Optimal redundancy allocation problems in engineering systems with dependent component lifetimes

On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes

“…As is shown in the proof of Corollary 1, (3.2) is naturally true for series systems. From the perspective of system structure, Corollary 1 revisits the optimal allocating strategy for series systems, and hence Theorem 1 serves as an essential generalization of the findings due to Jeddi and Doostparast .…”

“…For two components X 1 and X 2 in series and an active redundancy S , (Theorem 2.2) proved that allocating S to the component X 1 leads to a system with stochastically longer lifetime than allocating it to the component X 2 if and only if Also they generalized this result to series systems of n components: it is better to allocate the redundancy to the component i than to the component j if and only if Note that the inequality (3.7) is equivalent to , which is just (3.4) for a series system of two components. Also, the condition (3.8) for series systems of n components is equivalent to (3.4).…”

“…For two components X 1 and X 2 in series and an active redundancy S, [9] (Theorem 2.2) proved that allocating S to the component X 1 leads to a system with stochastically longer lifetime than allocating it to the component X 2 if and only if…”

On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes

“…For series and parallel systems with one redundancy component, Belzunce et al (2011Belzunce et al ( , 2013 investigated the optimal allocation policy under the assumption that the redundancy component lifetime and the base component lifetimes are dependent. Later on, Jeddi and Doostparast (2016) derived some sufficient and necessary conditions guaranteeing the existence of the usual stochastic order on the resultant system lifetime and partially generalized the findings of Belzunce et al (2011). Following the second line, for k-out-of-n systems with dependent component lifetimes, You and Li (2014) and You et al (2016) studied the optimal allocation of active redundancy components with their lifetimes independent of the base component lifetimes.…”

“…Except for Kotz, Lai, and Xie (), Belzunce, Martínez‐Puertas, and Ruiz (), You and Li (), Jeddi and Doostparast () and You, Fang, and Li (), fewer works on redundancy allocation for coherent systems with mutually dependent component lifetimes are found in the literature. Among the references in the literature regarding dependent component lifetimes, one line presumes that the base and redundancy component lifetimes may be dependent, and the other assumes independence between the base component lifetimes and the redundancy component lifetimes.…”