STOCHASTIC ANALYSIS WITH OPERATIONAL CALCULUS IN RELIABILITY
No Thumbnail Available
Date
2025-05-05
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Saudi Digital Library
Abstract
Our dissertation models several reliability systems subject to occasional random shocks of random magnitudes W1,W2,..occurring at times tau0, tau2,..In Model 1, the underlying system becomes inoperational if it wears out due to aging specified by a monotone increasing continuous function Delta identifying system's wear at any time t>=0 . The system is deemed inoperational if delta crosses a sustainability threshold at some moment T=(delta )^-1(D). The precise time T is difficult to identify making the realistic failure time randomly delayed and thus identified at some opportune observation epoch. The system can also fail due to damages by external shocks, some of which are harmless and some other - critical categorized through their magnitudes relative to a specified threshold H1 . The kth shock is harmless if Wk< =H1and critical if Wk >H1 . It takes a total of N critical shocks to knock the system down. In a nutshell, the system fails if it is worn out assessed at some random observation point or if it is hit by a total of N critical shocks whichever of the two events comes first.
In Model 2, we introduce four types of shocks that land at the system: again harmless and critical (as in Model 1) and additionally extreme and delta-shocks. The kth shock is extreme if Wk>H2 where H1
In Model 3, we exclude harmless shocks from those we deemed delta . Namely, a shock can only be delta when it is critical or extreme and when the previous critical shock is not extreme and lags within an interval of delta-length. In this model we had to restructure the stream of shocks by dropping those defined as harmless and study the system on a conditional probability space. In all three models we obtain closed-form joint distributions of the time-to-failure shock count upon failure, delta-shock count, and cumulative damage to the system on failure, among other less significant characteristics. In particular, the reliability function (a quintessential merit in reliability modeling) directly followed from the marginal distribution of the failure time. We treated the systems as generalized random walk processes and use embellished variants of discrete operational calculus. We demonstrate analytical tractability of our formulas through various examples and special cases. The accuracy has also been validated through Monte Carlo simulation.
Description
Keywords
Competing Failure Processes Extreme Shocks N-Critical Shocks System Multiple -Shocks Random Walk Fluctuation Theory Discrete Operational Calculus Time To Failure Pre Failure Time Reliability Function Closed Form System Degradation Critical Shocks Fatal Shocks Marked Point Process Position Dependent Marking Continuous Operational Calculus Laplace-Carson transform
Citation
Al-Jahani, Hend Hamdan, "STOCHASTIC ANALYSIS WITH OPERATIONAL CALCULUS IN RELIABILITY" (2025). Theses and Dissertations. 1567. https://repository.fit.edu/etd/1567