On the application of inverted Dirichlet distribution for reliability inference of completely censored components with dependence structure

The inverted Dirichlet distribution has been widely used in a variety of applications involving multivariate categorical data. However, censoring issues leading to implicit forms of associated reliability functions hinder the use of the inverted Dirichlet distribution in reliability applications. This paper discusses a new application of the inverted Dirichlet distribution for modeling the lifetimes of completely censored components with dependence structure. For this purpose, we propose a frailty approach to overcome the computational challenges faced in the likelihood inference for the inverted Dirichlet distribution based on completely censored data. Maximum likelihood estimates (MLEs) and asymptotic confidence intervals are derived under the proposed modeling framework. Monte Carlo simulations are performed for evaluating the performance of the proposed model and the associated method. Finally, an illustration of the proposed model and the associated inferential methods with light-emitting diode data is described in detail. The analysis shows the usefulness in applying the inverted Dirichlet distribution for small sample-sized multivariate lifetime data.