Probabilistic sensitivity analysis of system availability using Gaussian processes

Alireza Daneshkhah, Tim Bedford

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The availability of a system under a given failure/repair process is a function of time which can be determined through a set of integral equations and usually calculated numerically. We focus here on the issue of carrying out sensitivity analysis of availability to determine the influence of the input parameters. The main purpose is to study the sensitivity of the system availability with respect to the changes in the main parameters. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulae are well known. Unfortunately, in more general cases availability is often a complicated function of the parameters without closed form solution. Thus, the computation of sensitivity measures would be time-consuming or even infeasible.

In this paper, we show how Sobol and other related sensitivity measures can be cheaply computed to measure how changes in the model inputs (failure/repair times) influence the outputs (availability measure). We use a Bayesian framework, called the Bayesian analysis of computer code output (BACCO) which is based on using the Gaussian process as an emulator (i.e., an approximation) of complex models/functions. This approach allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than other methods.

The emulator-based sensitivity measure is used to examine the influence of the failure and repair densities' parameters on the system availability. We discuss how to apply the methods practically in the reliability context, considering in particular the selection of parameters and prior distributions and how we can ensure these may be considered independent—one of the key assumptions of the Sobol approach. The method is illustrated on several examples, and we discuss the further implications of the technique for reliability and maintenance analysis.
Original languageEnglish
Pages (from-to)82-93
Number of pages12
JournalReliability Engineering & System Safety
Volume112
Early online date26 Nov 2012
DOIs
Publication statusPublished - Apr 2013

Fingerprint

Sensitivity analysis
Availability
Repair
Integral equations

Keywords

  • Sensitivity analysis
  • Gaussian process
  • system avilability
  • Sobol indices
  • dependency
  • computer code model output

Cite this

Probabilistic sensitivity analysis of system availability using Gaussian processes. / Daneshkhah, Alireza; Bedford, Tim .

In: Reliability Engineering & System Safety, Vol. 112, 04.2013, p. 82-93.

Research output: Contribution to journalArticle

@article{8446b87d602e435897550b9c007f3bf1,
title = "Probabilistic sensitivity analysis of system availability using Gaussian processes",
abstract = "The availability of a system under a given failure/repair process is a function of time which can be determined through a set of integral equations and usually calculated numerically. We focus here on the issue of carrying out sensitivity analysis of availability to determine the influence of the input parameters. The main purpose is to study the sensitivity of the system availability with respect to the changes in the main parameters. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulae are well known. Unfortunately, in more general cases availability is often a complicated function of the parameters without closed form solution. Thus, the computation of sensitivity measures would be time-consuming or even infeasible.In this paper, we show how Sobol and other related sensitivity measures can be cheaply computed to measure how changes in the model inputs (failure/repair times) influence the outputs (availability measure). We use a Bayesian framework, called the Bayesian analysis of computer code output (BACCO) which is based on using the Gaussian process as an emulator (i.e., an approximation) of complex models/functions. This approach allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than other methods.The emulator-based sensitivity measure is used to examine the influence of the failure and repair densities' parameters on the system availability. We discuss how to apply the methods practically in the reliability context, considering in particular the selection of parameters and prior distributions and how we can ensure these may be considered independent—one of the key assumptions of the Sobol approach. The method is illustrated on several examples, and we discuss the further implications of the technique for reliability and maintenance analysis.",
keywords = "Sensitivity analysis, Gaussian process, system avilability, Sobol indices, dependency, computer code model output",
author = "Alireza Daneshkhah and Tim Bedford",
year = "2013",
month = "4",
doi = "10.1016/j.ress.2012.11.001",
language = "English",
volume = "112",
pages = "82--93",
journal = "Reliability Engineering and System Safety",
issn = "0951-8320",
publisher = "Elsevier",

}

TY - JOUR

T1 - Probabilistic sensitivity analysis of system availability using Gaussian processes

AU - Daneshkhah, Alireza

AU - Bedford, Tim

PY - 2013/4

Y1 - 2013/4

N2 - The availability of a system under a given failure/repair process is a function of time which can be determined through a set of integral equations and usually calculated numerically. We focus here on the issue of carrying out sensitivity analysis of availability to determine the influence of the input parameters. The main purpose is to study the sensitivity of the system availability with respect to the changes in the main parameters. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulae are well known. Unfortunately, in more general cases availability is often a complicated function of the parameters without closed form solution. Thus, the computation of sensitivity measures would be time-consuming or even infeasible.In this paper, we show how Sobol and other related sensitivity measures can be cheaply computed to measure how changes in the model inputs (failure/repair times) influence the outputs (availability measure). We use a Bayesian framework, called the Bayesian analysis of computer code output (BACCO) which is based on using the Gaussian process as an emulator (i.e., an approximation) of complex models/functions. This approach allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than other methods.The emulator-based sensitivity measure is used to examine the influence of the failure and repair densities' parameters on the system availability. We discuss how to apply the methods practically in the reliability context, considering in particular the selection of parameters and prior distributions and how we can ensure these may be considered independent—one of the key assumptions of the Sobol approach. The method is illustrated on several examples, and we discuss the further implications of the technique for reliability and maintenance analysis.

AB - The availability of a system under a given failure/repair process is a function of time which can be determined through a set of integral equations and usually calculated numerically. We focus here on the issue of carrying out sensitivity analysis of availability to determine the influence of the input parameters. The main purpose is to study the sensitivity of the system availability with respect to the changes in the main parameters. In the simplest case that the failure repair process is (continuous time/discrete state) Markovian, explicit formulae are well known. Unfortunately, in more general cases availability is often a complicated function of the parameters without closed form solution. Thus, the computation of sensitivity measures would be time-consuming or even infeasible.In this paper, we show how Sobol and other related sensitivity measures can be cheaply computed to measure how changes in the model inputs (failure/repair times) influence the outputs (availability measure). We use a Bayesian framework, called the Bayesian analysis of computer code output (BACCO) which is based on using the Gaussian process as an emulator (i.e., an approximation) of complex models/functions. This approach allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than other methods.The emulator-based sensitivity measure is used to examine the influence of the failure and repair densities' parameters on the system availability. We discuss how to apply the methods practically in the reliability context, considering in particular the selection of parameters and prior distributions and how we can ensure these may be considered independent—one of the key assumptions of the Sobol approach. The method is illustrated on several examples, and we discuss the further implications of the technique for reliability and maintenance analysis.

KW - Sensitivity analysis

KW - Gaussian process

KW - system avilability

KW - Sobol indices

KW - dependency

KW - computer code model output

U2 - 10.1016/j.ress.2012.11.001

DO - 10.1016/j.ress.2012.11.001

M3 - Article

VL - 112

SP - 82

EP - 93

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

ER -