Inspection Intervals for Fail-Safe Structure

The Fail-Safe principle as applied to aircraft structural design implies that there is insufficient knowledge of the life capability of the design. Control of inspection intervals is not supported by risk calculations, yet only a sample of aircraft is inspected, at intervals whose duration is rapidly increased. This paper provides risk estimates based on a simple mathematical model. Catastrophic failure is treated in two stages modeled respectively by 2-parameter and 3-parameter Weibull distributions. Bayes inferences are made about the scale parameter using in-service survivor times. Only those cases are treated for which no failures have occurred. This results in a suggested form of inspection policy. A separate non-Bayes analysis confirms the Bayes risk estimate; thus the assumed improper prior is interesting. This prior, the only simple one which is tractable for the case of no failures, transforms, for the exponential distribution, to the uniform prior, in contrast to the hyperbolic one usually used. The analysis is simplistic but provides a ball-park estimate which would otherwise be unavailable. It can be used with caution as a check on inspection programs already derived by other means. It can also serve in tutorial demonstration of the statistical effects of the various parameters, to airworthiness managers. Possibly it might form the basis of a more sophisticated analysis.