Degradation Analysis of Probabilistic Parallel Choice Systems

TL;DR

This paper introduces probabilistic parallel choice operators to analyze system degradation, deriving generalized formulas for system parameters like MTTF, MTBF, and SFR using a generalized exponential distribution.

Contribution

It presents a novel probabilistic approach to model parallel paths in systems, enabling more accurate degradation analysis and parameter estimation.

Findings

Derived new formulas for MTTF, MTBF, and SFR.

Utilized a generalized exponential distribution for component lifetimes.

Provided a comprehensive framework for probabilistic system degradation analysis.

Abstract

Degradation analysis is used to analyze the useful lifetimes of systems, their failure rates, and various other system parameters like mean time to failure (MTTF), mean time between failures (MTBF), and the system failure rate (SFR). In many systems, certain possible parallel paths of execution that have greater chances of success are preferred over others. Thus we introduce here the concept of probabilistic parallel choice. We use binary and $n$-ary probabilistic choice operators in describing the selections of parallel paths. These binary and $n$-ary probabilistic choice operators are considered so as to represent the complete system (described as a series-parallel system) in terms of the probabilities of selection of parallel paths and their relevant parameters. Our approach allows us to derive new and generalized formulae for system parameters like MTTF, MTBF, and SFR. We use a generalized exponential distribution, allowing distinct installation times for individual components, and use this model to derive expressions for such system parameters.