Abstract
In this article we introduce new classes of life distributions namely new better (worse) than used in expectation at specific age t0 NBUE-t0 (NWUE-t0) and harmonic new better (worse) than used in expectation at specific age t0 HNBUE-t0 (HNWUE-t0). The closure properties under various reliability operations such as convolution, mixture, mixing and the homogeneous Poisson shock model of these classes are studied. Furthermore, nonparametric tests are proposed to test exponentiality versus the NBUE-t0 and HNBUE-t0 classes. The critical values and the powers of this tests are calculated to assess the performance of the tests. It is shown that the proposed tests have high efficiencies for some commonly used distributions in reliability. Sets of real data are used as examples to elucidate the use of the proposed tests for practical problems.
Highlights
Certain classes of life distributions and their variations have been introduced in reliability, the applications of these classes of life distributions can be seen in engineering, social, biological science, maintenance and biometrics
In this article we introduce new classes of life distribution at specific age t0
The following example shows that the NBUE-t0 class is not preserved under mixtures
Summary
Certain classes of life distributions and their variations have been introduced in reliability, the applications of these classes of life distributions can be seen in engineering, social, biological science, maintenance and biometrics. For example Barlow and Proschan (1981), Deshpand et al (1986) and Cao and Wang (1991), gave definitions of several classes of distributions, NBU, NBU(2) and NBUE. In this article we introduce new classes of life distribution at specific age t0. X is new better than used in expectation at specific age t0 (denoted by X ∈ NBUE-t0) if. X is harmonic new better than used in expectation at specific age t0 (denoted by X ∈ HNBUE-t0) if.
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