• 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.

• 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.

• 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.

• 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.7 no.1
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• pp.119-127
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• 1996

The concepy of positive aging describles the adverse effects of age on the lifetime of units. Various aspects of this concepts 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 distribution under residual life functions and equilibrium distributions.

• International Journal of Reliability and Applications
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• v.2 no.2
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• pp.81-97
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• 2001

Lifetesting problems have been the subject of investigations for over three decades. Most suggested approaches are markedly different from those used in the related but wider goodness of fit problems. In the current investigation, it is demonstrated that a goodness of fit approach is possible in many lifetesting problems and that It results in simpler procedures that are asymptotically equivalent or better than standard ones. They may also have superior finite sample behavior. Several perennial classes are addressed here. The class of increasing failure rate (IFR) and the class of new better than used (NBU) are addressed first. In addition, we provide testing for a newer and practical class of new better than used in convex ordering (NBUC) due to Cao and Wang (1991). Other classes can be developed similarly and this point is illustrated with the classes of new better than used in expectation (NBUE) and harmonic new better than used in expectation (HNBUE).

• International Journal of Reliability and Applications
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• v.4 no.3
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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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• v.16 no.1
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• pp.27-34
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• 2015

Based on increasing concave ordering a new class of life distribution is introduced. The new class of life distribution is named used better than aged in increasing concave ordering and is denoted by UBAC(2). The implication of our proposed class of life distribution with other classes is given. The properties of UBAC(2) under convolution, discrete mixture and formation of a coherent system are studied. Finally a characterization of the proposed class of life distributions by Laplace transform is discussed.