Estimation of Reliability for Stress-Strength Cascade Model

Abstract

The study endeavors to provide statistical inference for a (1 + 1) cascade system for exponential distribution under joint effect of stress-strength attenuation factors. Estimators of reliability function are obtained using Maximum Likelihood Estimator (MLE) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) of the parameters. Asymptotic distribution of the parameters is also obtained. Comparison between estimators is made using data obtained through simulation experiment.

Weibull Reliability Estimation of (3+1) Cascade Model

“…Here , if the active unit 𝑈 1 is a failure then the standby component 𝑈 4 is activated, where 𝑋 4 = m𝑋 1 𝑎𝑛𝑑 𝑌 4 = 𝑘𝑌 1 , if the active unit 𝑈 1 is a failure then the standby component 𝑈 4 is activated , where 𝑋 4 = m𝑋 2 𝑎𝑛𝑑 𝑌 4 = 𝑘𝑌 2 and if the active unit 𝑅 3 is a failure then the standby component 𝑅 4 is activated , where 𝑋 4 = m𝑋 3 𝑎𝑛𝑑 𝑌 4 = 𝑘𝑌 3 Where "k" and "m " denote the stress and strength attenuation factors respectively, such that 0 < 𝑚 < 1 and 𝑘 > 1 Reddy (2016) [15] presents of 𝑅 = 𝑝(𝑋 > 𝑌) by discussing model stressstrength of a cascade , assuming all the parameters are independent and following Weibull stressstrength distribution in one parameter and calculating first four cascade reliability for different stress-strength values. Mutkekar and Munoli (2016) [13], (1+1) exponential distribution cascade model is derived with the common effect of the force and stress reduction factors. Kumar and Vaish (2017) [12], discussed that Gompertz distribution is stress and that strength is power distribution parameters.…”

Weibull reliability estimation for (2+1) cascade model

“…Singh (2013) [4] considered system reliability of ncascade system with strength following exponential distribution and stress following normal distribution. Mutkekar and Munoli (2016) [7] study endeavors to provide the statistical inference for a (1+1) the cascade system for exponential distribution under common effect of strength-stress attenuation factors. The main aim of this paper is to discuss derivation of mathematical formula of the reliability in special (2+1) Cascade model with strength-stress for weibull distribution by using ML, MO, LS and WLS methods and comparison the results of estimation methods by using the mean square error that will get from the simulation study.…”

Cascade and System Reliability for Exponential Distributions

“…The n-cascade system survive with loss of m components by k number of attacks [7]. [8] studied about estimation of reliability for stress-strength cascade model by comparison between estimators made using data obtained through simulation experiment [8,9,10].…”