Technical Uncertainty and Value of Information with Application to Optimal Network Component Replacement

Optimal age replacement policies for network components such as cables, overhead lines or transformers are usually identified based on gathered knowledge about the state of a component and its stochastic deterioration process. In this context, uncertainty is an important challenge because current information about the aging process may be false. Especially in the context of innovative use of newly developed network equipment some experience knowledge from similar equipment might exist or pre-testing under laboratory conditions could allow setting up hypothesis about the characteristics of aging. Nonetheless, substantial uncertainty is still common in replacement. An example in this context is the lifetime of PE tubes in gas networks, which is not very well explored due to the fact that no tubes older than 40 years exist. The length of the aging process as well as the expected starting date can be inferred only to some confidence probability. Apart from newly developed equipment, production imperfections like the Water treeing Effect in cable insulations led to very early replacement of complete lots of cables because the insulation deteriorated much earlier than initially expected. Hence, the question arises how these different sources of uncertainty will impact the network operator's replacement decision. Further it is of interest how much value can be attributed to the reduction of the uncertainty. In this paper, an optimal replacement strategy in an analytical stationary state model is derived explicitly with local and global optima. Based on a discrete mixture model of failure rates under perfect replacement, we show how different assumptions about the underlying type of uncertainty will affect the replacement decision. In a further step, the value of information representing the cost difference between a state of parameter certainty and the state of parameter uncertainty is derived. Trough the course of some applications, it is shown that the value of information increases with the level of uncertainty. Some exemplary calculations are presented to show that the magnitude of the value of information is significant.