• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2004년도 정기학술대회
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• pp.167-175
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• 2004

A nonparametric procedure is proposed to test the exponentiality against the hypothesis that one life distribution has a greater residual life times than the other life distribution. Such a hypothesis turns out to be equivalent to the one that one failure rate is greater than the other and so the proposed test works as a competitor to more IFR tests by Kochar (1979, 1981) and Cheng (1985). Our test statistic utilizes the U-statistics theory and a large sample nonpara metric test is established. The power of the proposed test is discussed by calculating the Pitman asymptotic relative efficiencies against several alter native hypotheses. A numerical example is presented to exemplify the proposed test.

• International Journal of Reliability and Applications
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• 제15권1호
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• pp.1-9
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• 2014

Let X and $X_t$ denote the lifetime and the residual life at age t, respectively. X is said to be a NBUL (new better than used in Laplace transform order) random variable if $X_t$ is smaller than X in Laplace order, i.e., $X_t{\leq}_{LT}X$. We propose a new test statistics for testing exponentiality versus NBUL class of life distribution. The tests by Hollender and Proschan (1975) and the generalized Hollender and Proschan test by Ains and Mitra (2011) are considered as special cases of the our of test statistics. Our proposed test statistics is simple, consistent and asymptotically normal. Efficiency and powers of the test statistics for some commonly used distributions in reliability are discussed. Finally, real examples are presented to illustrate the theoretical results.

• International Journal of Reliability and Applications
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• 제11권2호
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• pp.139-151
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• 2010

The main objective of this study is to present a new approach to obtain moment inequalities for the new better than renewal used (NBRU) class of life distributions. In order to achieve our main objective, the moment inequalities for NBRU class of life distribution using the new approach has been derived and then a new test for testing exponentiality against NBRU class based on these inequalities has been constructed. Then we calculate the Pitman asymptotic efficiency for the proposed test using some alternative distributions and comparing it with the other tests. Moreover, we make a comparison between Pittman asymptotic efficiencies (PAE's) and PAE's of some other tests. A simulation study is conducted to calculate the upper critical values and the power estimate of the proposed test for some common alternatives. Finally, we apply the suggested test to some real data.

• International Journal of Reliability and Applications
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• 제7권2호
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• pp.141-153
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• 2006

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

• 응용통계연구
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• 제4권2호
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• pp.157-170
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• 1991

본 논문은 척도모수와 위치모수가 알려지지 않은 상황에서의 지수분포성 적합도 검정문제를 다루고 있다. 기존의 검장방법들과는 달리 누적분포 함수와 경험분포 함수 사이의 편차의 $L_1$-norm에 바탕을 두고 둔 새로운 검정방법이 제시되었으며, Monte Carlo 방법에 의하 여 검정통계량의 임계치를 구하였다. 그리고 표본의 크기가 작은 경우에 한하여 제시된 검 전통계량의 분포가 파악되었다. 한편 이 검정방법의 검정력을 기존의 검정방법들과 비교하 기 위하여 응용분야에서 흔히 사용되는 몇가지 분포형태에 대하여 검정력을 측정하였다. 그 결과, 새로운 검정방법이 보수적인 검정임에도 불구하고 다른 검정방법에 비하여 상대적으 로 검정력이 우수한 것으로 나타났다.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.113-129
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• 2003

Based on moments inequalities new testing procedures are derived for testing exponentiality against new renewal better than used (NRBU) and renewal new better than used (RNBU). These classes play an important role in formulating repair or replacement policies. The asymptotic Pitman efficiency of (NRBU) and (RNBU) testes are studied. Selected critical values are tabulated for sample sizes n=5(1) 50. The power estimates for some commonly used life distributions in reliability are also calculated. Some set of real data is used as an example to elucidate the use of the proposed test statistic for practical reliability analysis. The problem in case of right-censored data is also handled.

• International Journal of Reliability and Applications
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• 제7권1호
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• pp.1-11
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• 2006

The better mean residual life at $t_0\;(BMRL-t_0)$ class of life distribution is introduced by Kulasekara and Park (1987). They proved that the $BMRL-t_0$ class contains the DMRL class, but it is a proper subclass of the NBUE class. In this paper we develop a new family of tests for testing exponentiality against the $BMRL-t_0\;(WMRL-t_0)$ alternatives based on the goodness of fit approach. It is shown that the suggested test is better than the one introduced by Kulasekara and Park (1987) in the sense of Pitman asymptotic efficiency values.

• International Journal of Reliability and Applications
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• 제4권3호
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• pp.141-156
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• 2003

Nonparametric families of aging distributions have been the subject of investigation from long period of time and still. Both probabilistic and statistical properties of these distributions were studied for such families as new better than used renewal failure rate (NBURFR) and new better average renewal failure rate (NBARFR) classes. They have been studied by Abouammoh and Ahmed (1992). In the present work, moment inequalities are derived for the above mentioned families that demonstrate that if the mean life is finite for any of them then all higher order moments exist. Next, based on these inequalities, new test procedures for exponentiality against these families are studied showing that it is simple and hold high relative efficiency for some commonly used alternatives. Dealing with censored data case also studied.

• Nuclear Medicine and Molecular Imaging
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• 제42권4호
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• pp.275-284
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• 2008

목적: 정상 성인에서 심근의 산소 소모량에 대한 참고범위를 구하고 시간-방사능 곡선(time-activity curve, TAC)에 재순환이 어떤 영향을 미치는지 알아보기 위하여 재순환 교정법과 수정 단일구획모델을 적용하여 심근 내 산소 소모량을 계산하고자 하였다. 대상 및 방법: 평균연령 $26.3{\pm}4.0$세인 9명의 지원자들에서 925 MBq (25mCi)의 $^{11}C$-Acetate (가천의과학대학교 뇌과학연구소)와 PET/CT (Biograph 6, 독일 지멘스사)를 사용하여 심근 산소 소모량을 계산하였다. 자료의 분석을 위하여 $MATLAB^{(R)}$ v7.1 (Mathworks. Inc., 미국), $Excel^{(R)}$ 2007 (Microsoft, 미국), $SPSS^{(R)}$ v12.0 (Apache Software Foundation, 미국) 등의 소프트웨어들을 사용하였다. PET/CT로 촬영한 영상으로부터 10초마다 12장, 다음 60초마다 5장, 다음 120초마다 3장, 그리고 마지막으로 300초마다 2장 등 0초일 때 1장을 포함하여 총 23개 프레임을 추출하였다. 수정 단일구획모델과 재순환 교정법을 적용하였다. 통계적 분석방법으로 정규성 검정, 분산분석(ANOVA), 사후분석(Post-Hoc analysis) 등을 이용하였고 p값으로 0.05를 적용하였다. 결과: 심근 산소 소모량의 참고범위는 중격 아래벽, 가쪽벽, 앞벽, 전체벽에서 각각 $3.18-4.64\;{\times}\;10^{-4}\;ml/g/sec$, $1.91-3.94\;{\times}\;10^{-4}\;ml/g/sec$, $4.31-6.40\;{\times}\;10^{-4}\;ml/g/sec$, $2.84-4.53\;{\times}\;10^{-4}\;ml/g/sec$ and $3.42-5.00\;{\times}\;10^{-4}\;ml/g/sec$ 등으로 계산되었다. 또한 시간-방사능 곡선의 형태에 관한 기존의 이중적 견해는 결국 재순환된 $^{11}C$-Acetate 때문이며 이 재순환을 교정하면 곡선은 근본적으로 단일 지수함수 형태를 띤다. 결론: $^{11}C$-Acetate 및 3차원 PET/CT로 심근의 산소 소모량을 효율적으로 평가할 수 있으며 안정상태에서는 재순환된 $^{11}C$가 거의 존재하지 않기 때문에 시간-방사능 곡선에 의미 있는 영향을 미치지 않는다..