The Computational Testing Procedure for the Comprehensive Lifetime Performance Index of Burr XII Products in Multiple Production Lines

Abstract

Extending from a single production line to multiple production lines, a comprehensive life performance index is proposed for evaluating the quality of lifetime products. The connection between the comprehensive lifetime performance index and the individual lifetime performance index is explored. For products with a lifetime following Burr XII distribution for the ith production line, the maximum likelihood estimation method and the corresponding asymptotic distribution for all lifetime performance indices are derived. Checking whether the comprehensive lifetime performance index has achieved the target value is essentially the same as testing whether each individual lifetime performance index has reached its corresponding target value. A testing procedure is proposed for a given significance level using the maximum likelihood estimator as the test statistic, and the power analysis is presented through graphical representations. For the power analysis, the impacts of sample size, the number of inspection intervals, the removal probability, the level of significance, and the number of production lines on the test power are analyzed, and the results show that there is a monotonic relationship between the test power and the above five impact factors. To illustrate how to apply the proposed testing procedure, we give one practical example with two production lines to test whether the comprehensive production process is capable.