Properties of Coherent Systems with Dependent Components

In this paper we obtain several mixture representations of the reliability function of the inactivity time of a coherent system under the condition that the system has failed at time t (> 0) in terms of the reliability functions of inactivity times of order statistics. Some ordering properties of the inactivity times of coherent systems with independent and identically distributed components are obtained, based on the stochastically ordered coefficient vectors between systems.

Section: Theorem 5 Assume That P(t) Is the Vector Of Coefficients Inmentioning

confidence: 99%

Mixture Representations of Inactivity Times of Conditional Coherent Systems and their Applications

Zhang

2010

“…From Table 1 of [9], it is easy to form a table for the conditional domination vectors similar to Table 1 above. The representation in (2.3) can be used to obtain a third mixture representation based on order statistics obtained from the component residual lifetime distribution as follows.…”

Section: ) and A I (T) = A If1:i (T)/f T (T)mentioning

confidence: 99%

“…. , a n ) satisfying n i=1 a i = 1 is referred to as the domination vector or the minimal signature (see [14] and [9], respectively). Then, we obtain…”

Section: Theorem 22 If T Is a Coherent System With Signaturementioning

confidence: 99%

Mixture Representations of Residual Lifetimes of Used Systems

Navarro

Samaniego

2008

The representation of the reliability function of the lifetime of a coherent system as a mixture of the reliability function of order statistics associated with the lifetimes of its components is a very useful tool to study the ordering and the limiting behaviour of coherent systems. In this paper, we obtain several representations of the reliability functions of residual lifetimes of used coherent systems under two particular conditions on the status of the components or the system in terms of the reliability functions of residual lifetimes of order statistics.

“…. , b n ), which depend only on the system structure, are called minimal and maximal signatures, respectively; see [19]. While some of the elements of a and b may be negative, the vectors obey the constraints …”

Section: )mentioning

confidence: 99%

Signature-Based Representations for the Reliability of Systems with Heterogeneous Components

Navarro

Samaniego

2011

Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.