Eryilmaz, SerkanEryılmaz, SerkanIndustrial Engineering2024-07-052024-07-05201050021-90021475-607210.1239/jap/12941705212-s2.0-80054728505https://doi.org/10.1239/jap/1294170521https://hdl.handle.net/20.500.14411/1607Eryilmaz, Serkan/0000-0002-2108-1781Let {X-i}(i=1)(n) be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable S-n,S-m to be the maximum number of Is within any m consecutive trials in {X-i}(i=1)(n). The random variable S-n,S-m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {X-i}(i=1)(n) consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of S-n,S-m for 2m >= n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.eninfo:eu-repo/semantics/openAccessBernoulli sequenceexchangeable binary trialreliabilityscan statisticsArticleQ347410841092WOS:000286958100015