Summary: The traditional statistical process control theory assumes that the characteristic values of the quality of the processes is a normal distribution. However, in the practical processes this hypothesis is untenable. The quality characteristics of the products are assumed to obey exponential distributions, and the process capability index is used to evaluate the life time performance of the products based on type II right-censored samples.
This study constructs a uniformly minimum variance unbiased estimator (UMVUE), and the confidence interval of the life time performance index is also given. Then the UMVUE of the life time performance index is utilized to develop a new hypothesis test. Finally, a practical example is illustrated that the test method is simple and easy to operate. Moreover, this method can be employed to determine whether the products achieve the required quality level.