Computational procedure of performance assessment of lifetime index of Pareto lifetime businesses based on confidence interval

In the service industries, the lifetime performance assessment is important. Hence, in the paper, process capability analysis is utilized to measure business performance. Moreover, the lifetime performance index CL is used as a means of measuring business performance, where L is the lower specification limit. Since the lifetime of businesses generally follow a Pareto distribution, so in the technology of data transformation, this study constructs a maximum likelihood estimator (MLE) of CL under the Pareto distribution with the right type II censored sample. The MLE of CL is then utilized to develop a confidence interval in the condition of known L. Finally, we give two examples and the Monte Carlo simulation to assess the behavior of confidence interval for the lifetime performance index CL under given confidence level. Moreover, the managers can then employ the confidence interval to determine whether the business performance adheres to the required level.