IIE Transactions (2004) 36, 401–415 Copyright C  “IIE” ISSN: 0740-817X print / 1545-8830 online DOI: 10.1080/07408170490426125 Statistical process control via context modeling of finite-state processes: an application to production monitoring IRAD BEN-GAL ∗ and GONEN SINGER Department of Industrial Engineering, Tel Aviv University, Ramat-Aviv, Tel Aviv 69978, Israel E-mail: bengal@eng.tau.ac.il Received April 2001 and accepted September 2003 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. 1.Introductionandliteraturereview In many industrial environments process outputs are often adjusted by applying feedback mechanisms and policies. As an example, the temperature in a chemical reactor is controlled by a thermostat; another example is when the allocation of parts to machines is based on machine queue information gathered by sensors. These feedback mecha- nisms, including closed-loop controllers, often create both linearandnonlinearautocorrelations(hereafter,termedin- terchangeably, as interdependence or dependencies) among the observations of the controlled output and increase its variation(Deming,1986;BoardmanandBoardman,1990). In extreme cases, the structure of these autocorrelations may be established by the dynamics of the observed out- put trajectories. However, such an identification is not a simple task in noisy environments, or when the feedback mechanism depends on many past observations. The Statistical Process Control (SPC) methodology has been developed independently of the Engineering Process Control (EPC) approach, which relies heavily on feed- back mechanisms. Although both strategies aim for qual- ity improvement, SPC concepts are in sharp contrast with EPC. Whereas EPC actively compensates for process dis- turbances by performing adjustments constantly, in SPC, a control action is taken only when there is statistical ev- idence that the process is out of control. This evidence is usually a point outside the limits on a control chart. ∗ Corresponding author Since traditional SPC methods assume an independent process (whereas conventional SPC methods for autocor- related process assume a known underlying model that is often used to transform the data), a major concern when integrating traditional SPC and EPC techniques is the de- pendenciesamongobservationsthatarecreatedbythefeed- back mechanisms. This point was recently stated in English etal. (2001):“whenconsideringtheintegrationofthesetwo approaches, the application of a control chart assumes in- dependenceoftheobservedprocessobservations.Theinde- pendence assumption is dramatically violated in processes subjected to process control. The chemical and petroleum industries, for example, have traditionally employed clas- sic proportional-integral-derivative (PID) control and have extended this effort in the past decade or two to implement optimal discrete time control systems. By the very nature of PID control, the observations of the process output are highly correlated.” In this paper, we propose a novel approach, termed Context-SPC(CSPC)tomonitorastate-dependentprocess of varying dependence order. Thus, not only that the mon- itored process be interdependent (either linearly or non- linearly), but also the nature and the order of this depen- dence might change in time according to the process state. The suggested method assumes a Markovian property of the process output without requiring a prior knowledge of its transition parameters. Moreover, the CSPC does not assume a closed-form time-series model, which is often required by conventional SPC approaches for dependent processes. The main disadvantages of the CSPC are its lim- itation to monitor processes with discrete measures over a 0740-817X C  2004 “IIE”