A change point estimation problem related to age replacement policies

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

doi:10.1016/j.orl.2019.12.005

Cited by 15 publications

(4 citation statements)

References 19 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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“…The increasing concave, the increasing convex and the usual stochastic orders remain valid under sums of independent random variables, see for example [37]. Thus, the results in (a), (b) and (c) come from (17).…”

Section: (B) Ifmentioning

confidence: 99%

“…Let us denote by F X i and f X i the survival and the density functions of X i = (X i | X i < T ), respectively, for i = 1, 2. Using (17), we have…”

Section: (B) Ifmentioning

confidence: 99%

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Further Results on Stochastic Orderings and Aging Classes in Systems With Age Replacement

Corujo

Valdés²

2021

Prob. Eng. Inf. Sci.

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Reliability properties associated with the classic models of systems with age replacement have been a usual topic of research. Most previous works have checked the aging properties of the lifetime of the working units using stochastic comparisons among the systems with age replacement at different times. However, from a practical point of view, it would also be interesting to deduce to which aging classes the lifetime of the system belongs, making use of the aging properties of the lifetime of its working units. The first part of this article deals with this problem. Further along, stochastic orderings are established between the systems with replacement at the same time using several stochastic comparisons among the lifetimes of their working units. In addition, the lifetimes of two systems with age replacement are compared as well. This is performed assuming stochastic orderings between the number of replacement until failure, and the lifetimes of their working units conditioned to be less or equal than the replacement time. Similar comparisons are accomplished considering two systems with age replacement where the replacements occur at a random time. Illustrative examples are presented throughout the paper.

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

2021

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A change point estimation problem related to age replacement policies

Cited by 15 publications

References 19 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

Further Results on Stochastic Orderings and Aging Classes in Systems With Age Replacement

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

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