Statistical Process Control in Count Time Series Models

Abstract

This thesis consider cumulative sum (CUSUM) charts based statistical process control (SPC) in count time series. Time series of counts have gained much attention in recent years in diverse fields such as manufacturing process, communication, queueing systems, medical science, crime and insurance. First, we considers the first-order integer-valued autoregressive (INAR) process with Katz family innovations to include a broad class of INAR(1) processes featuring equi-, over-, and under-dispersion. Its probabilistic properties such as ergodicity and stationarity are investigated. Further, a SPC procedure based on the CUSUM control chart is considered to monitor autocorrelated count processes. The CUSUM-type test statistic with conditional least square (CLS) and squared difference (SD) estimator for the PINAR(1) model and its application to the diagnostic of control chart are also investigated. Also, we propose an upper one-sided CUSUM-type chart based on the considered CUSUM statistic for an effective detection and a change point estimation. For enhanced monitoring Markov counting process with excessive zeros. we consider three control charts, namely cumulative sum (CUSUM) chart with a delay rule (CUSUM-DR), conforming run length (CRL)-CUSUM chart, and the combined Shewhart CRL-CUSUM chart. Moreover, for an easy implementation of the attribute<br/> fixed sampling interval (FSI) and variable sampling internal (VSI) CUSUM control charts, an R package, attrCUSUM, is developed.<br/>