Extreme dispersions of semicoherent and mixed system lifetimes. (English) Zbl 06441355

Miziuła, Patryk; Rychlik, Tomasz

J. Appl. Probab. 52, No. 1, 117-128 (2015).

Summary: We consider semicoherent and mixed systems with exchangeable components. We present sharp lower and upper bounds on various dispersion measures (in particular, variance and median absolute deviation) of the system lifetime, expressed in terms of the system signature and the dispersion of a single component lifetime. We construct joint exchangeable distributions of component lifetimes with two-point marginals which attain the bounds in the limit.

MSC:

62N05	Reliability and life testing
60E15	Inequalities; stochastic orderings
62G30	Order statistics; empirical distribution functions

Keywords:

semicoherent system; mixed system; Samaniego signature; exchangeable random variables; sharp bound; dispersion measure; variance; median absolute deviation