  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 dependency structure between components becomes a meaningful exercise. The
Extended Sequential Order Statistics model allows us to model a dependence
structure between heterogeneous components in load sharing systems. However,
the results may suggest that the risk of failure decreases as components fail
sequentially, which can be counterintuitive, especially when data is 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.
