Reliability computation under dynamic stress–strength modeling with cumulative stress and strength degradation. Issue 4 (21st April 2017)

• Record Type: Journal Article
• Authors: Bhuyan, Prajamitra; Dewanji, Anup
• Is Part Of: Communications in statistics. Volume 46:Issue 4(2017)
• Page Start: 2701
• Page End: 2713
• Publication Date: 2017-04-21
• Subjects: Compound distribution -- Gamma bridge sampling -- Gamma process -- Inversion theorem -- Point process -- Random strength degradation -- Simulation method; 62 Statistics, 62Nxx Survival analysis and censored data; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2015.1057288
• Languages: English
• ISSNs: 0361-0918

Abstract

ABSTRACT: Reliability function is defined under suitable assumptions for dynamic stress–strength scenarios where strength degrades and stress accumulates over time. Methods for numerical evaluation of reliability are suggested under deterministic strength degradation and cumulative damage due to shocks arriving according to a point process, in particular a Poisson process, using simulation method and inversion theorem. These methods are specifically useful in the scenarios where damage distributions do not possess closure property under convolution. The method is also extended for non-identical, dependent damage distributions as well as for random strength degradation. Results from inversion method is compared with known approximate methods and also verified by simulation. As it turns out, the simulation method seems to have an edge in terms of computational burden and has much wider domain of applicability.