On Non-Occurrence of the Inspection Paradox

Diana Rauwolf () and Udo Kamps
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Diana Rauwolf: Department of Mathematics, RWTH Aachen University, D-52056 Aachen, Germany
Udo Kamps: Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany

Stats, 2024, vol. 7, issue 2, 1-13

Abstract: The well-known inspection paradox or waiting time paradox states that, in a renewal process, the inspection interval is stochastically larger than a common interarrival time having a distribution function F , where the inspection interval is given by the particular interarrival time containing the specified time point of process inspection. The inspection paradox may also be expressed in terms of expectations, where the order is strict, in general. A renewal process can be utilized to describe the arrivals of vehicles, customers, or claims, for example. As the inspection time may also be considered a random variable T with a left-continuous distribution function G independent of the renewal process, the question arises as to whether the inspection paradox inevitably occurs in this general situation, apart from in some marginal cases with respect to F and G . For a random inspection time T , it is seen that non-trivial choices lead to non-occurrence of the paradox. In this paper, a complete characterization of the non-occurrence of the inspection paradox is given with respect to G . Several examples and related assertions are shown, including the deterministic time situation.

Keywords: random inspection time; renewal process; inspection interval; waiting time paradox (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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