New classes at Specific Age: Properties and Testing hypotheses

Abstract

In this article we introduce new classes of life distributions namely new better (worse) than used in expectation at specific age t 0 NBUE-t 0 (NWUE-t 0 ) and harmonic new better (worse) than used in expectation at specific age t 0 HNBUE-t 0 (HNWUE-t 0 ). 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-t 0 and HNBUE-t 0 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.

Reliability Class Testing and Hypothesis Specification: NBRULC−t∘ Characterizations with Applications for Medical and Engineering Data Modeling

“…Given that t • is a given or definite period of interest, it is reasonable to assume that t • is known. See Renea and Samanieg [11] for NBU−t • , Ahmad [12], Zehui and Xiaohu [13] for IFRA−t • and NBU−t • , Mahmoud et al [14] for NBUE−t • , Mahmoud et al [15] for NBURFR−t • , Pandit and Anuradha [16] for NBU−t • , Gadallah [17] for NBU mg f − t • , Abdul Alim [18] for NBUFR−t • , Mahmoud et al [19] for NBUL−t • , Elbatal [20] for NBUC−t • and NBU(2)−t • , and EL-Sagheer [21] for NBRUL−t • . The main objective of the research is that in nonparametric testing of life distributions, we discovered a lack of test efficiency and a weak test power.…”