Abstract
The notion of a coherent system allows us to formalize how the random lifetime of the system is connected to the random lifetimes of its components. These connections are also generators of new pliant distributions, being those of various mixes of minimum and maximum of random variables. In this paper, a new four-parameter lifetime probability distribution is introduced by using the notion of a coherent system. Its structural properties are assessed and evaluated, including the analytical study of its main functions, stochastic dominance results, moments, and moment generating function. The proposed distribution, in particular, is proving to be efficient at fitting data with slight negative skewness and platykurtic as well as leptokurtic nature. This is illustrated by the analysis of three relevant real-life data sets, two in reliability and another in production, exhibiting the significance of the introduced model in comparison to various well-known models in statistical literature.
Highlights
Coherent systems are very important in reliability theory and data analysis
A n-component system is said to be coherent if its structure function is monotonic, and it contains no irrelevant components
We suppose that they are independent and subjected to the following distributional assumptions: U1 follows the exponential distribution with parameter λ1 > 0, U2 follows the exponential distribution with parameter λ2 > 0, and U3 follows the Weibull
Summary
The notion of a coherent system allows us to formalize how the random lifetime of the system is connected to the random lifetimes of its components These connections are generators of new pliant distributions, being those of various mixes of minimum and maximum of random variables. The proposed distribution, in particular, is proving to be efficient at fitting data with slight negative skewness and platykurtic as well as leptokurtic nature. This is illustrated by the analysis of three relevant real-life data sets, two in reliability and another in production, exhibiting the significance of the introduced model in comparison to various well-known models in statistical literature
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