ReliabilityTheory (version 0.3.1)

computeSystemSignature: Compute the signature of a system

Description

The system signature (Samaniego, 2007) is an alternative to the structure function as a starting point for a structural reliability analysis. This automatically computes the signature of the specified system or network. Here, system implies components are unreliable whereas network implies links are unreliable.

Usage

computeSystemSignature(sys, cutsets=NULL, frac=FALSE)
computeNetworkSignature(sys, cutsets=NULL, frac=FALSE)

Value

computeSystemSignature returns a numeric probability vector which is the system/network signature.

Arguments

sys

a system object representing the system whose types are to be set. This should have been created by a call to createSystem.

cutsets

if the cut-sets of the system or network are already known they may be passed in as a list of numeric vectors. This can save time because cut-set computation is the slowest part of the algorithm. Leaving as NULL causes the function to find the cut sets itself.

frac

if TRUE then the function prints out signature elements as fractions rather than returning a decimal signature vector.

Author

Louis J.M. Aslett (https://www.louisaslett.com/)

Details

The signature of a system is the probability vector \(\mathbf{s}=(s_1, \dots, s_n)\) with elements: $$s_i = P(T = T_{i:n})$$ where \(T\) is the failure time of the system and \(T_{i:n}\) is the ith order statistic of the n component failure times. Likewise the network signature is the same but where components are reliable and it is links which fail. See Samaniego (2007) for details.

The system or network is specified by means of a system object, whereby each end of the system is denoted by nodes named s and t which are taken to be perfectly reliable. It is easy to construct the appropriate reliability block diagram representation using the function createSystem. Note that each physically distinct component should be separately numbered when constructing this object.

References

Samaniego, F. J. (2007), System Signatures and Their Applications in Engineering Reliability, Springer.

See Also

computeSystemSurvivalSignature

Examples

# Find the signature of two component series system (which is just s=(1, 0))
computeSystemSignature(createSystem(s -- 1 -- 2 -- t))

# Find the signature of two component parallel system (which is just s=(0, 1))
computeSystemSignature(createSystem(s -- 1:2 -- t))

# Find the signature of the five component 'bridge' system (which
# is s=(0, 0.2, 0.6, 0.2, 0))
computeSystemSignature(createSystem(s -- 1 -- 2 -- t, s -- 3 -- 4 -- t, 1:2 -- 5 -- 3:4))