Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives

Khan, Ruhul Ali; Bhattacharyya, Dhrubasish; Mitra, Manimala

doi:10.1007/s00362-021-01226-3

Cited by 7 publications

(2 citation statements)

References 43 publications

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“…In this section, we study the interrelationships between the BFR family of [23], the IDMRL family of [24], the NWBUE family of [47], and the IDMTTF family of [27]. In the context of the abovementioned non-monotonic ageing classes, see the recent works [13,14,15,26,30,31,34]. Exploiting 'total time on test' (TTT) transform characterizations, [47] established that the NWBUE family of life distributions contains both IDMRL and BFR classes.…”

Section: Interrelationships Among Non-monotonic Ageing Classesmentioning

confidence: 99%

On some properties of distributions possessing a bathtub-shaped failure rate average

Khan

Bhattacharyya²,

Mitra³

2023

J. Appl. Probab.

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The life distribution of a device subject to shocks governed by a homogeneous Poisson process is shown to have a bathtub failure rate average (BFRA) when the probabilities $\bar{P}_k$ of surviving k shocks possess the corresponding discrete property. We prove closure under the formation of weak limits for BFRA distributions and explore related moment convergence issues within the BFRA family. Similar results for increasing and decreasing failure rate average distributions are obtained either independently or as consequences of our results. We also establish some results outlining the positions of various non-monotonic ageing classes such as bathtub failure rate, increasing initially then decreasing mean residual life, new worse then better than used in expectation, and increasing initially then decreasing mean time to failure in the hierarchy. Finally, an open problem is posed and a partial solution provided.

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Section: Interrelationships Among Non-monotonic Ageing Classesmentioning

confidence: 99%

On some properties of distributions possessing a bathtub-shaped failure rate average

Khan

Bhattacharyya²,

Mitra³

2023

J. Appl. Probab.

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“…Our objective is to provide an overview of these advancements. Researchers in statistics and reliability analysis have looked at testing exponentiality problems using different age classes of life distributions from a variety of angles; for more information, see Bryson and Siddiqui [1], Bhattacharyya et al [2], Barlow and Proschan [3], Klefsjo [4], Khan et al [5], Kumazawa [6], Mahmoud et al [7,8], Majumder and Mitra [9], Bhattacharyya et al [10], Navarro [11], Abu-Youssef et al [12], Ghosh and Mitra [13], Navarro and Pellerey [14], El-Morshedy et al [15], EL-Sagheer et al [16] Gadallah et al [17], Mansour [18], Ghosh and Mitra [19], Majumder and Mitra [20], Lai and Xie [21], Etman et al [22], Ghosh and Majumder [23], Bakr and Al-Babtain [24], and Ghosh and Mitra [25] and Alqifar et al [26]. The goodness-of-fit test indicates whether the data in one's sample correspond to the data one would anticipate seeing in the actual population.…”

Section: Introductionmentioning

confidence: 99%

The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data

et al. 2023

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The majority of approaches proposed in the past few decades to solve life test problems have differed markedly from those used for closely related, yet broader, issues. Due to the complexity of data that are generated each day 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 has been created. This domain is referred to as life classes, where specific probability distributions are presented. In this study, it is shown that the use of the quality-of-fit technique to solve problems involving life testing makes sense, and produces simpler processes that are roughly equivalent or superior to those used in traditional procedures. They may also behave better in limited samples. This work investigates a novel quality-of-fit test statistic; it is based on an exponential transform and is compared to the best renewal used Laplace test in increasing convex ordering (NBRULC). Evidence for approach normality is provided. The calculated variables include powers, Pitman asymptotic effectiveness, and critical points. Methods on how to handle censored data were also studied. Our experiments have real-world applications in the fields of medicine and engineering.

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Testing convexity of the generalised hazard function

Lando

2022

Stat Papers

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Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives

Cited by 7 publications

References 43 publications

On some properties of distributions possessing a bathtub-shaped failure rate average

On some properties of distributions possessing a bathtub-shaped failure rate average

The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data

Testing convexity of the generalised hazard function

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