Birnbaum Importance for Linear Consecutive- -out-of- Systems With Sparse


Since Birnbaum importance was introduced in 1969, there have been a lot of than twenty sorts of importance measures therefore way. Among the various measures, Birnbaum importance plays an extraordinarily necessary role because many importance measures are outlined underneath its illumination and have relationships with it. A heap of work has been in serious trouble Birnbaum importance in consecutive-$k$ systems since the systems were introduced. As a result of the issues in practice are increasingly difficult, in 2007, Zhao proposed consecutive-$k$ systems with sparse $d$ , which is an extension of the current consecutive-$k$ systems. In this paper, we tend to study Birnbaum importance for linear consecutive-$k$-out-of-$n$ systems with sparse $d$ . Some equations on Birnbaum importance are proposed. With these equations, the ranking of components in the system on the basis of Birnbaum importance is given; and then some patterns of ranking are presented. Finally, 2 numerical examples are given to illustrate the results obtained in this paper.

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