Statistical modelling and saddle-point approximation of tail probabilities for accumulated splice loss in fibre-optic networks

Tail probabilities are calculated by saddle-point approximation in a probabilistic-statistical model for the accumulated splice loss that results from a number of fusion splices in the installation of fibre-optic networks. When these probabilities, representing the risk of exceeding a specified total loss, can be controlled and kept low, the requirements on the individual losses can be substantially relaxed from their customary settings. As a consequence, it should be possible to save considerable installation time and cost. The probabilistic model, which can be theoretically motivated, states that the individual loss is basically exponentially distributed, but with a Gaussian contribution added and truncated at a set value, and that the loss is additive over splices. An extensive set of installation data fitted well with this model, except for occasional high losses. Therefore, the model described was extended to allow for a frequency of unspecified high losses of this sort. It is also indicated how the model parameters can be estimated from data.