Assessing the lifetime performance index with Lomax distribution based on progressive type I interval censored sample.

In manufacturing industry, the lifetime performance index is applied to evaluate the larger-the-better quality features of products. It can quickly show whether the lifetime performance of products meets the desired level. In this article, first we obtain the maximum likelihood estimator of with two unknown parameters in the Lomax distribution on the basis of progressive type I interval censored sample. With the MLE we proposed, some asymptotic confidence intervals of are discussed by using the delta method. Furthermore, the MLE of is used to establish the hypothesis test procedure under a given lower specification limit . In addition, we also conduct a hypothesis test procedure when the scale parameter in the Lomax distribution is given. Finally, we illustrate the proposed inspection procedures through a real example. The testing procedure algorithms presented in this paper are efficient and easy to implement.