Analysis of stress rupture data on fiber composites. Part 2. Determining uncertainty and removing bias in estimates

Stress rupture is a failure mode for unidirectional continuous fiber composites that is of increasing concern in composite overwrapped pressure vessels (COPVs). Stress rupture is a catastrophic failure mode with a large variance in failure times due to inherent randomness. Prediction of a composite structure's resistance to stress rupture is typically based on extensive testing at higher loads than used in service. The resulting datasets are then analyzed within the framework of a statistical model to determine an estimate of the probability that a composite structure will survive for a given lifetime under a particular load profile. For instance, in life safety applications the interest would be in ensuring a very small corresponding failure probability, such as one in a million. The statistical model parameters can be estimated in many ways, one of which is to use a maximum likelihood approach, but these estimates are of questionable value in the absence of a measure of their uncertainty. This paper presents a procedure for determining the uncertainty in such estimates, as well as removing any inherent bias. Details of the procedure are fully illustrated using data generated on model carbon/epoxy COPVs tested at the NASA White Sands Test Facility. This procedure is based in Monte-Carlo simulation of 'typical' datasets, which are then analyzed using the same method as the original dataset, thus giving a distribution of estimates. This distribution allows for quantification of uncertainty and bias. The Monte-Carlo procedure can also be used to evaluate experimental test design to determine the expected amount of uncertainty for a given test setup.