Coherent structures and unimodality

Abstract

This paper is concerned with the preservation of unimodality under coherent structures of independent components having a common life distribution function. This result in a way generalizes a result of Alam [1], as Alam's result indirectly also deals with preservation of unimodality for (n – i + 1)-out-of-n systems of independent and identically distributed components. The usefulness of this property of coherent systems in obtaining sharper upper bounds on the reliability of the concerned system has been illustrated below for a bridge structure with components having a gamma life distribution function.

On unimodality of the lifetime distribution of coherent systems with failure-dependent component lifetimes

“…component lifetimes (see also Huang and Ghosh (1982) and Dharmadhikari and Joag-Dev (1988)). Following this, Sabnis and Nair (1997) generalized Alam's result to the setting of coherent systems. Moreover, the results on k-out-of-n systems have also been extended in another direction.…”

“…Unimodality has been studied by Sabnis and Nair (1997) for coherent systems with i.i.d. component lifetimes.…”

Low-stiction magnetic bearing for satellite application

“…2 Hence, for maximizing the axial stiffness in the case of the selected airgap of 0.8 mm, the tooth width also has to be 0.8 mm. But considering the fabricational difficulties, tooth width has been finalized as 1 mm.…”

Limiting survival functions of self‐similar structures

“…This function h is commonly referred to as the reliability polynomial of the structure. Some interesting recent developments in the reliability of structures and networks which do not involve limiting distribution functions are found in Ross and Jun [11], Lomonosov [5], Ross and Derman [10], Petakos and Tsapelas [9], Sabnis and Nair [12], and Lynn, Singpurwalla, and Smith [6].…”