Date of Award

Fall 2011

Degree Type


Degree Name

Master of Science (MSc)


Mathematics and Statistics


Roman Viveros-Aguilera


Angelo Canty, Shui Feng



Committee Member

Angelo Canty, Shui Feng


Several control schemes for monitoring process mean shifts, including cumulative sum (CUSUM), weighted cumulative sum (WCUSUM), adaptive cumulative sum (ACUSUM) and exponentially weighted moving average (EWMA) control schemes, display high performance in detecting constant process mean shifts. However, a variety of dynamic mean shifts frequently occur and few control schemes can efficiently work in these situations due to the limited window for catching shifts, particularly when the mean decreases rapidly. This is precisely the case when one uses the residuals from autocorrelated data to monitor the process mean, a feature often referred to as forecast recovery. This thesis focuses on detecting a shift in the mean of a time series when a forecast recovery dynamic pattern in the mean of the residuals is observed. Specifically, we examine in detail several particular cases of the Autoregressive Integrated Moving Average (ARIMA) time series models. We introduce a new upper-sided control chart based on the Exponentially Weighted Moving Average (EWMA) scheme combined with the Fast Initial Response (FIR) feature. To assess chart performance we use the well-established Average

Run Length (ARL) criterion. A non-homogeneous Markov chain method is developed for ARL calculation for the proposed chart. We show numerically that the proposed procedure performs as well or better than the Weighted Cumulative Sum (WCUSUM) chart introduced by Shu, Jiang and Tsui (2008), and better than the conventional CUSUM, the ACUSUM and the Generalized Likelihood Ratio Test (GLRT) charts. The methods are illustrated on molecular weight data from a polymer manufacturing process.


This thesis is submitted by Weiping Tang on August 2, 2011.

McMaster University Library