Chadjiconstantinidis, StathisEryilmaz, SerkanIndustrial Engineering2024-07-052024-07-0520230932-50261613-979810.1007/s00362-022-01351-72-s2.0-85136057241https://doi.org/10.1007/s00362-022-01351-7https://hdl.handle.net/20.500.14411/2433For a sequence of multi-state trials with l possible outcomes denoted by {1, 2, ..., l}, let E be the event that at least k(1) consecutive is followed by at least k(2) consecutive 2s,..., followed by at least k(l) consecutive ls. Denote by T-r the number of trials for the rth occurrence of the event E in a sequence of multi-state trials. This paper studies the distribution of the waiting time random variable T-r when the sequence consists of independent and identically distributed multi-state trials. In particular, distributional properties of T-r are examined via matrix-geometric distributions.eninfo:eu-repo/semantics/closedAccessMatrix-geometric distributionPatternProbability generating functionRunsWaiting timeArticleQ364513731390WOS:0008402787000010