| Popis: |
Count data are often encountered in manufacturing and service industries due to ease of data collection. These counts can be useful in process monitoring to detect shifts of a process from an in-control state to various out-of-control states. It is usually assumed that the observations are independent and identically distributed. However, in practice, observations may be autocorrelated and this may adversely affect the performance of the control charts developed under the assumption of independence. In this thesis, the cumulative sum (CUSUM) control chart for monitoring autocorrelated processes of counts is investigated. To describe the autocorrelation structure of counts, a Poisson integer-valued autoregressive moving average model of order 1, Poisson INAR(1), is employed. Changes in the process mean in both positive and negative directions are taken into account while designing the CUSUM chart. A trivariate Markov Chain approach is utilized for evaluating the performance of the chart. |
