Fuzzy reliability analysis with only censored data

• In some cases, failure times cannot be observed, having only censored data.
• Estimation methods are not applicable and a high degree of uncertainty is present.
• Fuzzy probability theory to involve the uncertainty and process knowledge is proposed.
• Fuzzy reliability and fuzzy time for inspection including uncertainty are obtained.
• RBI method is used to establish inspection frequency, based on a fuzzy target risk.

It is expected that samples in reliability analysis contain both censored and complete failure data; thus, the maximum likelihood method is used to estimate the parameters of the related distribution. Nonetheless, samples may contain only censored data; therefore introducing a high degree of uncertainty which does result in non-viability for either the likelihood method or for statistical inference. This paper proposes the use of fuzzy probability theory to account for the uncertainty and the prior knowledge of the process in the parameters׳ estimation, for censored data. The proposed method was applied to risk based inspection. Results demonstrate that our method represents a reliable option for using the expert knowledge about the component and the physics of the failure mode. Additionally, an inspection time was estimated based on target risk; the results confirm that the methodology could be used to develop maintenance plans.