Estimating the Occurrence Rate for Alpha-Series Process in Rayleigh Distribution

The geometric process is sometimes appropriate for reliability and scheduling problems. Some previous studies suggested a possible alternative that alpha-series as to the when it decreases with time, decreasing shows expected number of events at an arbitrary time does not exist. In contrast, (ASP) exists under some conditions. this paper, we assumed first arrival followed Rayleigh distribution (RD). modified moment estimator was proposed estimate parameters in compare maximum likelihood estimators. A simulation conducted two real-data application intervals between successive failures Mosul Dam power station Nineveh governorate Iraq provided illustrate results. When initial occurrence indicated be RD, rate ASP investigated study. Estimators are generated using (MM), (ML) approaches. According study's findings, MM outperforms ML estimator. all cases, RD provides better data than renewal (RP) real sets. test statistic has been devised determine if conforms ASP.