## Abstract

The estimation of the reliability curve for technical systems is an important building block in determining maintenance policies. For a complex technical system, reliability calculations are usually based on the reliability of its components. Data on component failures is however often scarce, and to obtain meaningful estimates for the reliability of a component, and in turn of the system, it is often necessary to include expert information in the analysis.

Such expert information could come, e.g., from the component manufacturer. However, this information should often be taken with a pinch of salt, as the manufacturer might over- or understate the component reliability (overstating to, e.g., outrival a competitor, or understating to, e.g., sell more replacements). Furthermore, components might just behave differently under the conditions of the present system.

We show how such uncertain information on components can be efficiently combined with test data using a flexible nonparametric approach imposing no restrictions on the failure time distributions. For each time point t in a grid of time points and each component type k, we count the number of components still functioning in the test data, and express expert information by an interval for the expected survival probability. This interval determines a corresponding set of Beta distributions, used as a set of prior distributions in a Bayesian setting.

This leads to a tractable imprecise probability model that produces a set of posterior predictive system reliability functions. It adequately reflects uncertainty in expert information, the amount of data, and furthermore provides prior-data conflict sensitivity: Observing data that are very surprising from the viewpoint of the expert leads to a larger set, mirroring the additional uncertainty due to this conflict. Making use of the survival signature, a recently developed alternative to the system signature, the method allows for arbitrary system layouts.

Such expert information could come, e.g., from the component manufacturer. However, this information should often be taken with a pinch of salt, as the manufacturer might over- or understate the component reliability (overstating to, e.g., outrival a competitor, or understating to, e.g., sell more replacements). Furthermore, components might just behave differently under the conditions of the present system.

We show how such uncertain information on components can be efficiently combined with test data using a flexible nonparametric approach imposing no restrictions on the failure time distributions. For each time point t in a grid of time points and each component type k, we count the number of components still functioning in the test data, and express expert information by an interval for the expected survival probability. This interval determines a corresponding set of Beta distributions, used as a set of prior distributions in a Bayesian setting.

This leads to a tractable imprecise probability model that produces a set of posterior predictive system reliability functions. It adequately reflects uncertainty in expert information, the amount of data, and furthermore provides prior-data conflict sensitivity: Observing data that are very surprising from the viewpoint of the expert leads to a larger set, mirroring the additional uncertainty due to this conflict. Making use of the survival signature, a recently developed alternative to the system signature, the method allows for arbitrary system layouts.

Original language | English |
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Publication status | Published - 4 Feb 2016 |

Event | Maintenance Research Day 2016, February 4, 2016, Utrecht, The Netherlands - Utrecht, Netherlands Duration: 4 Feb 2016 → 4 Feb 2016 http://www.maintenanceresearch.nl/ |

### Conference

Conference | Maintenance Research Day 2016, February 4, 2016, Utrecht, The Netherlands |
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Country/Territory | Netherlands |

City | Utrecht |

Period | 4/02/16 → 4/02/16 |

Internet address |