Statistical properties of the failure time distribution for [formula omitted] steels

Abstract

A generalised three-parameter gamma distribution was fitted to three creep failure data sets obtained from BSCC. The log normal, Weibull, gamma and exponential distributions are nested within this generalised distribution and emerge when the parameters of the generalised distribution take on particular values. Standard statistical tests for parameter restrictions were then used to identify which of the above-named distributions are most supported by the data. Confidence limits for 50%, 10% and 1% quantiles of log failure time were computed using distributions most and least supported by the data. The extent to which such uncertainty about distributional form effects the size of confidence limits was also analysed. At the three stress and temperature ranges studied, the log normal distribution was best supported by the data, the Weibull distribution was least supported, whilst the two-parameter gamma and exponential distributions were rejected by the data. In each case a wide variety of three-parameter gamma distributions were supported by the data and this significantly increased the confidence limits at the lower quantile ranges.