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This article suggests a new Statistical Process Control (SPC) approach for data-rich environments. The proposed approach is based on the theory of fractal geometry. In particular, a monitoring scheme is developed that is based on fractal representation of the monitored data at each stage to account for online changes in monitored processes. The proposed fractal-SPC enables a dynamic inspection of non-linear and state-dependent processes with a discrete and finite state space. It is aimed for use with both univariate and multivariate data. The SPC is accomplished by applying an iterated function system to represent a process as a fractal and exploiting the fractal dimension as an important monitoring attribute. It is shown that data patterns can be transformed into representing fractals in a manner that preserves their reference (in control) correlations and dependencies. The fractal statistics can then be used for anomaly detection, pattern analysis, and root cause analysis. Numerical examples and comparisons to conventional SPC methods are given. [ABSTRACT FROM AUTHOR]

The classical funnel experiment was used by Deming to promote the idea of statistical process control (SPC). The popular example illustrates that the implementation of simple feedback rules to stationary processes violates the independence assumption and prevents the implementation of conventional SPC. However, Deming did not indicate how to implement SPC in the presence of such feedback rules. This pedagogical gap is addressed here by introducing a simple feedback rule to the funnel example that results in a nonlinear process to which the traditional SPC methods cannot be applied. The proposed method of Markov-based SPC, which is a simplified version of the context-based SPC method, is shown to monitor the modified process well. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Conventional Statistical Process Control (SPC) schemes fail to monitor nonlinear and finite-state processes that often result from feedback-controlled processes. SPC methods that are designed to monitor autocorrelated processes usually assume a known model (often an ARIMA) that might poorly describe the real process. In this paper, we present a novel SPC methodology based on context modeling of finite-state processes. The method utilizes a series of context-tree models to estimate the conditional distribution of the process output given the context of previous observations. The Kullback-Leibler divergence statistic is derived to indicate significant changes in the trees along the process. The method is implemented in a simulated flexible manufacturing system in order to detect significant changes in its production mix ratio output. [ABSTRACT FROM AUTHOR]

Most statistical process control (SPC) methods are not suitable for monitoring nonlinear and state-dependent processes. This article introduces the context-based SPC (CSPC) methodology for state-dependent data generated by a finite-memory source. The key idea of the CSPC is to monitor the statistical attributes of a process by comparing two-context at any monitoring period of time. The first is a reference tree that represents the "in control" reference behavior of the process; the second is a monitored tree, generated periodically from a simple of sequenced observations, that represents the behavior of the process at that period. The Kullback-Leibler (KL) statistic is used to measure the relative "distance" between these two trees, and an analytic distribution of this statistic is derived. Monitoring the KL statistic ample of buffer-level monitoring in a production system demonstrates the viability of the new method with respect to conventional methods. [ABSTRACT FROM AUTHOR]