On the Uncertainty Properties of the Conditional Distribution of the Past Life Time

Kayid, Mohamed; Shrahili, Mansour

doi:10.3390/e25060895

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…To handle this difficulty, investigators have newly proposed uncertainty bounds for the component lifetimes in coherent systems. This approach is explored in works such as [18,21,22] and the related literature. In the next theorem, we obtain bounds for CE (T t ) based on the CE of the parent distribution CE (X t ).…”

Section: Bounding the Cumulative Entropy Of Past Lifetimementioning

confidence: 99%

“…Recently, Kayid [19] investigated the Tsallis entropy of coherent systems when all components are alive at time t. Mesfioui et al [20] have also delved into the Tsallis entropy such systems, adding to the current body of captivating research in this area. More recently, Kayid and Shrahili [21,22] investigated the Shannon differential and Renyi entropy of coherent systems when all components have failed at time t. The aim of this study is to examine the uncertainty properties of the lifetimes of coherent systems, with a particular focus on the cumulative past entropy. In fact, when all components have failed at time t, we focus on coherent systems consisting of n components by utilizing the system signature.…”

Section: Introductionmentioning

confidence: 99%

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Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

Shrahili,

Kayid

2023

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This paper explores the cumulative entropy of the lifetime of an n-component coherent system, given the precondition that all system components have experienced failure at time t. This investigation utilizes the system signature to compute the cumulative entropy of the system’s lifetime, shedding light on a crucial facet of a system’s predictability. In the course of this research, we unearth a series of noteworthy discoveries. These include formulating expressions, defining bounds, and identifying orderings related to this measure. Further, we propose a technique to identify a preferred system on the basis of cumulative Kullback–Leibler discriminating information, which exhibits a strong relation with the parallel system. These findings contribute significantly to our understanding of the predictability of a coherent system’s lifetime, underscoring the importance of this field of study. The outcomes offer potential benefits for a wide range of applications where system predictability is paramount, and where the comparative evaluation of different systems on the basis of discriminating information is needed.

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Section: Bounding the Cumulative Entropy Of Past Lifetimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

Shrahili,

Kayid

2023

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System Level Extropy of the Past Life of a Coherent System

Kayid,

Alshehri

2023

Journal of Mathematics

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In this paper, we take a new approach to uncertainty in a coherent system, where components are assumed to be all inactive in a given time. In particular, the signature-based method is used to quantify the extropy of the past lifetime of the system, which serves as a valuable indicator of its predictability. The results provide several key findings, including some bounds and stochastic ordering aspects for this measure. We also introduce a new formula to select the system that is preferable based on its relative extropy in the past. The results of this work can provide insights for designing systems to improve their reliability and resilience.

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Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

Shrahili,

Kayid

2023

Preprint

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In this paper, we investigate the cumulative historical entropy of the lifetime of an n-component coherent system under the assumption that all system components have failed at time t. Using the system signature, we can calculate the cumulative historical entropy of the system’s lifespan, which is an important aspect in determining a system’s predictability. This research produces a number of significant results, including expressions, bounds, and ordering aspects for this measure. In addition, we offer a method for finding a preferred system based on cumulative Kullback-Leibler discriminating information that is closely related to the parallel system. These findings provide important insights into the predictability and dependability of coherent systems, emphasizing the importance of this field.

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On the Uncertainty Properties of the Conditional Distribution of the Past Life Time

Cited by 3 publications

References 27 publications

Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

System Level Extropy of the Past Life of a Coherent System

Cumulative Entropy of Past Lifetime for Coherent Systems at the System Level

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