A partition based test to identify periodic events with application to quality control
This thesis is devoted to the study of a new partition based test to identify periodic observations. We follow the framework for generalizing the Kolmogorov- Smirnov test proposed by Feltz and Goldin in 1992. We create and implement a partition based test to identify periodic events (with arbitrary period), where there is also a background of nonperiodic observations such as noise. The periodic observations may be related to a violation of the theoretical density such as periodic spikes of current in an electric circuit. By identifying the characteristics of a defect distribution, we may be able to locate the cause of that defect. The Kolmogorov-Smirnov test is generalized to create partitions of the real line. We report some critical values and powers of the test obtained through simulation techniques. The underlying null defect distribution is assumed to be uniform, and we confine our study to one dimension. After periodic defects have been identified and eliminated, we can then monitor the process for a given period using the appropriate Cuscore statistic and Cuscore chart. The Cuscore chart will check any recurrence of the periodic observations because the Cuscore statistic is customized to be sensitive to this kind of departure.