Piecewise modelling and parameter estimation of repairable system failure rate

Lifetime failure data usually presents a bathtub-shaped failure rate, and random failure phase dominates its life cycle. Relatively large errors always existed when single distribution model is used for analysis and modelling. Therefore, a bathtub-shaped reliability model based on piecewise intensity function was proposed for repairable system. Parameter estimation was studied by using maximum likelihood method in conjunction with two-stage Weibull process interval estimation and Artificial Bee Colony Algorithm. The proposed model and estimation approach fit the failure rate under bathtub curve very well, adequately reflect the duration of random failure phase, and guarantee the feasibility of quantitative analysis. Moreover, the estimated critical point of bathtub curve could be calculated. At last, the proposed model was applied in the reliability analysis of a repairable Computer Numerical Control system, and the validity of the proposed model and its parameter estimation method were verified.