Identification of marginal and joint CDFs using bivariate type I interval multiply censored data for RBDO of a pick-up device of a pilot mining robot

Abstract

In this paper, joint probability distribution for the size and mass of deep-sea manganese nodules is investigated and reliability-based design optimization (RBDO) of a deep-sea pilot mining robot is performed. As the size and mass of the manganese nodules are strongly correlated and their data are given as bivariate type I interval multiply censored data, a new statistical modeling method should be developed to deal with these issues. However, this is significantly difficult as the conventional methods cannot resolve these issues and there is no prior knowledge of the two physical properties. The proposed method, which employs the multinomial distribution to define the likelihood function and the Akaike information criterion to select the fittest marginal distribution and copula, provides a systematic approach to find the joint probability distribution using the type I interval multiply censored data. To demonstrate the accuracy and effectiveness of the proposed method, two numerical examples are tested. Then, the RBDO of the pilot mining robot is performed using the joint probability distribution resulted from the proposed method.