The analysis finds sharp bounds for expected values of reliability functions in k-independent random variables, implying implications for semicoherent systems.
The present study investigates the problem of determining sharp bounds for key reliability and distributional characteristics associated with order statistics. We establish pointwise sharp two-sided bounds for linear combinations of joint distribution functions and joint reliability functions of selected order statistics based on k-independent and identically distributed random variables. The proposed framework is general and also applies to arbitrarily dependent observations. The obtained results provide exact bounds for the expected values of functions of order statistics corresponding to finite-valued random variables. Furthermore, the study yields the best possible upper and lower bounds for the joint reliability function of semicoherent systems with shared exchangeable k-independent components.
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Okolewski et al. (2025) studied this question.
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