The lifetime performance index is widely used in the manufacturing industry to assess the capability and effectiveness of production processes. A new overall lifetime performance index is proposed when multiple parts of products are produced in multiple dependent production lines. Each individual lifetime performance index for a single production line is connected to the overall lifetime performance index for multiple independent or dependent production lines. The overall lifetime performance index increases with the overall process yield. We analyze the maximum likelihood estimators for the individual lifetime performance indices using progressively type I interval-censored samples while the lifetime of the ith part of products follows a Gompertz distribution for either independent or dependent cases. To determine whether the overall lifetime performance index meets the desired target value, the maximum likelihood estimator for the individual index is utilized separately to conduct the testing procedures about the overall lifetime performance index for either independent or dependent cases. Power analysis of the multiple testing procedure is illustrated with figures, and key findings are summarized. A simulation study is conducted for the test powers. Lastly, a practical example involving products with two parts is presented to demonstrate the application of the proposed testing algorithm. Given the asymmetry of the lifetime distribution, this research aligns with the study of asymmetric probability distributions and their diverse applications across various fields.
