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

Abstract

In manufacturing industry, the lifetime performance index $C_L$ 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 $C_L$ 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 $C_L$ are discussed by using the delta method. Furthermore, the MLE of $C_L$ is used to establish the hypothesis test procedure under a given lower specification limit L. 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.

Keywords: 62N03; Lomax distribution; conforming rate; lifetime performance index; maximum likelihood estimator; progressive type I interval censored sample; testing procedure algorithm.