Reliability prediction using an unequal interval grey model

Abstract

An unequal interval grey model is constructed to predict component reliability using meantime between failure data. The initial grey model developed focuses on predicting failure tendencies using equal time intervals or an equally spaced interval sequence for small sample sizes. Using this approach, the grey model does a poor job of predicting component reliabilities. To better predict component reliability at a random failure time an unequal time interval grey model is constructed. An improved formula expression for the first-order accumulated generation operator is developed. Using this formula and the whitened equation for the grey differential model, yields a higher prediction precision for the improved unequal interval grey model. A numerical example is used to illustrate the method mentioned above. These results are compared with parametric estimates found using the maximum likelihood method as well as with Kaplan-Meier nonparametric estimates of reliability. The results indicate that the unequal time interval grey model is capable of predicting component reliabilities better than maximum likelihood estimation approach and the Kaplan-Meier nonparametric methods.