• Structural Engineering and Mechanics
• /
• v.32 no.1
• /
• pp.55-69
• /
• 2009

A quasi ideal importance sampling simulation method combined in the conditional expectation is proposed for the structural reliability estimation. The quasi ideal importance sampling joint probability density function (p.d.f.) is so composed on the basis of the ideal importance sampling concept as to be proportional to the conditional failure probability multiplied by the p.d.f. of the sampling variables. The respective marginal p.d.f.s of the ideal importance sampling joint p.d.f. are determined numerically by the simulations and partly by the piecewise integrations. The quasi ideal importance sampling simulations combined in the conditional expectation are executed to estimate the failure probabilities of structures with multiple failure surfaces and it is shown that the proposed method gives accurate estimations efficiently.

• Proceedings of the Korean Reliability Society Conference
• /
• 2002.06a
• /
• pp.367-386
• /
• 2002

The Present paper is devoted to a study of the performance, in large samples, of a conditional maximum likelihood estimator(CMLE) for the parameter ${\lambda}$ in a pure birth processes(PBP). To conduct the conditional inference for the PBP, we drove the likelihood function of time-inhomogeneous Poisson processes. The limiting distributions of CMLE under the likelihoods $L_{t}$ or $\overline{L_{t}}$ are investigated. We found that the CMLE is asymptotically efficient with respect to the both $L_{t}$ or $\overline{L_{t}}$ under the efficiency criterion of Weiss & Wolfowitz(1974).

• Journal of the Korea Safety Management & Science
• /
• v.1 no.1
• /
• pp.135-143
• /
• 1999

This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that the failure rate pattern follows a bimodal mixed Weibull distribution. The procedure will consider warranty period as a factor of the total expected bum-in cost. A cost model is formulated to find the optimal burn-in time that minimizes the expected burn-in cost. Conditional reliability for warranty period will be discussed. An illustrative example is included to show how to use the cost model in practice.

• ETRI Journal
• /
• v.14 no.4
• /
• pp.19-27
• /
• 1992

Since. as is well known, direct computation of the reliability for a large-scaled and complex net work generally requires exponential time, a variety of alternative methods to estimate the network reliability using simulation have been proposed. Monte Carlo sampling is the major approach to estimate the network reliability using simulation. In the paper, a dynamic Monte Carlo sampling method, called conditional minimal cut set (CMCS) algorithm, is suggested. The CMCS algorithm simulates a minimal cut set composed of arcs originated from the (conditional) source node until s-t connectedness is confirmed, then reduces the network on the basis of the states of simulated arcs. We develop the importance sampling estimator and the total hazard estimator and compare the performance of these simulation estimators. It is found that the CMCS algorithm is useful in reducing variance of network reliability estimator.

• Journal of the Korean Statistical Society
• /
• v.28 no.4
• /
• pp.399-413
• /
• 1999

• Journal of the Korean Geotechnical Society
• /
• v.23 no.3
• /
• pp.51-59
• /
• 2007

A reliability-based approach that can systematically model various sources of uncertainty is presented in the context of slope stability. Expressions for characterization of soil properties are developed in order to incorporate sampling errors, spatial variability and its effect of spatial averaging. Reliability analyses of slope stability with different statistical representations of soil properties show that the incorporation of sampling error, spatial correlation, and conditional simulation leads to significantly lower probability of failure than that obtained by using simple random variable approach. The results strongly suggest that the spatial variability and sampling error have to be properly incorporated in slope stability analysis.

• Journal of the Korean Statistical Society
• /
• v.26 no.3
• /
• pp.407-416
• /
• 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 Safety Management and Science Conference
• /
• 1999.11a
• /
• pp.147-155
• /
• 1999

This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that the failure rate pattern follows a bimodal mixed Weibull distribution. The procedure will consider warranty period as a factor of the total expected burn-in cost. A cost model is formulated to find the optimal burn-in time that minimizes the expected burn-in cost. Conditional reliability for warranty period will be discussed. An illustrative example is included to show how to use the cost model in practice.

• Journal of Applied Reliability
• /
• v.1 no.2
• /
• pp.183-192
• /
• 2001

Jelinski-Moranda model and modified Jelinski-Moranda model in software reliability are studied and we consider maximum likelihood estimator and Bayes estimates of the number of faults and the fault-detection rate per fault. A gibbs sampling approach is employed to compute the Bayes estimates, future survival function is examined. Model selection based on prequential likelihood of the conditional predictive ordinates. A numerical example with simulated data set is given.

• International Journal of Reliability and Applications
• /
• v.7 no.2
• /
• pp.127-140
• /
• 2006

AIn this paper we introduce and study a multivariate notions of mean inactivity time (MIT) functions. Basic properties of these functions are derived and their relationship to the multivariate conditional reversed hazard rate functions is studied. A partial ordering, called MIT ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to reversed hazard rate ordering is pointed out. Finally, using the MIT ordering, a bivariate and multivariate notions of IMIT (increasing mean inactivity time) class is introduced and studied.