Imperfect repair continuous proportional intensity model for repairable systems and its application

Considering that traditional imperfect repair model was difficult to use in practice, a new continuous proportional intensity model with closed-form solutions was proposed based on the theory of bounded intensity process. The characteristics of the model were discussed, the formula of point maximum likelihood estimators for model parameters, as well as the important reliability indices such as the conditional reliability at given time, the s-expected number of failures, and the cumulative mean time between failure were all derived, the interval estimators of model parameters and reliability indices were given by using the Fisher information matrix method and delta method, and the assessment criterion of model was provided based on Akaike information criterion and the index of goodness-of-fit test. An example of real failure data from numerical control machine tools was taken to prove the proposed method. The results show that the closed-form solutions and confidence bounds of reliability indices for NC machine tools are obtained and the method can be well applied in practical. ©, 2015, Central South University of Technology. All right reserved.