Author

# Yan Lumelskii

Bio: Yan Lumelskii is an academic researcher. The author has contributed to research in topics: Nonparametric statistics & Parametric statistics. The author has an hindex of 2, co-authored 2 publications receiving 480 citations.

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01 Mar 2003

TL;DR: A survey of applications theory and general estimation procedures for stress strength models can be found in this paper, along with examples and details on applications and their application in the context of point estimation and statistical inference.

Abstract: Stress-strength models - history, mathematical tools and survey of applications theory and general estimation procedures parametric point estimation parametric statistical inference nonparametric methods special cases and generalizations examples and details on applications

387 citations

11 Dec 2013

TL;DR: The stress strength model and its generalizations are discussed in this article, where the authors propose a generalization of the stress-strength model to the generalization model and generalize it.

Abstract: The stress-strength model and its generalizations , The stress-strength model and its generalizations , کتابخانه دیجیتال جندی شاپور اهواز

184 citations

##### Cited by

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TL;DR: In this article, a general reliability model is developed based on degradation and random shock modeling, which is then extended to a specific model for a linear degradation path and normally distributed shock load sizes and damage sizes.

Abstract: For complex systems that experience Multiple Dependent Competing Failure Processes (MDCFP), the dependency among the failure processes presents challenging issues in reliability modeling. This article, develops reliability models and preventive maintenance policies for systems subject to MDCFP. Specifically, two dependent/correlated failure processes are considered: soft failures caused jointly by continuous smooth degradation and additional abrupt degradation damage due to a shock process and catastrophic failures caused by an abrupt and sudden stress from the same shock process. A general reliability model is developed based on degradation and random shock modeling (i.e., extreme and cumulative shock models), which is then extended to a specific model for a linear degradation path and normally distributed shock load sizes and damage sizes. A preventive maintenance policy using periodic inspection is also developed by minimizing the average long-run maintenance cost rate. The developed reliability and ma...

314 citations

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TL;DR: In this paper, the authors proposed a generalized exponential distribution for analyzing bathtub failure data, which has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions.

Abstract: Mudholkar and Srivastava [1993. Exponentiated Weibull family for analyzing bathtub failure data. IEEE Trans. Reliability 42, 299–302] introduced three-parameter exponentiated Weibull distribution. Two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. Generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, closeness of this distribution to some of the well-known distribution functions are discussed in this article.

284 citations

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TL;DR: The asymptotic distribution of the maximum likelihood estimator of R is obtained and the confidence interval of R can be obtained, and two bootstrap confidence intervals are proposed.

Abstract: This paper deals with the estimation of R=P[Y

226 citations

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TL;DR: In this article, the estimation of the stress-strength parameter R = P(Y < X) when X and Y are independent Lindley random variables with different shape parameters is dealt with.

Abstract: This article deals with the estimation of the stress-strength parameter R = P(Y < X) when X and Y are independent Lindley random variables with different shape parameters. The uniformly minimum variance unbiased estimator has explicit expression, however, its exact or asymptotic distribution is very difficult to obtain. The maximum likelihood estimator of the unknown parameter can also be obtained in explicit form. We obtain the asymptotic distribution of the maximum likelihood estimator and it can be used to construct confidence interval of R. Different parametric bootstrap confidence intervals are also proposed. Bayes estimator and the associated credible interval based on independent gamma priors on the unknown parameters are obtained using Monte Carlo methods. Different methods are compared using simulations and one data analysis has been performed for illustrative purposes.

140 citations

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TL;DR: The overall conclusion is that the WH normal approximation provides a simple, easy-to-use unified approach for addressing various problems for the gamma distribution.

Abstract: In this article we propose inferential procedures for a gamma distribution using the Wilson–Hilferty (WH) normal approximation. Specifically, using the result that the cube root of a gamma random variable is approximately normally distributed, we propose normal-based approaches for a gamma distribution for (a) constructing prediction limits, one-sided tolerance limits, and tolerance intervals; (b) for obtaining upper prediction limits for at least l of m observations from a gamma distribution at each of r locations; and (c) assessing the reliability of a stress-strength model involving two independent gamma random variables. For each problem, a normal-based approximate procedure is outlined, and its applicability and validity for a gamma distribution are studied using Monte Carlo simulation. Our investigation shows that the approximate procedures are very satisfactory for all of these problems. For each problem considered, the results are illustrated using practical examples. Our overall conclusion is tha...

121 citations