Log-linear process modeling for repairable systems with time trends and its applications in reliability assessment of numerically controlled machine tools

Abstract

Two non-homogeneous Poisson processes including the power law process and the log-linear process with reliability improvement or deterioration are analyzed. Based on Akaike information criterion and Bayesian information criterion, the best model of failure data is presented. The point maximum likelihood and interval estimators of the parameters, as well as seven reliability indices of the log-linear process model, such as cumulative mean time between failures, cumulative number of failures, reliability at a given time, and warranty time given reliability are given. In tests for failure time trends, both the graphical methods, including the cumulative failures versus time plot and the total-time-on-test plot, and the analytical methods including the Laplace, the Military Handbook, and the Lewis–Robinson tests are used. Three real cases for failure data with failure truncation and time truncation of multiple numerically controlled machine tools are given to illustrate the use of the proposed models.