Reliability analysis of repairable and non-repairable systems with common-cause failures

Using Spice Circuit Simulation Program in Reliability Analysis ofRedundant Systems with Non‐Repairable Units and Common‐CauseFailures

“…Also shown in Table I are the results obtained using the Laplace transform method (Eqs. (45) and (46) of [2]). From Table I Po(t)…”

“…(25)-(29) with the aid of, Laplace transforms yields the state probabilities. However, this approach is deeply involved in a sea of algebra [2]. Following the procedure described in the previous section, assuming that Eq.…”

“…In practice most component failures are hardly statistically independent. Thus, common-cause failure, where a single failure event can propagate and cause failure of more than one unit in the system, has attracted the attention of many investigators in the area of system reliability and availability [1][2][3][4][5][6][7][8]. There are several reasons which can lead to common cause failures [5].…”

“…Figure shows the state space diagram of a non-repairable N identical unit parallel system with one identical warm standby [2]. As long as one unit is operating normally, the system is considered in an up-state.…”

“…dPN+3 t) dt --/coPo(t) q-.clP1 (t) + Ac2P2(t) +"" + .cN+IPN+I(t) (10) where (dPn(t)/dt) represents the differentiation of the nth-state probability Pn(t), at time 0, P0(0)= and Pk(0)= 0, for k= 1,2,3,...,N+3. Equations (1)-(10) can be solved using the Laplace transform method [1][2][3][4][5], yielding expressions for the probability, P,(t), that the overall system under consideration is in state n at time for n=0, 1,...,N+3. Alternatively, the steady state probabilities, Pn, n=0, 1,...,N+ 3 can be obtained by setting the derivatives with respect to time, of Eqs.…”