Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Entropy

Abstract

This paper deals with a reliability system hit by three types of shocks ranked as harmless, critical, or extreme, depending on their magnitudes, being below (Formula presented.), between (Formula presented.) and (Formula presented.), and above (Formula presented.), respectively. The system’s failure is caused by a single extreme shock or by a total of N critical shocks. In addition, the system fails under occurrences of M pairs of shocks with lags less than some (Formula presented.) ((Formula presented.) -shocks) in any order. Thus, the system fails when one of the three named cumulative damages occurs first. Thus, it fails due to the competition of the three associated shock processes. We obtain a closed-form joint distribution of the time-to-failure, shock count upon failure, (Formula presented.) -shock count, and cumulative damage to the system on failure, to name a few. In particular, the reliability function directly follows from the marginal distribution of the failure time. In a modified system, we restrict (Formula presented.) -shocks to those with small lags between consecutive harmful shocks. We treat the system as a generalized random walk process and use an embellished variant of discrete operational calculus developed in our earlier work. We demonstrate analytical tractability of our formulas which are also validated, through Monte Carlo simulation. © 2024 by the authors.

DOI

10.3390/e26060444

Publication Date

2024

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