Estimation with extended sequential order statistics: A link function approach

Abstract

The model of extended sequential order statistics (ESOS) comprises of two valuable characteristics making the model powerful when modelling multi-component systems. First, components can be assumed to be heterogeneous and second, component lifetime distributions can change upon failure of other components. This degree of flexibility comes at the cost of a large number of parameters. The exact number depends on the system size and the observation depth and can quickly exceed the number of observations available. Consequently, the model would benefit from a reduction in the dimension of the parameter space to make it more readily applicable to real-world problems. In this article, we introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model. These functions model the relation between model parameters of a component across levels. By construction the proposed ‘link estimates’ conveniently yield ordered model estimates. We demonstrate how those ordered estimates lead to better results compared to their unordered counterparts, particularly when sample sizes are small.