Eryılmaz, Serkan2023-06-162023-06-1620080021-90021475-6072https://doi.org/10.1239/jap/1231340230https://hdl.handle.net/20.500.14365/2279Recently, Makri, Philippou and Psillakis (2007b) studied the exact distribution of success run statistics defined on an urn model. They derived the exact distributions of various success run statistics for a sequence of binary trials generated by the Polya-Eggenberger sampling scheme. In Our study we derive the joint distributions of run statistics defined on the multicolor urn model using a simple unified combinatorial approach and extend some of the results of Makri, Philippou and Psillakis (2007b). As a consequence of our results, we obtain the joint distributions of success and failure runs defined on the two-color urn model. The results enable us to compute the characteristics of particular consecutive-type systems and start-up demonstration tests.eninfo:eu-repo/semantics/openAccessConsecutive-k, r-out-of-n: DFM systemDirichlet measuremulticolor Polya sampling schememultistate exchangeable trialrunsstart-up demonstration testwaiting timeSuccess RunsMultistate TrialsConsecutive-KMarkov-ChainJoint DistributionsQuality-ControlControl ChartsLongest RunsSequenceLengthArticle10.1239/jap/12313402302-s2.0-58449119116