Method-of-moments estimators of a scale parameter based on samples from a coherent system

Abstract

In this paper, we study the estimation of a scale parameter from a sample of lifetimes of coherent systems with a fixed structure. We assume that the components are independent and identically distributed having a common distribution which belongs to a scale parameter family. Some results are obtained as well for dependent (exchangeable) components. To this end, we will use the representations for the distribution function of a coherent system based on signatures. We prove that the efficiency of the estimators depends on the structure of the system and on the scale parameter family. In the dependence case, it also depends on the baseline copula function.

Predicting failure times of coherent systems

“…Therefore, the main task for future research is to extend these results to systems with heterogeneous components. Another further research is to develop parametric inference procedures for specific systems, reliability functions and copulas to estimate the unknown parameters in the model (i.e., the parameters in the reliability function and/or the survival copula), see, for example, Macci and Navarro (2023), Yang et al (2016) and the references therein.…”

“…It was used in Navarro and Buono (2023) to predict $$$ k $$$‐out‐of‐$$$ n $$$ systems. When we only have training data available, we could use the empirical QR techniques to estimate these QR curves or to estimate the parameters in the copula and/or in the components' distributions, see Example 4.1 and Koenker (2005), Macci and Navarro (2023), Nelsen (2006), Takeuchi et al (2006).…”