### Abstract

Language | English |
---|---|

Number of pages | 28 |

Journal | Technometrics |

Early online date | 12 Sep 2017 |

DOIs | |

Publication status | E-pub ahead of print - 12 Sep 2017 |

### Fingerprint

### Keywords

- multi-attribute utility
- Bayesian design of experiments
- design for reliability
- Benter model

### Cite this

*Technometrics*. https://doi.org/10.1080/00401706.2017.1377637

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**Emulation of utility functions over a set of permutations : sequencing reliability growth tasks.** / Wilson, Kevin J; Henderson, Daniel A; Quigley, John.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Emulation of utility functions over a set of permutations

T2 - Technometrics

AU - Wilson, Kevin J

AU - Henderson, Daniel A

AU - Quigley, John

PY - 2017/9/12

Y1 - 2017/9/12

N2 - We consider Bayesian design of experiments problems in which we maximise the prior expectation of a utility function over a set of permutations, for example when sequencing a number of tasks to perform. When the number of tasks is large and the expected utility is expensive to compute, it may be unreasonable or infeasible to evaluate the expected utility of all permutations. We propose an approach to emulate the expected utility using a surrogate function based on a parametric probabilistic model for permutations. The surrogate function is fitted by maximising the correlation with the expected utility over a set of training points. We propose a suitable transformation of the expected utility to improve the fit. We provide results linking the correlation between the two functions and the number of expected utility evaluations to undertake. The approach is applied to the sequencing of reliability growth tasks in the development of hardware systems, in which there is a large number of potential tasks to perform and engineers are interested in meeting a reliability target subject to minimising costs and time. An illustrative example shows how the approach can be used and a simulation study demonstrates the performance of the approach more generally.

AB - We consider Bayesian design of experiments problems in which we maximise the prior expectation of a utility function over a set of permutations, for example when sequencing a number of tasks to perform. When the number of tasks is large and the expected utility is expensive to compute, it may be unreasonable or infeasible to evaluate the expected utility of all permutations. We propose an approach to emulate the expected utility using a surrogate function based on a parametric probabilistic model for permutations. The surrogate function is fitted by maximising the correlation with the expected utility over a set of training points. We propose a suitable transformation of the expected utility to improve the fit. We provide results linking the correlation between the two functions and the number of expected utility evaluations to undertake. The approach is applied to the sequencing of reliability growth tasks in the development of hardware systems, in which there is a large number of potential tasks to perform and engineers are interested in meeting a reliability target subject to minimising costs and time. An illustrative example shows how the approach can be used and a simulation study demonstrates the performance of the approach more generally.

KW - multi-attribute utility

KW - Bayesian design of experiments

KW - design for reliability

KW - Benter model

U2 - 10.1080/00401706.2017.1377637

DO - 10.1080/00401706.2017.1377637

M3 - Article

JO - Technometrics

JF - Technometrics

SN - 0040-1706

ER -