Cost benefit analysis of a complex system with correlated failures and repairs

Cost‐benefit analysis of a two‐unit standby system with post‐repair, activation time and correlated failures and repairs

“…By taking the Laplace transform of equations ( 1)-(5) we can obtain A 0 * (s). Using this result, the steady state availability of the system is given by: where: 3) -p 67 (3) ) -p 64 (p 46 (5,2,3) + p 47 (5,2,3) )] 2) )p 64 + p 14 (2) p 60 ] + T 6 [p 14 (2) (p 46 (5,2,3) + p 47 (5,2,3) )…”

“…By taking the Laplace transform of equations ( 7)-(11) we can get B 10 * (s) and the steady-state probability that the assistant repairman is busy is given by: where: 2) ) (1 -p 66 (3) -p 67 (3) ) -p 64 (p 46…”

“…It is assumed that the repair by the assistant repairman is satisfactory with probability p (= 1 -q). It has also been observed in day-to-day life that there exist systems [2,3] in which the repair time of a unit depends on its failure time. Keeping these facts in mind, we present a two-unit cold standby system with post-repair, activation time and correlated failure and repair times.…”

Reliability models based on bivariate exponential distributions

“…Suppose that the failed duplicate unit is non-repairable and replaced with an identical duplicate unit available instantaneously. Under this set-up, bivariate exponential distributions are the most commonly used models for the joint distribution of failure and repair/replacement times (see, for example, [13,17,25,14,26,18,15,16,[19][20][21][22][23][24]46]). If X and Y represent the failure time and the repair/replacement time, respectively, then the sum R = X + Y and the ratio W = X/(X + Y ) will be quantities of immediate interest.…”

“…Apart from being of interest in the statistical issues of reliability, these distributions have attracted many practical applications in reliability problems. Some recent references of applications from reliability journals are: [6,13,17,25,14,26,18,15,16,[19][20][21][22][23][24][44][45][46]. In these applications, one often encounters the problem of determining the sum and the ratio of the components of bivariate exponential distributions.…”