• International Journal of Reliability and Applications
• /
• v.4 no.2
• /
• pp.71-77
• /
• 2003

We propose, in this paper, the discrete version of NBU$_{Mg}$and show that the NBU$_{Mg}$ class is preserved under both the non-homo geneous poisson shock model and the general shock model.

• Journal of the Korean Data and Information Science Society
• /
• v.7 no.1
• /
• pp.59-68
• /
• 1996

In this paper, we consider how to estimate New Better Than Used (NBU) survival curves from randomly right censored data. We propose several possible NBU estimators and study their properties. Numerical studies indicate that the proposed estimators are appropriate in practical use. Some useful examples are presented.

• The Korean Journal of Applied Statistics
• /
• v.16 no.2
• /
• pp.395-406
• /
• 2003

In this thesis, we propose a test statistic for testing exponentiality against NBU alternatives. Our test statistics is based on a linear function of the order statistics and is readily applied in the case of small sample as well as large sample. The exact and asymptotic distribution of the test statistics is derived and asymptotic efficiencies are studied. Our new test is easier to compute and performs better for several alternatives than test of Hollander and Proschan(1972).

• International Journal of Reliability and Applications
• /
• v.7 no.1
• /
• pp.13-25
• /
• 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
• /
• v.13 no.2
• /
• pp.57-69
• /
• 2012

Our goal in this paper is to establish inequalities for the moments of new better than used in the moment generating function class ($NBU_{mgf}$). Using these inequalities we propose a new test for exponentiality versus $NBU_{mgf}$ class. Pitman's asymptotic relative efficiency, power and critical values of this test are calculated to assess the performance of the test. We proposed also a new test for exponentiality versus $NBU_{mgf}$ in the right censored data. Sets of real data are used as an example to elucidate the use of the proposed test for practical problems.

• International Journal of Reliability and Applications
• /
• v.5 no.4
• /
• pp.155-162
• /
• 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
• /
• v.17 no.2
• /
• pp.107-119
• /
• 2016

A new concept of aging classes namely new better (worse) than used at age $t_0$ in moment generating function order, $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$) is introduced. For the classes $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, nonparametric test is proposed, the asymptotic normality of the class is established and the asymptotic null variance is estimated. The percentiles and powers of this test are tabulated. The asymptotic efficiencies for some alternatives distributions are derived. Finally sets of real data are used as examples to elucidate the use of the proposed test in practical application.

• International Journal of Computer Science & Network Security
• /
• v.22 no.6
• /
• pp.91-96
• /
• 2022

The photocatalytic degradation of salicylic acid takes place in several stages involving coupled phenomena, such as the transport of molecules and the chemical reaction. The systems of transport equations and the photocatalytic reaction are numerically solved using COMSOL Mutiphysics (CM) simulation software. CM will make it possible to couple the phenomena of flow, the transport of pollutants (salicylic acid) by convection and diffusion, and the chemical reaction to the catalytic area (bauxite or TiO2 doped by nanoparticles). The simulation of the conversion rate allows to correctly fit the experimental results. The temporal simulation shows that the reaction reaches equilibrium after a transitional stage lasting over one minute. The outcomes of the study highlight the importance of diffusion in the boundary layer and the usefulness of injecting micro-agitation into the microchannel flow. Under such conditions, salicylic acid degrades completely.

• Journal of Korean Society for Quality Management
• /
• v.27 no.2
• /
• pp.143-151
• /
• 1999

In this thesis, a new test statistic is proposed for testing exponentiality against New Better than Used (NBU) alternatives. Our test statistic, which is based on a quadratic function of the order statistics from the sample, is readily applied in the case of small sample. Also, Our test statistic is more simple than the test statistic of Hollander and Proschan(1972).

• International Journal of Reliability and Applications
• /
• v.8 no.2
• /
• pp.175-182
• /
• 2007

In this note, some comments concerning the testing procedures for the problems of stochastic comparison, testing IFR and testing NBU ageing properties are presented showing that the tests proposed in Belzunce, Candel and Ruiz(1998) are cumbersome to calculate and do not have as good asymptotic Pittman efficacies as simpler others already in the literature. This is done via new presentations of the measures on which Belzunce et al. base their tests.