Reliability computation under dynamic stress–strength modeling with cumulative stress and strength degradation

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.

Optimal replacement policy under cumulative damage model and strength degradation with applications

“…The strength of the unit is described by K (t) which is continuous and decreasing in time t. Note that, under the present stress-strength interface, there are two different types of failure modes, either due to strength degradation at or below the existing level of accumulated stress, or due to arrival of a shock resulting in the increased stress exceeding or equaling the strength at that time (See Bhuyan and Dewanji 2017b). Then a unit fails when its strength reduces to zero even if no shock arrives by that time.…”

“…Hence, the strength of a unit may reasonably be described by a deterministic curve which is decreasing in time. Recently, computation and estimation of reliability under such cumulative damage model has been considered by Bhuyan and Dewanji (2017a;2017b).…”

Reliability estimation for momentum wheel bearings considering frictional heat

“…Stress-strength interference (SSI) model has been widely used in the reliability estimation [1,2,25,36]. In SSI model, Stress represents a number of factors promoting the failure while strength represents ability of resisting the failure of products.…”

Software Reliability Based on Renewal Process Modeling for Error Occurrence Due to Each Bug With Periodic Debugging Schedule

“…In this section, we do not make any assumption about the functional form of the renewal distribution f . To find the non-parametric MLE of ν, one needs to maximize the likelihood function (1) with respect to ν and the density function f . Toward this, one notices that the renewal distribution f is not involved in the first factor ν/(ν − M (d) )!…”

“…Toward this, one notices that the renewal distribution f is not involved in the first factor ν/(ν − M (d) )! in (1). Therefore, in order to estimate f for a given ν, the product of all terms, excluding ν!/(ν − M (d) )!, should be considered.…”