• Communications for Statistical Applications and Methods
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• v.31 no.5
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• pp.497-519
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• 2024

In reliability analysis, the probability P(Y < X) is significant because it denotes availability and dependability in a stress-strength model where Y and X are the stress and strength variables, respectively. In reliability theory, the inverse Lomax distribution is a well-established lifetime model, and the literature is developing inference techniques for its reliability attributes. In this article, we are interested in estimating the stress-strength reliability R = P(Y < X), where X and Y have an unknown common scale parameter and follow the inverse Lomax distribution. Using Bayesian and non-Bayesian approaches, we discuss this issue when both stress and strength are expressed in terms of lower record values. The parametric bootstrapping techniques of R are taken into consideration. The stress-strength reliability estimator is investigated using uniform and gamma priors with several loss functions. Based on the proposed loss functions, the reliability R is estimated using Bayesian analyses with Gibbs and Metropolis-Hasting samplers. Monte Carlo simulation studies and real-data-based examples are also performed to analyze the behavior of the proposed estimators. We analyze electrical insulating fluids, particularly those used in transformers, for data sets using the stress-strength model. In conclusion, as expected, the study's results showed that the mean squared error values decreased as the record number increased. In most cases, Bayesian estimates under the precautionary loss function are more suitable in terms of simulation conclusions than other specified loss functions.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04b
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• pp.447-454
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• 1998

The main object of the study is that axial force-moment relationships for high strength concrete structures using reliability theory(Linear statstical method, Monte Carlo Simulation) including probability conception. And mean stress factors and centroid factors proposed to high strength concrete structures using reliability theory(Linear statstical method, Monte Carlo Simulation). Finally, The established experimental data for axial force-moment relationships are compared to the analytical data(data for Linear statstical method and Monte Carlo Simulation) for axial force-moment relationships in this analytical method.

• Proceedings of the Korea Concrete Institute Conference
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• 1997.10a
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• pp.500-506
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• 1997

The main object of the study is that axial force-moment relationships for high strength concrete structures using reliability theory probability conception. And mean stress factors and centroid factors proposed to high strength concrete structures using reliability theory. Finally, the established experimental data for axial force-moment relationships are compared to the analytical data for the axial force-moment relationships in this analytical method.

• 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 Aerospace System Engineering
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• v.15 no.2
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• pp.16-25
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• 2021

Reliability of fatigue strength on Aircraft Composites(GFRP) Structures was assessed in this paper. Fatigue strength of GFRP was used through the existing fatigue test data with Monte Carlo method. The S_a-N_f curve of composites fatigue strength was assumed as normal distribution and reliability was analyzed using SSIT model. Fatigue stress was designed IAW ASTM F3114-15 with special safety factor of S_sf=1.2~2.0. Reliability was calculated by analytic method and FORM. Sensitivity for the effect of mean and standard deviation of fatigue strength as well as fatigue stability was evaluated. This result can be usefully applied to reliability and fatigue design for composite structures of light weight aircraft.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.2
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• pp.223-230
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• 2012

The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.407-416
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• 1997

Suppose that { $X_{i}$ } is a stationary AR(1) process and { $Y_{j}$ } is an ARX process with { $X_{i}$ } as exogeneous variables. Let $Y_{j}$ $^{*}$ be the stochastic process which is the sum of $Y_{j}$ and a nonstochastic trend. In this paper we consider the problem of estimating the conditional probability that $Y_{{n+1}}$$^{*}$ is bigger than $X_{{n+1}}$, given $X_{1}$, $Y_{1}$$^{*}$,..., $X_{n}$ , $Y_{n}$ $^{*}$. As an estimator for the tolerance probability, an Mann-Whitney statistic based on least squares residuars is suggested. It is shown that the deviations between the estimator and true probability are stochatically bounded with $n^{{-1}$2}/ order. The result may be applied to the stress-strength reliability theory when the stress and strength variables violate the classical iid assumption.umption.n.

• Proceedings of the Korea Concrete Institute Conference
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• 1995.04a
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• pp.231-236
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• 1995

The object of this thesis is an analytical study on flexural deformation of high strength concrete structures using reliability theory. Using the established experimental data that have been presented in various documents the stress-strain relationship curves of high strength(500kgf/$\textrm{cm}^2$)models are proposed. Based on both methods of logarithm regression analysis and multiple regression analysis adopted in order to establish the relationships between design parameters, response random variables and flexural deformation analyzed using Monte Carlo simulation and Simpson composite formula. Additional random variables are introduced to incorporate both the confidence in the analytical accuracy of engineering mechanics associated with structural response quantities and the uncertainty in the construction quality control. The result is expected to accomodate other important design parameter of high strength concrete design in treating reliability theory that practicing engineers, structural engineering often face.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.475-480
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• 1997

It is common to assum identical allowable safety factors in static strength, defined by mean stress and in fatigue, defined by stress amplitude. Under the load with asymmetrical cycles the safety factor is not the same. In this paper, with the consideration of unequal allowable safety factors a general method for estimating fatigue reliability of a machine element under a combined state of stress is derived based on the theory proposed by Prof. Kececioglu and normal distribution. The calculation of fatigue reliability for limited life is discussed with example.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.355-371
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• 2018

The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.