In practice, Process capability indices such as lifetime performance index CL indicate the relationships between the actual process performance and the manufacturing specifications, where L is the lower specification limit and it is known. Progressive first-failure censoring scheme is quite useful in many practical situations where lifetime of a product is quite high and test facilities are scarce but test material is relatively cheap. This study, under the assumption of two-parameter exponential distribution andby applying data transformation constructs a uniformly minimum variance unbiased estimator (UMVUE) of CL based on a progressive first-failure censored sample. Then the UMVUE of CL is utilized to develop the new hypothesis testing procedure. Finally, two illustrative examples are given to assess the behavior of this test statistic for testing null hypothesis under given significance level.

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