Some results on information properties of coherent systems

Abstract

Mathematics Subject Classification: 62N05; 94A17This paper considers information properties of coherent systems when component lifetimes are independent and identically distributed. Some results on the entropy of coherent systems in terms of ordering properties of component distributions are proposed. Moreover, various sufficient conditions are given under which the entropy order among systems as well as the corresponding dual systems hold. Specifically, it is proved that under some conditions, the entropy order among component lifetimes is preserved under coherent system formations.The findings are based on system signatures as a useful measure from comparison purposes. Furthermore, some results on the system's entropy are derived when lifetimes of components are dependent and identically distributed. Several illustrative examples are also given.

Further results on the generalized cumulative entropy

“…. , from (37) and (38) Hence, noting that CE n (X 1 ) = 1 2 n+1 , we immediately have that CE n ( F m ) is an unbiased and consistent estimator for the generalized cumulative entropy of a population uniformly distributed in [0, 1].…”

“…It is also invoked to deal with information in the context of theoretical neurobiology, thermodynamics, and reliability theory. For some recent applications of Shannon's entropy to the ordering of coherent systems see Toomaj et al [38] and references therein. In many realistic situations such as survival analysis and reliability engineering, one has information about the past lifetime, i. e. the time elapsed after failure till time t, given that the unit has already failed.…”

On the information properties of working used systems using dynamic signature

“…It is easy to check that Therefore, the upper bound in (26) is sharper than the upper bound in (25). The optimal index r ⋆ , when all components of the systems are working, has been computed by Toomaj et al 26 for coherent systems with 3 and 4 components. From Table 1, it can be seen that for all systems, the upper bound in (26) is smaller than the bound in (25) and H ( s n ( n )). It is worth mentioning that like H ( s n ( n )), the new upper bound is unable to order JS(0, s ); see the last column in Table 1.…”

Tsallis Entropy of a Used Reliability System at the System Level

“…It is suitable to study the behavior of the uncertainty of the new system in terms of Tsallis entropy. For other applications and researchers concerned with measuring the uncertainty of reliability systems, we refer readers to [ 15 , 16 , 17 , 18 ] and the references therein. In contrast to the work of Alomani and Kayid [ 14 ], the aim of this work is to study some uncertainty properties of a coherent system consisting of n components and having the property that at time all components of the system are alive.…”