Engineering method for estimating reliability growth

Estimation of model parameters is the starting point of estimation of reliability growth. Existing estimation methods, in our opinion, suffer from the shortcoming of point estimation of model parameters. Practical engineering needs interval estimates of model parameters rather than point estimates. We aim to present an engineering estimation method that is based on interval analysis of model parameters. Based on the nonparametric model of the multi-system synchronous development, the linear regression theory is employed to obtain the point estimations of a and b, the reliability growth model parameters expressed in the intensity function λ(t) = abt^b-1. Some accurate distributions of the process parameters in the regression can be given. The intervals of model parameter b and process parameters are calculated corresponding to the given confidence levels directly. By the use of the equivalent transformation from the confidence intervals of b and some process parameter, the approximate confidence interval of the model parameter a is derived. By employing the interval-step-dividing method, the interval of the mean time between failure (MTBF) is analyzed corresponding to the given confidence intervals of a and b. The engineering example illustrates the rationality of the presented method. The curve of the lower boundary of MTBF vs confidence in the example provides more information for engineering application.