# Compute the expected lifetime of a given system

### Description

Computes the expected lifetime of a system/network specified by its signature or graph structure when the components have Exponential lifetime distribution with specified rate. Useful for ordering systems/networks by expected lifetime.

### Usage

1 2 3 | ```
expectedSystemLifetimeExp(g, rate=1)
expectedNetworkLifetimeExp(g, rate=1)
expectedSignatureLifetimeExp(s, rate=1)
``` |

### Arguments

`g` |
an |

`s` |
the signature vector of the system/network whose expected lifetime is to be computed. |

`rate` |
the rate parameter of the Exponential distribution. |

### Details

The system or network can be specified by means of an `igraph`

object, whereby each end of the system is denoted by nodes names "s" and "t" which are taken to be perfectly reliable. It is easy to construct the appropriate graph representation using the function `graph.formula`

.

Alternatively, the signature may be provided instead (the other functions simply use the graph object to compute the signature).

### Value

All the functions return a single scalar value which is the expected lifetime.

### Note

Please feel free to email aslett@stats.ox.ac.uk with any queries or if you encounter errors when running this function.

### Author(s)

Louis J.M. Aslett aslett@stats.ox.ac.uk (http://www.louisaslett.com/)

### References

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

### See Also

`computeSystemSignature`

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
# Find the expected lifetime of two component series system
expectedSystemLifetimeExp(graph.formula(s -- 1 -- 2 -- t))
# Find the expected lifetime of two component series system using it's signature directly
expectedSignatureLifetimeExp(c(1,0))
# Find the expected lifetime of two component parallel system
expectedSystemLifetimeExp(graph.formula(s -- 1:2 -- t))
# Find the expected lifetime of two component parallel system using it's signature directly
expectedSignatureLifetimeExp(c(0,1))
``` |

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