On random weighted coherent systems based on a new structure-based performance measure

The performance level of a random weighted r-out-of-n system is measured by its total capacity. However, this measure is not meaningful for an arbitrary coherent structure as it does not involve the structure of the system. To overcome this drawback, we introduce here a new notion of performance measure (namely, the structural capacity) and then define three different notions of random weighted coherent systems, namely, Type-I, Type-II and Type-III systems. We then derive explicit formulas for computing the reliabilities of these systems. We further give a signature-based reliability representation for these systems. Further, we derive the Birnbaum marginal and joint reliability importance measures for the components of these systems and subsequently provide an algorithm for computing the same. Then, we study several ordering results based on these importance measures. For the Type-III random weighted coherent system, we introduce a new structure-based weighted importance measure and provide an algorithm for its evaluation. The developed results are illustrated through several numerical examples. Finally, we carry out the reliability estimation for a random weighted coherent system using two different simulated data sets.