Predicting failures in power plant components

Slowly growing defects in the components of a certain power station unit have led to intermittent failure of the unit with consequent loss of generation and cost of repairs. An expensive nondestructive testing (NDT) programme regularly identifies and removes many of the defects while the unit is off-line, but its effectiveness is restricted to defects above a certain detection size as well as to those in accessible parts of the unit. Cooperation between engineers and mathematicians, stimulated by a need to prioritize NDT schedules and make decisions on large-scale component replacement, has led to the development of a stochastic model which predicts future failures in the unit given any number of proposed strategies. A frequency distribution of defect sizes is obtained by scaling up the distribution found in a sample of components removed from the unit. Then, using a simple crack-propagation model, the growth of thousands of defects is simulated (a Monte Carlo procedure) to get a distribution of finishing depths given an initial depth and a growth period. Defect populations, growth patterns, and inspections are all represented by matrices whose products supply the mean failure predictions. To date, predictions and failure experience have matched very well, although confidence must decline as the time scale of predictions increases. The model is in current use to evaluate rival strategies, the aim being to minimize total costs.