Testing exponentiality against a trend change in mean time to failure in age replacement

Izadi, Muhyiddin; Manesh, Sirous Fathi

doi:10.1080/03610926.2019.1702693

Cited by 11 publications

(1 citation statement)

References 26 publications

(33 reference statements)

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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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