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Information Journal Paper

Title

Reliability Equivalence Factors of Series and Parallel Systems in Proportional Hazards Model

Pages

  253-273

Abstract

 Introduction Redundancy is a commonly used technique to increase the reliability of a system. However, because of some limitations, such as high cost and space, this method cannot always be used. These constraints can be overcome by using a Reduction Method, which involves improving the system’, s reliability by reducing the failure rate of some of its components by a constant factor 0 < ,< 1. Based on the reduction factor, the concept of Reliability Equivalence Factors was introduced by Rade (1993). The reliability equivalence factor (REF) is a factor as 0 < ,< 1 by which the failure rates of some system components are reduced such that the system reliability reaches the reliability of a system that is improved via an arbitrary method. The REF is a valuable tool for comparing the different ways of system improvements. Consider a coherent system of order n, with component lifetimes T1, : : :, Tn. If P(Ti > t) = ,F, i(t) for some , i > 0 and i = 1, : : :, n, then the mutually s-independent lifetime variables T = (T1, : : :, Tn) follow the proportional hazard rates (PHR) model, where ,F is the baseline survival function and ,= (, 1, : : :, , n) is the proportional hazard vector. In this paper, we apply the Reduction Method in series and parallel systems under the PHR model and discuss the relation of the REF and , . Material and Methods We discuss that the Reduction Method can be considered as a special case of the PHR model and then, based on REF, compare the homogeneous and heterogeneous strategies in the PHR model. Results and Discussion This paper considers the conditions in which the lifetimes of two series or parallel systems are stochastically ordered. We then discuss how the REF can be used to improve and equivalent the system lifetimes. The REFs are often obtained by numerical methods and mathematical packages in literature. In this paper, based on survival and mean Reliability Equivalence Factors, the equivalence between the Reduction Method and heterogeneous strategy in the PHR model for the parallel and series systems with independent components is investigated. We present closed formulas for the REF of series and parallel systems when the lifetimes of components follow the PHR model. Sufficient conditions for the relative ageing comparisons of the improved series and parallel systems under the PHR model and Reduction Method are also developed. Conclusion There is a close relationship between the PHR model and the Reduction Method. We apply this relation and find some conditions for the equivalence of the lifetimes of two series or parallel systems. We also compare the lifetimes of two series systems under the PHR model and the Reduction Method based on the ageing faster orders in terms of the hazard and the reversed hazard rates. By a study on the Reduction Method and heterogeneous strategy in the PHR model for the series system with the component reliability vector , F (t) = ( ,F(t), : : :, ,F(t)), we find that the improved systems by the Reduction Method and heterogeneous strategy in the PHR model are equivalent in the sense of ageing faster order in the hazard rate. For the parallel and series systems with the component reliability vector , F (t) = ( ,F(t), : : :, ,F(t)), we also find the sufficient condition under that the improved systems by the Reduction Method age faster than those systems, improved by heterogeneous strategy in the PHR model.

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    APA: Copy

    ETMINAN, J., KHANJARI, M., & CHAHKANDI, M.. (2023). Reliability Equivalence Factors of Series and Parallel Systems in Proportional Hazards Model. JOURNAL OF STATISTICAL SCIENCES, 16(2 ), 253-273. SID. https://sid.ir/paper/1021865/en

    Vancouver: Copy

    ETMINAN J., KHANJARI M., CHAHKANDI M.. Reliability Equivalence Factors of Series and Parallel Systems in Proportional Hazards Model. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2023;16(2 ):253-273. Available from: https://sid.ir/paper/1021865/en

    IEEE: Copy

    J. ETMINAN, M. KHANJARI, and M. CHAHKANDI, “Reliability Equivalence Factors of Series and Parallel Systems in Proportional Hazards Model,” JOURNAL OF STATISTICAL SCIENCES, vol. 16, no. 2 , pp. 253–273, 2023, [Online]. Available: https://sid.ir/paper/1021865/en

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