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Performance analysis of simultaneous control schemes for the process mean (vector) and (co)variance (matrix)

Ramos, Patrícia F.

PhD Thesis, Instituto Superior Tecnico, University of Lisbon, 2013

Walter A. Shewhart altered the course of industry on May 16, 1924, with a historic memorandum to his superiors at Bell Laboratories, namely George D. Edwards. In this memorandum Shewhart proposed the control chart, a tool used to track process performance over time and to detect changes in parameters which can indicate a deterioration in quality. Simultaneous schemes for the process mean () and variance (2) are essential to satisfy Shewhart's dictum that proper process control implies monitoring both location and dispersion. Misleading signals (MS) can occur while using these simultaneous schemes and correspond to valid signals that lead to a misinterpretation of a shift in \mu (resp. \sigma^2) as a shift in \sigma^2 (resp.\mu). The main question regarding MS is not whether they occur or not, but rather how frequently they occur, thus, the importance of the probability of a misleading signal (PMS).
Capitalizing on the stochastic monotonicity properties of the run length of the individual charts for  and 2, we assess the impact of autocorrelation on the PMS in simultaneous schemes for the mean and variance of stationary processes (Chap. 2, Secs. 2.1-2.4) and also the impact of falsely assuming independent and identically distributed output (Chap. 2, Sec. 2.5). The concept of MS is extended to a multivariate normal setting and the impact of changes in the mean vector and covariance matrix on PMS is analysed (Chap. 3). We conclude by presenting the major contributions of this dissertation, our ongoing research, and a few recommendations for further work (Chap. 4).