Evaluating reliability of facility location using the kth nearest distance distribution

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The purpose of this research is to evaluate the reliability of facility location when some of the facilities are closed. The distribution of the distance from customers to the kth nearest facility is derived for regular and random patterns of facilities. As an application of the kth nearest distance, we examine the distance to the nearest open facility when some of the facilities are closed. The kth nearest distance distribution on a road network is also obtained to confirm that the distance on a continuous plane gives an estimate for the network distance.