### Abstract

The availability of a system under a failure/repair process, is a function of time which can be calculated numerically. The sensitivity analysis of this quantity with respect to change in parameters is the main objective of this paper. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulas are well known. Unfortunately, in more general cases this quantity could be a complicated function of the parameters. Thus, the computation of the sensitivity measures would be infeasible or might be time-consuming. In this paper, we present a Bayesian framework originally introduced by Oakley and O'Hagan [7] which unifies the various tools of probabilistic sensitivity analysis. These tools are well-known to Bayesian Analysis of Computer Code Outputs, BACCO. In our case, we only need to quantify the availability measure at a few parameter values as the inputs and then using the BACCO to get the interpolation function/ sensitivity to the parameters. The paper gives a brief introduction to BACCO methods, and the availability problem. It illustrates the technique through the use of an example and makes a comparison to other methods available.

Original language | English |
---|---|

Title of host publication | Advances in Mathematical Modeling for Reliability |

Publisher | Delft University Press |

Pages | 46-62 |

Number of pages | 17 |

ISBN (Print) | 9781586038656 |

Publication status | Published - 1 May 2008 |

Externally published | Yes |

### Fingerprint

### Keywords

- Availability
- Bayesian analysis
- Computer models
- Emulator
- Gaussian process
- Sensitivity analysis

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Advances in Mathematical Modeling for Reliability*(pp. 46-62). Delft University Press.

**Sensitivity analysis of a reliability system using Gaussian processes.** / Bedford, Tim; Quigley, John; Walls, Lesley; Daneshkhah, Alireza; Alkali, Babakali; Hardman, Gavin.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Mathematical Modeling for Reliability.*Delft University Press, pp. 46-62.

}

TY - CHAP

T1 - Sensitivity analysis of a reliability system using Gaussian processes

AU - Bedford, Tim

AU - Quigley, John

AU - Walls, Lesley

AU - Daneshkhah, Alireza

AU - Alkali, Babakali

AU - Hardman, Gavin

PY - 2008/5/1

Y1 - 2008/5/1

N2 - The availability of a system under a failure/repair process, is a function of time which can be calculated numerically. The sensitivity analysis of this quantity with respect to change in parameters is the main objective of this paper. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulas are well known. Unfortunately, in more general cases this quantity could be a complicated function of the parameters. Thus, the computation of the sensitivity measures would be infeasible or might be time-consuming. In this paper, we present a Bayesian framework originally introduced by Oakley and O'Hagan [7] which unifies the various tools of probabilistic sensitivity analysis. These tools are well-known to Bayesian Analysis of Computer Code Outputs, BACCO. In our case, we only need to quantify the availability measure at a few parameter values as the inputs and then using the BACCO to get the interpolation function/ sensitivity to the parameters. The paper gives a brief introduction to BACCO methods, and the availability problem. It illustrates the technique through the use of an example and makes a comparison to other methods available.

AB - The availability of a system under a failure/repair process, is a function of time which can be calculated numerically. The sensitivity analysis of this quantity with respect to change in parameters is the main objective of this paper. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulas are well known. Unfortunately, in more general cases this quantity could be a complicated function of the parameters. Thus, the computation of the sensitivity measures would be infeasible or might be time-consuming. In this paper, we present a Bayesian framework originally introduced by Oakley and O'Hagan [7] which unifies the various tools of probabilistic sensitivity analysis. These tools are well-known to Bayesian Analysis of Computer Code Outputs, BACCO. In our case, we only need to quantify the availability measure at a few parameter values as the inputs and then using the BACCO to get the interpolation function/ sensitivity to the parameters. The paper gives a brief introduction to BACCO methods, and the availability problem. It illustrates the technique through the use of an example and makes a comparison to other methods available.

KW - Availability

KW - Bayesian analysis

KW - Computer models

KW - Emulator

KW - Gaussian process

KW - Sensitivity analysis

UR - http://www.scopus.com/inward/record.url?scp=84880184725&partnerID=8YFLogxK

M3 - Chapter

SN - 9781586038656

SP - 46

EP - 62

BT - Advances in Mathematical Modeling for Reliability

PB - Delft University Press

ER -