Coherent systems with multistate components

Caldarola, L

doi:10.1016/0029-5493(80)90102-8

Cited by 70 publications

(15 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If {X (t)} is stochastically monotone (which is not guaranteed from the monotonicity of {X(t)}) and E ∩ C is irreducible (with respect to {X (t)}), then we can use the lower bound of Theorem 2. If {X (t)} is not monotone, then we may construct a monotone R with R ≤ Q and use (5) to compute a bound.…”

Section: Bounds For the Reliability Functionmentioning

confidence: 99%

“…Hence we rather have a partial ordering, with "functioning" being better than each of the failure states, while no other pairs of states are comparable. More specifically, Caldarola 5 argued that it would be very hard to decide whether or not the state "failed closed" of a curcuit breaker is more failed than the state "failed open". In addition, for a given component the ordering of the states may depend upon the system to which the component belongs.…”

Section: Introductionmentioning

confidence: 99%

“…A supercomponent involving m binary components would then for example have 2 m partially ordered states. This idea was considered by Caldarola 5 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bounds for the Reliability of Multistate Systems with Partially Ordered State Spaces and Stochastically Monotone Markov Transitions

Lindqvist

2003

Int. J. Rel. Qual. Saf. Eng.

View full text Add to dashboard Cite

Consider a multistate system with partially ordered state space E, which is divided into a set C of working states and a set D of failure states. Let X(t) be the state of the system at time t and suppose {X(t)} is a stochastically monotone Markov chain on E. Let T be the failure time, i.e., the hitting time of the set D. We derive upper and lower bounds for the reliability of the system, defined as Pm(T > t) where m is the state of perfect system performance.

show abstract

Section: Bounds For the Reliability Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bounds for the Reliability of Multistate Systems with Partially Ordered State Spaces and Stochastically Monotone Markov Transitions

Lindqvist

2003

Int. J. Rel. Qual. Saf. Eng.

View full text Add to dashboard Cite

show abstract

“…Griffth [3] presented an axiomatic development of multi-state systems and studied two weaker ones in three types of coherence based on the strength of the relevancy axiom. Recent years, multi-state system enlarged from the binary components and systems has been greatly investigated and improved [4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A study of complete lattice in multi-state coherent system reliability analysis

Pang

Lai

2013

2013 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering (QR2MSE)

View full text Add to dashboard Cite

Systematic reliability analysis of a multi-state coherent system (MCS) is presented in this paper. Most available models for reliability purpose are addressed under the following assumptions: (1). the state sets of the system and its components are totally ordered. (2). the system and its components are considered to be in one of two states: perfect functioning or complete failure. However, both of the two model assumptions over-simplify the reality and limit the model application. In this paper, the multi-state coherent system is analyzed on the assumption that the state sets of the system and its components are complete lattices from probabilistic and possibilistic point of view.

show abstract

“…Yu et al [19] relaxed this assumption and introduced a partially ordered state set to define a generalized multistate monotone coherent system. An alternative approach that does not use ordered state set is proposed by Caldarola in [5]. In his method, each state of a component is assigned a Boolean variable that indicates whether or not the component is in a particular state.…”

Section: Introductionmentioning

confidence: 99%

A BDD-based algorithm for analysis of multistate systems with multistate components

Zang

Wang

Sun

et al. 2003

IEEE Trans. Comput.

View full text Add to dashboard Cite

In this paper, a new algorithm based on Binary Decision Diagram (BDD) for the analysis of a system with multistate components is proposed. Each state of a multistate component is represented by a Boolean variable, and a multistate system is represented by a series of multistate fault trees. A Boolean algebra with restrictions on variables is used to address the dependence among these Boolean variables that collectively represent the same component and a new BDD operation is proposed to realize this Boolean algebra. Due to the nature of the BDD, the sum of disjoint products (SDP) can be implicitly represented, which avoids huge storage and high computational complexity for large multistate systems. Some applications are given to illustrate the use of our new algorithm.

show abstract

Coherent systems with multistate components

Cited by 70 publications

References 4 publications

Bounds for the Reliability of Multistate Systems with Partially Ordered State Spaces and Stochastically Monotone Markov Transitions

Bounds for the Reliability of Multistate Systems with Partially Ordered State Spaces and Stochastically Monotone Markov Transitions

A study of complete lattice in multi-state coherent system reliability analysis

A BDD-based algorithm for analysis of multistate systems with multistate components

Contact Info

Product

Resources

About