameters a ij for each {i, j} is of greater importance. In order to estimate individual scale parameters, an additional expression must be obtained, in the following way, (8) which, in turn, gives…”

“…The binary system is the simplest case of a MSS having only two distinctive states (perfect functioning and complete failure). The basic concepts of MSS reliability were introduced in the 70's and the 80's (Murchland, 1975;Natvig, 1982 and1985). Readers interested in the history of MSS reliability theory are referred to the work of Lisnianski and Levitin (2003) and Natvig (2011).…”