Selection of failure time within test time interval for group reliability data analysis

Group reliability data are common in reliability test. In the parameter estimation for group data, probability plotting is usually considered as a simple and fast method. When the interval times are small, the mid-point of test time intervals is heuristically considered as the failure time of those devices that failed during the time interval, especially for the group data with different inspection interval. The upper endpoint of test time interval is another alternative when the units under consideration have a common inspection schedule and all unfailed units have run beyond all failed units. However, the accuracy of the estimation in considering the mid-point or endpoint of the test time interval has not been evaluated rigorously. The effect of sample size, the width of the test time interval, and the life distribution of the devices on the accuracy of the estimation have not been investigated. From this study, we find that, for different distributions, different selection of failure time will affect the accuracy of estimated parameters. In order to have maximum accuracy in parameter estimation, an optimum time point within test time interval is proposed for different distribution. Here probability plotting is used for analyzing singly censored group data with common inspection schedule. Relative error of the estimated parameters is used to determine the estimation accuracy with respect to selected failure time within a test time interval for group data analysis. Three common types of life distributions, namely the exponential, normal and lognormal distributions, are investigated.