Factors Affecting the Shape Parameter in the Weibull Distribution with Respect to Predicting Earliest Failures by SCC

摘要

The purpose of this discussion is to describe an approach to predicting the earliest failures by corrosion and to compare this with conventional approaches that are largely based on evaluating the mean value of data or on using only engineering judgment. The essence of the approach proposed here involves using a statistical framework typified by the Weibull distribution with its statistical parameters quantified with physical quantities from the seven principal variables that control corrosion: e.g. pH, potential, species, metal composition, metal structure, temperature, and stress. The most important parameter affecting early failures is the shape parameter, beta, as used in the Weibull distribution. The Weibull beta is observed to vary from about unity to about six in most studies but may be somewhat lower and possibly more than 10. Values for beta from similar testing exhibit good agreement. While values for theta and to exhibit intuitively expected patterns, values for beta do not always follow such patterns. While it would be expected for beta to be proportional to stressors, such as temperature, stress, and concentration, this only occurs in about half the cases examined. Applying beta to predictions must be undertaken with great care. Low values of beta in the range of unity are most important since, for example, at a failure probability of 10 .4 the time to failure with a beta =l is 10~(-4) of the mean failure time. This means that for a theta=-10 years, the earliest failure would occur in about half a day. It is shown that the values of beta can be related to terms of physical processes. It is possible to provide reasonable insights into predicting early failures with an approach involving an estimation of theta and taking a conservative value for beta. It is emphasized here that the values of beta are implicit in combinations of the materials, environments and applications. The values of beta are more in the category of cause rather than result.