• International Journal of Reliability and Applications
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• v.17 no.1
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• pp.51-63
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• 2016

Stress function of ball bearing is function of multiple stochastic factors and this system is so complex that analytical expression for reliability is difficult to obtain. To address this pressing problem, in this article, we have made an attempt to approximate system reliability of this important item based on reliability bounds under the stress strength setup. This article also provides level of error of this item. Numerical analysis has been adopted to show the closeness between the upper and lower bounds of this item.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.631-639
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• 2003

Bayes estimates of reliability for the stress-strength system are obtained with respect to LINEX loss function. A reference prior distribution of the reliability is derived and Bayes estimates of the reliability are also obtained. These Bayes estimates are compared with corresponding estimates under squared-error loss function.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.83-98
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• 2017

Stress-strength reliability problems arise frequently in applied statistics and related fields. In the context of reliability, the stress-strength model describes the life of a component, which has a random strength X and is subjected to random stress Y. The component fails at the instant that the stress applied to it exceeds the strength and the component will function satisfactorily whenever X > Y. The problem of estimation the reliability parameter in a stress-strength model R = P[Y < X], when X and Y are two independent two-parameter Lindley random variables is considered in this paper. The maximum likelihood estimator (MLE) and Bayes estimator of R are obtained. Also, different confidence intervals of R are obtained. Simulation study is performed to compare the different proposed estimation methods. Example in real data is used as practical application of the proposed procedure.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.113-118
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• 2003

In this paper, We assume that strengths of two components system follow a bivariate pareto distribution. And these two components are subjected to a common stress which is independent of the strength of the components. We obtain maximum likelihood estimator(MLE) for the system reliability from stress-strength relationship. Also we derive asymptotic properties of the MLE and present a numerical study.

• International Journal of Reliability and Applications
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• v.13 no.1
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• pp.37-47
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• 2012

In this article we attempted reliability analysis of a component under the stress-strength pattern with both classical as well as Bayesian techniques. The main focus is made to develop the theory for dealing the reliability problems in various circumstances for bivariate environmental set up in context of Bayesian paradigm. A stress-strength based model describes the life of a component which has strength (Y) and is subjected to stress(X). We develop the Bayes and moment estimators of reliability of a component for each of the three possible conditions, under the assumption that the two stresses (i.e. $X_1$ and $X_2$) on a component are dependent and follow a Bivariate exponential (BVE) of Marshall-Olkin distribution, the strength of a component (Y) following exponential distribution is independent of the stresses. The simulation study is performed with Markov Chain Monte Carlo technique via Gibbs sampler to obtain the estimates of Bayes estimators of reliability, are compared with moment estimators of reliabilities on the basis of absolute biases.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.111-118
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• 1999

We treat the problem of estimating reliability R(t) = P[Y(t) < X(t)] in the time dependent strength-stress model in which a unit of strength X(t) is subjected to environmental stress Y(t) at time t. In this paper two nonparametric approaches to estimate of R(t) are analyzed and compared with parametric method by simulation.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.4
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• pp.537-547
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• 2015

A Monte Carlo (MC) simulation was conducted to predict the reliability of a newly developed pyrotechnic pin puller. The reliability model is based on the stress-strength interference model that states that failure occurs if the stress exceeds the strength. In this study, the stress is considered to be the energy consumed by movement of a pin shaft, and the strength is considered to be the energy generated by pyrotechnic combustion for driving the pin shaft. Failure of the pin puller can thus be defined as the consumed energy being greater than the generated energy. These energies were calculated using a performance model formulated in the previous study of the present authors. The MC method was used to synthesize the probability densities of the two energies and evaluate the reliability of the pin puller. From a probabilistic perspective, the calculated reliability was compared to a deterministic safety factor. A sensitivity analysis was also conducted to determine which design parameters most affect the reliability.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.277-284
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• 1998

The reliability and an estimate for it are derived for series-parallel and parallel-deries stress-strength model under assumption that all components are subjected to a common stress. We also obtain the asymptotic normal distribution of the estimate.

• Journal of Applied Reliability
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• v.11 no.4
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• pp.319-330
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• 2011

We consider the stress-strength model in which a unit of strength $T_2$ is subjected to environmental stress $T_1$. An important measure considered in stress-strength model is the reliability parameter R=P($T_2$ > $T_1$). The greater the value of R is, the more reliable is the unit to perform its specified task. In this article, we consider the situations in which $T_1$ and $T_2$ are both independent and dependent, and have certain bivariate distributions as their joint distributions. To study the effect of dependency on R, we investigate several bivariate distributions of $T_1$ and $T_2$ and compare the values of R for these distributions. Numerical comparisons are presented depending on the parameter values as well.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.263-273
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• 1998

In this paper, we consider some approximate testings for the reliability of the stress-strength model when the stress X and strength Y each depends linearly on some explanatory variables z and w, respectively. We construct a bootstrap procedure for testing for various values of the reliability and compare the power of the bootstrap test with the test based on Mann-Whitney type estimator by Park et.al.(1996) for small and moderate sample size.