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Characterizations through scale relations between coherent systems
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DOI：10.1016/j.fss.2026.109993.png)
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Abstract
En 中文
We study different characterizations of probability models based on scale relations between coherent systems with dependent and identically distributed components. The main result identifies the distributions for which there exists a general scale relation between the series system and the components’ lifetimes. This process leads us to functional equations for the reliability function. A similar result holds for parallel systems. In both cases, we provide a general solution determining the diagonal section function of the underlying copula that determines the dependence structure between the component lifetimes. This solution can be extended to general coherent systems by using the concept of distortion function. The theoretical results are illustrated with several examples. In particular, we explore relations between k-out-of-n systems (order statistics). Some inference procedures are proposed as well to show how to check these characterizations in practice.
Keywords:
Reliability
scale models
distorted distributions
copula
functional equations
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