• International Journal of Reliability and Applications
• /
• 제16권2호
• /
• pp.81-98
• /
• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

• International Journal of Reliability and Applications
• /
• 제17권1호
• /
• pp.1-19
• /
• 2016

The Exponentiated Quasi Lindley (EQL) distribution which is an extension of the quasi Lindley Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions, the moments and moment generating function, the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally an application of the model with a real data set is presented for the illustration of the usefulness of the proposed distribution.

• Journal of the Korean Data and Information Science Society
• /
• 제7권2호
• /
• pp.257-262
• /
• 1996

본 논문은 스플라인 희귀모형에서 평활모수를 추정할 때 사전 작업으로 영향력 진단을 하는 문제를 다룬다. 평활모수의 추정방법으로 일반화최대우도함수법을 사용할 때, 얻어지는 추정 치에 영향을 주는 관측치를 진단하는 측도를 제안하고, 찾아낸 영향력 관측치를 수정하여 올바른 평활모수 추정치를 찾는 방법을 소개한다.

• 대한기계학회논문집A
• /
• 제33권12호
• /
• pp.1482-1487
• /
• 2009

In this study statistical analysis was performed for NDI(Non-Destructive Inspection) results of F100 engine front seal support assembly. NDI results can be statistically considered as Quantal Response Data. It is found that the suitable probability distribution to the failure data is normal distribution through MLE(Maximum Likelihood Estimation) of the Quantal Response Data. Moreover, Cumulative Distribution Function, failure rate function and B-Life are calculated on the supposed distribution.

• 산업경영시스템학회지
• /
• 제35권2호
• /
• pp.98-105
• /
• 2012

This paper describes the Bayesian approach for reliability demonstration test based on the samples from a finite population. The Bayesian approach involves the technical method about how to combine the prior distribution and the likelihood function to produce the posterior distribution. In this paper, the hypergeometric distribution is adopted as a likelihood function for a finite population. The conjugacy of the beta-binomial distribution and the hypergeometric distribution is shown and is used to make a decision about whether to accept or reject the finite population judging from a viewpoint of faulty goods. A numerical example is also given.

• Journal of the Korean Data and Information Science Society
• /
• 제25권2호
• /
• pp.431-438
• /
• 2014

Type I hybrid censoring scheme is the combination of the Type I and Type II censoring scheme introduced by Epstein (1954). Epstein considered a hybrid censoring sampling scheme in which the life testing experiment is terminated at a random time $T^*$ which is the time that happens rst among the following two; time of the kth unit is observed or time of the experiment length set in advance. The likelihood function of this scheme from the Rayleigh distribution cannot be solved in a explicit solution and thus we approximate the function by the Taylor series expansion. In this process, we propose four dierent methods of expansion skill.

• 한국신뢰성학회지:신뢰성응용연구
• /
• 제1권1호
• /
• pp.47-54
• /
• 2001

This paper considers the parameter estimation problem of the failure intensity function and maintenance effect in a repairable system. We propose estimation procedures for repairable systems on which preventive maintenance is performed. The failure process is modeled by a proportional age reduction model [Brown, Mahoney and Sivazlian(1983)] which is useful to model the imperfect effect of preventive maintenance. When failure and maintenance (preventive) times are given, the maximum likelihood method is used to estimate the maintenance effect and the parameters of intensity function, simultaneously We obtain the maximum likelihood estimators using a genetic algorithm. A numerical example is also presented.

• International Journal of Reliability and Applications
• /
• 제18권2호
• /
• pp.65-82
• /
• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• Journal of the Korean Data and Information Science Society
• /
• 제20권3호
• /
• pp.467-474
• /
• 2009

시스템의 한 부품이 고장 나면 고장 난 부품이 분담하던 부하가 고장 나지 않은 다른 부품에 전가되어 다른 부품의 고장률에 영향을 주는 부하분배시스템에 대한 연구가 신뢰성 공학과 생물의학 분야에서 다양하게 이루어져왔다. 본 연구에서는 최소수명을 보증하는 부하분배체계의 체계단위수명 시험에서 부품의 수명관측이 불가능하며 체계의 수명관측이 가능한 경우에, 중도절단된 체계 고장데이터를 이용하여 부하분배체계의 평균수명과 체계 신뢰도의 최우추정치와 추정오차를 줄일 수 있는 수정된 최우추정치를 구하고 컴퓨터 모의실험을 통하여 그 성능을 비교한다.

• 전기학회논문지
• /
• 제62권1호
• /
• pp.101-104
• /
• 2013

We computed Cramer-Rao bound for estimating amplitude and decay parameters of exponentially decaying function under Poisson noise. Since Cramer-Rao bound is the lowest variance bound for any unbiased estimator, the computed Cramer-Rao bound can be used for evaluating the performance of estimators under Poisson noise. In addition, we show that the performance of maximum-likelihood estimator is close to the Cramer-Rao bound by simulations.