Weibull reliability estimation for (2+1) cascade model

Abstract

<jats:p>In this paper endeavors to submit reliability (R) of a special (2+1) stress-strength Cascade model for Weibull distribution. Expressions for the model reliability are obtained when the strength and stress are weibull random variables with known shape and unknown scale parameters. Four different methods (ML, Mo, LS and WLS) are used to estimate the reliability and make a comparison between them in simulation study with program made by MATLAB 2016 using criterion MSE, where it found that the best estimator between the four estimators was ML.</jats:p>

Doubly Type II Censoring of Two Stress-Strength System Reliability Estimation for Generalized Exponential-Poisson Distribution

“…Let 𝑋~𝐺𝐸𝑃(𝛼, 𝜆, 𝜃) be strength random variable and 𝑌 1 ~𝐺𝐸𝑃(𝛽 1 , 𝜆, 𝜃), 𝑌 2 ~𝐺𝐸𝑃(𝛽 2 , 𝜆, 𝜃) and 𝑌 3 ~𝐺𝐸𝑃(𝛽 3 , 𝜆, 𝜃)are the stresses random variables, then the reliability can be obtained as follows [6]:…”

Estimating Reliability for Frechet (3+1) Cascade Model

“…Khaleel [9] found the reliability of a model of one component that has strength and is subjected to four stresses. Khaleel and Karam [12,14] derived the reliability function of the cascade model for two primary components and a backup component. Doloi and Gogoi [15] Find the reliability function of a model consisting of The cascade model in the form 3+1 consists of the components( A 1 , A 2 , A 3 and A 4 ) where the components ( A 1 , A 2 and A 3 ) are the basic units and necessary for the model to work, while component (A 4 ) is a redundancy component in an active-standby state and is activated in the event of failure of one of the basic components ( A 1 , A 2 and A 3 ) and replaces the failed component, so the model continues to work and the stress on the component t (A 4 ) increases by (k) and its strength by (m), where (k and m) are attenuation factors.…”

Weibull Reliability Estimation of (3+1) Cascade Model

“…When a system unit fails, it is replaced by a standby unit and the stress changed 𝑘 Times the previous stress. In a previous study Karam and presented a study of (2+1) Cascade model, which the model consists of two main components and one redundancy standby [9]. In this paper, we assumed that the (3+1) of Cascade with ( 𝑈 1 , 𝑈 2 , 𝑈 3 𝑎𝑛𝑑 𝑈 4 ) Units ,in which three units 𝑈 1 , 𝑈 2 , 𝑈 3 𝑎𝑛𝑑 𝑈 4 are work and the unit 𝑈 4 is a standby unit .…”

“…Kumar and Vaish (2017) [12], discussed that Gompertz distribution is stress and that strength is power distribution parameters. Karam and Khaleel (2018) [9] derived a special (2+1) stress-strength reliability cascade model for the distribution of Weibull. Khaleel and Karam (2019) [10] discussed the reliability of the (2+1) cascade inverse distribution Weibull model, reliability can be found when reverse Weibull random variables with unknown parameters scale and known shape parameter are distributed with strength-stress and used six different estimations mothed to estimate reliability.…”