Multivariate stress–strength reliability model and its evaluation for coherent structures

Eryılmaz, Serkan

doi:10.1016/j.jmva.2008.01.015

Cited by 45 publications

(13 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Literature review reveals the importance of the estimation of Stress-strength reliability under various lifetime distributions. In this regard mention may be made to Kotz et al (2003), Baklizi (2008aBaklizi ( , 2008b, Eryilmaz (2008aEryilmaz ( , 2008bEryilmaz ( , 2010Eryilmaz ( , 2011, Krishnamoorthy et al (2007Krishnamoorthy et al ( , 2009Krishnamoorthy et al ( , 2010, Krishnamoorthy and Lin (2010), Kundu and Raqab (2009), Rezaei et al (2010). Recently, Rao (2012Rao ( , 2013) studied the estimation of reliability in a multicomponent stress-strength model.…”

Section: Introductionmentioning

confidence: 99%

Estimation of R3 = Pr(Y3 > max(Y1, Y2)) for Exponential Distribution

Kundu¹

2017

JAS

View full text Add to dashboard Cite

This paper deals with the estimation of the reliability function R3 = Pr(Y3 > max (Y1, Y2)), when the random variables Y1, Y2 and Y3 are independent exponential with respective unknown location parameters µ1, µ2 and µ3. Here we have derived several estimators of R3 which includes uniformly minimum variance unbiased estimator (UMVUE), Bayes estimator (BE) and generalized Bayes estimator(GBE). Moreover, we have compared these estimators based on their risks under different loss functions.

show abstract

Section: Introductionmentioning

confidence: 99%

Estimation of R3 = Pr(Y3 > max(Y1, Y2)) for Exponential Distribution

Kundu¹

2017

JAS

View full text Add to dashboard Cite

show abstract

“…Eryilmaz anḋ Işçioǧlu(2011) deviated from binary level stress-strength models and proposed the following multistate level stress-strength model given in (1.1) below. See also Eryilmaz (2008aEryilmaz ( , 2008b.…”

Section: Introductionmentioning

confidence: 99%

EM Algorithm and Positive Quadrant Dependence in the context of Multi-State Stress-Strength Model

Sabnis¹,

Jain²,

Verma³

2016

JSTA

View full text Add to dashboard Cite

This research article is related to a multi-state stress-strength model proposed by Eryilmaz andİşçioǧlu (2011). It deals with (i) demonstration of the use of EM algorithm for the estimation of parameters of distributions of random variables representing strength and two stress levels. The numerical results are illustrated using exponential distribution for each of the random variables under consideration, and (ii) comparison of results under the assumption of the random variables representing two stress levels being independent vis-à-vis they being positively quadrant dependent (PQD). The corresponding numerical results are based on Farlie-GumbelMorgenstern PQD distribution having non-identical exponential distributions as marginal distributions, and the distribution of strength variable is also an exponential distribution with a different parameter. As far as the EM algorithm related exercise is concerned, the numerical results, by and large, show that the EM algorithm, the one which makes clever use of data by pretending presence of missing observations, provides efficient estimators of the parameters than those provided by direct use of maximum likelihood (ML) estimators. For the latter exercise related to the PQD property, the numerical results highlight the fact that not only it is incorrect to assume two random variables representing two stress levels to be independent when in fact they are dependent, but the degree of dependence also can not be ignored.

show abstract

“…Extensive works have been done for the reliability of the component and its estimation under different choices for stress and strength distributions ( [1], [2], [4], [7], [9], [10], [13], [17], [18] In a multistate system, state distribution is often used to indicate the distribution of each component in different state. The performance of the component is represented in terms of its state distribution.…”

Section: Introductionmentioning

confidence: 99%

Erlang Strength Model for Exponential Effects

Gökdere

Gürcan

2015

Open Physics

View full text Add to dashboard Cite

All technical systems have been designed to perform their intended tasks in a specific ambient. Some systems can perform their tasks in a variety of distinctive levels. A system that can have a finite number of performance rates is called a multi-state system. Generally multi-state system is consisted of components that they also can be multi-state. The performance rates of components constituting a system can also vary as a result of their deterioration or in consequence of variable environmental conditions. Components failures can lead to the degradation of the entire multi-state system performance. The performance rates of the components can range from perfect functioning up to complete failure. The quality of the system is completely determined by components. In this article, a possible state for the single component system, where component is subject to two stresses, is considered under stress-strength model which makes the component multi-state. The probabilities of component are studied when strength of the component is Erlang random variables and the stresses are independent exponential random variables. Also, the probabilities of component are considered when the stresses are dependent exponential random variables.

show abstract

Multivariate stress–strength reliability model and its evaluation for coherent structures

Cited by 45 publications

References 8 publications

Estimation of<i> R</i><sub><i>3</i></sub> = Pr(<i>Y<sub>3</sub> </i>> max(<i>Y<sub>1</sub>, Y<sub>2</sub></i>)) for Exponential Distribution

Estimation of<i> R</i><sub><i>3</i></sub> = Pr(<i>Y<sub>3</sub> </i>> max(<i>Y<sub>1</sub>, Y<sub>2</sub></i>)) for Exponential Distribution

EM Algorithm and Positive Quadrant Dependence in the context of Multi-State Stress-Strength Model

Erlang Strength Model for Exponential Effects

Contact Info

Product

Resources

About