Comparison of Coherent Systems with Dependent Components Based on the Reversed Mean Residual Life Order

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Khaleghpanah Noughabi E.; CHAHKANDI M.; REZAEI M.

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Journal: JOURNAL OF STATISTICAL SCIENCES Year:2023 | Volume:16 | Issue:2 Page(s): 349-372

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Information Journal Paper

Title

Comparison of Coherent Systems with Dependent Components Based on the Reversed Mean Residual Life Order

Author(s)

Khaleghpanah Noughabi E. | CHAHKANDI M. | REZAEI M. | Issue Writer Certificate

Keywords

Distortion function

Reversed mean residual

Life order

Ageing

Coherent system

Abstract

Introduction The stochastic comparison of Coherent systems is an essential task in the reliability theory. Several results have been provided for the systems with independent and identically distributed (IID) components. System signatures are helpful tools in the study and comparison of Coherent systems in the IID case. However, system signatures have some restrictions for comparing the systems with identically distributed (ID) components. Recently, Navarro et al. (٢, ٠, ١, ٣, ) showed that the system reliability function could be expressed as a distorted function of the common reliability function of the components. This representation allows us to present different comparison results in a unified way in the ID case. In this paper, by using the concept of Distortion function, we propose a new representation of the Reversed mean residual lifetime (RML) of a Coherent system with ID component lifetimes. We provide some sufficient conditions for the RML ordering of two Coherent systems. Comparison results are also presented based on the faster Ageing order in the Reversed mean residual lifetime. Material and Methods We use the copula function to explore the structural dependency of the components and then present comparison results based on the representation of the system distribution as a distorted distribution function of the common components’,distribution. In some factual situations, we may observe the phenomenon of crossing Reversed mean residual lifetimes and variance residual lifetimes. Then, we can not compare the corresponding lifetimes in usual stochastic orders. Relative Ageing orders enable us to compare the lifetimes in these cases. Results and Discussion We want to order a Coherent system with ID components in the RML. A new representation of the mean inactivity time of a Coherent system with ID components is obtained. This representation is used to compare the RMLs of two Coherent systems. Some sufficient conditions such that one Coherent system dominates another system concerning Ageing faster order in the reversed mean and variance residual Life orders are also discussed. These results are derived based on a representation of the system reliability function as a distorted function of the common reliability function of the components. Some examples are given to explain the results. Conclusion In this paper, we study the RML ordering of Coherent systems based on Distortion function. We show that the Distortion function of a Coherent system and its integral play an important role in the RML comparison of Coherent systems. We also find a sufficient condition for the RML ordering of two Coherent systems. We study RML orderings of all Coherent systems with 1-3 IID and DID components under the FGM survival copula. The effect of the dependency is also verified in the RML comparisons. Finally, we focus on the Ageing faster order in terms of RML and introduce a new Ageing faster order in terms of reversed variance residual lifetime. We provide sufficient conditions under which one Coherent system is Ageing faster than another one with respect to the proposed orders.

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APA: Copy

Khaleghpanah Noughabi, E., CHAHKANDI, M., & REZAEI, M.. (2023). Comparison of Coherent Systems with Dependent Components Based on the Reversed Mean Residual Life Order. JOURNAL OF STATISTICAL SCIENCES, 16(2 ), 349-372. SID. https://sid.ir/paper/1021910/en

Vancouver: Copy

Khaleghpanah Noughabi E., CHAHKANDI M., REZAEI M.. Comparison of Coherent Systems with Dependent Components Based on the Reversed Mean Residual Life Order. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2023;16(2 ):349-372. Available from: https://sid.ir/paper/1021910/en

IEEE: Copy

E. Khaleghpanah Noughabi, M. CHAHKANDI, and M. REZAEI, “Comparison of Coherent Systems with Dependent Components Based on the Reversed Mean Residual Life Order,” JOURNAL OF STATISTICAL SCIENCES, vol. 16, no. 2 , pp. 349–372, 2023, [Online]. Available: https://sid.ir/paper/1021910/en

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