一类多状态连续n中取k(G)系统的可靠性计算

Reliability calculation for a kind of multi-state consecutive k-out-of-n: G system

为了计算多状态连续n中取k(G)系统的可靠性,引入4个定理,将满足引理的多状态系统转换为二元状态系统。分别推导了多状态线形连续k/n(G)系统和环形连续k/n(G)系统的可靠性计算公式。证明了固定k值增加一个新部件,若部件可靠性独立同分布,线形和环形系统可靠性均增加;若部件可靠性独立但不同分布,环形系统存在一个极值,新增加部件可靠性大于这个极值时得到的新系统可靠性增加,反之系统可靠性下降。

Multi-state consecutive k-out-of-n： G system is converted into a binary system by four lemmas in order to evaluate its reliability. Formulas of linear/circular multi-state consecutive k-out-of-n：a system are proposed and deduced. It is proved that, when a new component is added to a system with any fixed k, if all components are independent to each other and identically distributed, the reliability of linear and circular consecutive system will increase; if components are independent to each other but is a threshold value in the circular system, the reliability bility of the newly added component is greater than that of of this new circular the threshold value, not identically distributed, there system will increase if the reliaotherwise the reliability will decrease.