Abstract—A load-sharing system has several components and the failure of one component can affect the lifetime of the surviving components. Since component failure does not equate to system failure for different system designs, the analysis of the dependence structure between components becomes a meaningful exercise. The extended sequential order statistics model allows us to model a dependence structure between heterogeneous components in loadsharing systems. However, the results may suggest that the risk of failure decreases as components fail sequentially, which can be counterintuitive, especially when data are scarce. We propose to 
address this issue by imposing an order restriction on the model parameters that represent increasing failure risks. This assumption corresponds more realistically to the physical properties of the system in many applications. We discuss the advantages of the newly proposed estimates and describe situations where they should be used with caution. 
Index Terms—Extended sequential order statistics (ESOS),
heterogeneous components, increasing risks, successive failures.