Stochastic Comparison of (n􀀀, 1)-out-of-n Systems from Multiple-Outlier Modified Proportional Hazard Rates Components in terms of Hazard Rate Order

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HOSSEINZADEH A.; Barmalzan GH.; SATTARI M.

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Journal: JOURNAL OF STATISTICAL SCIENCES Year:2022 | Volume:16 | Issue:1 Page(s): 91-108

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Information Journal Paper

Title

Stochastic Comparison of (n􀀀, 1)-out-of-n Systems from Multiple-Outlier Modified Proportional Hazard Rates Components in terms of Hazard Rate Order

Author(s)

HOSSEINZADEH A. | Barmalzan GH. | SATTARI M. | Issue Writer Certificate

Keywords

Hazard rate ordering

Multiple-outlier modified proportional hazard rates model

Submajorization order

(n 􀀀

1)-out-of-n systems

Abstract

Introduction Fail-safe systems ((n 􀀀,1)-out-of-n Systems) are commonly used in many day-to-day applied structures. A fail-safe is a special design feature that will respond when a failure occurs so that no harm happens to the system itself. The brake system in a train is an excellent example of a fail-safe system in which the brakes are held in off-position by air pressure. If a brake line splits or a carriage becomes separated, the air pressure will be lost,in that case, the brakes will be applied by a local air reservoir. However, another classic example of a fail-safe system is an elevator in which brakes are held off brake pads by tension, and if the tension gets lost, the brakes latch on the rails in the shaft, thus preventing the elevator from falling off. There are many other such fail-safe systems in common use. Balakrishnan et al. (2015) established necessary and sufficient conditions for comparing two fail-safe systems with independent homogeneous exponential components in terms of mean residual life, dispersive, hazard rate and likelihood ratio orders. Their results specifically showed how an (n−, ١, )-out-of-n system consisting of heterogeneous components with exponential lifetimes could be compared with any (m−, ١, )-out-of-m system consisting of homogeneous components with exponential lifetimes. Similarly, Zhang et al. (2019) presented sufficient (and necessary) conditions on the lifetimes of components and their survival probabilities from random shocks for comparing the lifetimes of two fail-safe systems in terms of standard stochastic, hazard rate and likelihood ratio orders. Cai et al. (2017) compared the hazard rate order of second-order statistics arising from two sets of independent multiple-outlier proportional hazard rates (PHR) samples. Material and Methods The comparison of essential characteristics associated with lifetimes of technical systems is an exciting topic in reliability theory since it usually enables us to approximate complex systems with simpler systems and subsequently obtain various bounds for important agreeing characteristics of the complex system. A convenient tool for this purpose is the theory of stochastic orderings. Results and Discussion This paper discusses the hazard rate order of (n􀀀, 1)-out-of-n systems arising from two sets of independent multiple-outlier modified proportional hazard rates components. Under certain conditions on the parameters and the Submajorization order between the sample size vectors, the hazard rate order between the (n􀀀, 1)-out-of-n systems from multiple-outlier modified proportional hazard rates is established. Conclusion In this paper, we have presented sufficient conditions for the hazard rate order between fail-safe systems. It will be of great interest to generalize the current work from lifetimes of fail-safe systems to those of k-out-of-n. Another problem of interest will be to consider the setting of general systems with several subsystems having dependent components and extend the results established here to this general case. We are currently working on these problems and hope to report those findings in a future paper.

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APA: Copy

HOSSEINZADEH, A., Barmalzan, GH., & SATTARI, M.. (2022). Stochastic Comparison of (n􀀀, 1)-out-of-n Systems from Multiple-Outlier Modified Proportional Hazard Rates Components in terms of Hazard Rate Order. JOURNAL OF STATISTICAL SCIENCES, 16(1 ), 91-108. SID. https://sid.ir/paper/1021453/en

Vancouver: Copy

HOSSEINZADEH A., Barmalzan GH., SATTARI M.. Stochastic Comparison of (n􀀀, 1)-out-of-n Systems from Multiple-Outlier Modified Proportional Hazard Rates Components in terms of Hazard Rate Order. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2022;16(1 ):91-108. Available from: https://sid.ir/paper/1021453/en

IEEE: Copy

A. HOSSEINZADEH, GH. Barmalzan, and M. SATTARI, “Stochastic Comparison of (n􀀀, 1)-out-of-n Systems from Multiple-Outlier Modified Proportional Hazard Rates Components in terms of Hazard Rate Order,” JOURNAL OF STATISTICAL SCIENCES, vol. 16, no. 1 , pp. 91–108, 2022, [Online]. Available: https://sid.ir/paper/1021453/en

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