On HNBUE class after specific age

Mahmoud, M. A. W.; Moshref, M.E.; Gadallah, A. M.

doi:10.1016/j.joems.2012.10.010

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…Increasing Failure Rate (IFR) and its extensions, (IFRA), New Better than Used (NBU) and its extensions, (NBUC), (NBUE), (HNBUE), (NBUL), NBRU, NBRUmgf, among many others, for more information, see Klefsjo [1], Ahmed [2], Deshpand et al [3], Al-Ruzaiza et al [4], Barlow and Proschan [5], Ahmed [6], Ahsanullah et al [7], Mahmoud et al [8], Ghosh and Mitra [9], and EL-Arishy et al [10] and references therein. These classifications help establish a common ground for discussing and analyzing aging-related phenomena across different scientific domains.…”

Section: Introductionmentioning

confidence: 99%

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

M.E. Bakr,

E. S. El-Atfy,

Oluwafemi Samson Balogun

et al. 2024

Eksploatacja i Niezawodność – Maintenance and Reliability

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This study deals with a novel category of life distributions called the new better than renewal used in moment generating function (NBRUmgf) class. It delves into the connections between this form of aging and established aging categories, along with its relevance in a shock model. Additionally, it explores how this aging concept remains consistent through certain reliability operations which is consider a very important tool in reliability engineering. The research computes Pitman's asymptotic efficiencies for this testing procedure, comparing them with alternative methods. Furthermore, the study furnishes a comprehensive table of percentiles for the test statistic associated with this proposed method. Furthermore, in order to showcase the relevance of the study's conclusions, we utilize distinct real-world datasets, which illustrate the effectiveness of our test across various types of real data.

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Section: Introductionmentioning

confidence: 99%

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

M.E. Bakr,

E. S. El-Atfy,

Oluwafemi Samson Balogun

et al. 2024

Eksploatacja i Niezawodność – Maintenance and Reliability

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Alqifari

Eliwa

Etman

et al. 2023

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Due to the complexity of the data being generated day in and day out in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability called the classes of life and determinant probability distributions has been presented. This article introduces novel statistical probability models for the reliability class of life test under different reliability processes in the age range t∘. Several probabilistic properties and features were derived and rigorously screened to test the new reliability class. According to the U-statistic, a novel hypothesis test was created to evaluate the exponentiality property. The comparative efficiency of the test according to Pitman’s asymptotic efficiency was examined and compared with other reliability classes. To prove the superiority of the new reliability class, some probability models were utilized, including the Weibull, Makeham, gamma, and linear failure rate models. Moreover, critical point simulations of the null Monte Carlo distribution and some applications of the censored and uncensored data were implemented to validate the class test listed by the reliability analysis.

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“…Indeed, moment-generating class and stochastic ordering have received considerable attention in the literature; see ArdiÇ, Akdemir, and € Ozdemir (2018), Zamani, Mohtashami Borzadaran, and Amini (2017), Kayid, Izadkhah, and Alshami (2016), Rajan and Tepedelenlio glu (2015), Gandotra, Gupta, and Bajaj (2014), Mahmoud, Moshref, and Gadallah (2014), Lee and Tepedelenlioglu (2014), Rajan (2014), Anis (2011), Elbatal (2007), Ahmed and Kayid (2004), Belzunce, Ortega, and Ruiz (2004), and Klar and M€ uller (2003). Recently, Michael, Anene, Akudo, and Nwabueze (2017) defined the generalized moment-generating function as,…”

Section: Introductionmentioning

confidence: 99%

On a New Stochastic Ordering and Aging Classes Based on the Generalized Moment-Generating Function: Theory and Applications

Mahdy

2019

American Journal of Mathematical and Management Sciences

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This article opens up new aging classes and new stochastic orders dependant on generalized moment-generating function, which plays a vital role in reliability theory, finance topics, stochastic orders, and economic theory. The article presents some important new implications concerning these classes and introduces characterizations of the Weibull distribution, exponential distribution, and Erlang distribution through newly suggested aging classes. In addition, we list a series of inequalities that provide bounds for generalized momentgenerating classes. Furthermore, a sufficient condition for allowing a probability distribution to have a new class is provided. The article also demonstrates the preservation properties of a new stochastic order under certain reliability operations, such as mixture and convolution. Moreover, some novel applications of classes and stochastic orders in random sum and shock models are provided.

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On HNBUE class after specific age

Cited by 4 publications

References 25 publications

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

Statistical Insights: Analyzing Shock Models, Reliability Operations and Testing Exponentiality for NBRUmgf Class of Life Distributions

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

On a New Stochastic Ordering and Aging Classes Based on the Generalized Moment-Generating Function: Theory and Applications

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