Process capability indices have been extensively employed to assess process performance in order to drive ongoing enhancements in quality and productivity, where the larger, the better for these lifetime performance indices. For multiple production lines, an overall lifetime performance index is proposed and the relationship between the overall lifetime performance index and the individual lifetime performance index is displayed. For products with lifetimes following the Weibull distribution for the ith production line, the maximum likelihood estimator and asymptotic distribution for the individual lifetime performance index were investigated so that the maximum likelihood estimator and asymptotic distribution for the overall lifetime performance index were also derived. Based on the pre-assigned target value of the overall lifetime performance index, the target value of an individual lifetime performance index could be determined. To test whether the overall lifetime performance index reached the target value was equivalent to testing whether the individual lifetime performance index reached the corresponding target value. The testing procedure based on the maximum likelihood estimator is given in this paper and the analysis of test power is displayed by figures. Finally, one practical example is given to illustrate the use of this testing algorithmic procedure to determine whether the overall production process was capable.
