Mathematical modeling and investigation of sensitivity of a multifaceted system

Abstract

The objective of this paper is to develop a mathematical model corresponding to a highly
complex engineering system and to study about the level of uncertainty. Here author has
considered a complicated system having three subsystems A, B and C connected in sequence.
A, B, and C are called subsystems. A is the controller unit, subsystem B has m similar units
arranged in sequence. Further, subsystem C is a very complicated subsystem having n units
and it will be in degraded state if load of any of its failed units becomes three. Subsystem C
consists of two units namely regular and key having loads 1 and 2 respectively. The repair
facility will repair the failed units in two situations, firstly if the system is in complete
breakdown state and secondly when the system is working but three consecutive failures have
occurred. Also whenever two key units fail, two repair facilities will repair the failed
components at the same time with dissimilar rates. The model has been solved with the help of
SVT, Laplace transformation and copula.