• International Journal of Reliability and Applications
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• v.5 no.4
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• pp.155-162
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• 2004

A new class of life distributions is studied. This class is defined based on comparing the residual life to the whole life in the moment generating function order giving "the new better than used in the moment generating function order ageing class ($NBU_{mgf}$)". Some new results of this class are given including some closere properties and characterizations. Finally testing exponentially against the $NBU_{mgf}$ class is also addressed.

• International Journal of Reliability and Applications
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• v.7 no.1
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• pp.13-25
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• 2006

A new class of life distributions is studied. This class is defined based on comparing the residual life time to the whole life in the moment generating function order giving 'the new better than used in the moment generating function order ageing class $(NBU_{mgf})$'. Fundamental properties of this class are given including some closure properties and characterizations. Finally, we consider new results about comparisons of age and block replacement policies when the underlying distribution belongs to $NBU_{mgf}$ aging classes.

• International Journal of Reliability and Applications
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• v.14 no.1
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• pp.1-9
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• 2013

A nonparametric procedure for testing exponentially against used better than aged in expectation (UBAE) class of life distributions is presented. We construct a test statistics based on scaled total time on test (TTT)-transformation, to test exponentiality against UBAE class of life distributions. The distribution of the statistic is investigated via simulation. Practical applications of the proposed test are presented.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.20-32
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• 1995

The concept of positive ageing describes the adverse effects of age on the lifetime of units. Various aspects of this concept are described in terms of conditional probability distribution of residual life times, failure rates, equilibrium distributions, etc. In this paper, we will consider some partial ordering relations of life distributions under residual life functions and equilibrium distributions. Under residual life distributions, we study the relationships of IFR, NBU and NBUFR classes and that of DMRL and NBUE classes, By using WLR ordering comparison between F and its equilibrium $H_F$, we can decide if F belongs to NBUFR class.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.45-51
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• 1993

For studies in reliability, biometry and survival analysis, the length biased distribution is frequently appropriate for certain natural sampling plans. So, we shall convey the preservation of some partial orderings under life length biasd distributions and closures of ILR and NBU classes under life length biasd distributions.

• International Journal of Reliability and Applications
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• v.10 no.2
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• pp.81-88
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• 2009

A non-parametric procedure is presented for testing exponentially against used better than aged in convex ordering class (UBAC) of life distributions based on u-test. Convergence of the proposed statistic to the normal distribution is proved. Selected critical values are tabulated for sample sizes 5(5)40. The Pitman asymptotic relative efficiency of my proposed test to tests of other classes is studied. An example of 40 patients suffering from blood cancer disease demonstrates practical application of the proposed test.

• Journal of the Korean Data and Information Science Society
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• v.12 no.2
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• pp.71-82
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• 2001

There are several ways to test the equality of two survival distributions under a variety of situations. Tests for equality of two distributions with life-table model for univariate independent response times are reviewed and introduced. It is developed that the methodology to test it for correlated response times where treatments are applied to different independent sets of cohorts. Data, which can be separated into two independent sets, from an angioplasty study where more than one procedure is performed on some patients are used to illustrate this methodology.

• International Journal of Reliability and Applications
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• v.13 no.1
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• pp.49-56
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• 2012

Using total time on test transform (TTT), a new approach is taken for testing exponentiality versus the unknown age, exponential better than equilibrium life in convex ordering (EBELC). Selected critical values are tabulated for sample size n =2(2)50 and powers of the test are estimated for some commonly used distributions in reliability. Finally real example is presented to illustrate the theoretical results.

• International Journal of Reliability and Applications
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• v.11 no.2
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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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• v.3 no.2
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• pp.91-98
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• 2002

A class of life distributions, whose mean residual life keeps stable at its earlier phase and then starts to decrease in time, is proposed to model the life of an element haying survived its burn-in. A strongly consistent estimator and a nonparametric testing procedure are developed to locate the occurrence of the change-point of the mean residual life. Finally, some numerical simulations are employed to be an illustration as well.