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Applications of the EWMA

This paper (1) describes a method for Algorithmic SPC using the EWMA, (2) compares the performance of this proposed method with adjustment strategies based on modified Shewhart charts, and (3) discusses two applications of Algorithmic SPC in the Monsanto Fibers Division. The first application is a manuał system for adjusting pump RPM to control a variable relating to the quality of nylon carpet staple fiber, and the second is an automatic system where pressure adjustments are madę to control an important ąuality measurement for textured continuous filament nylon carpet yam.

Use Of The EWMA For Forecasting And Control

The Process Model For many industrial processes where the controlled variable is measured in the laboratory with a freąuency of about once per shift, the following model can be used to describe the variation in the controlled variable about its target:

Y_t - Target = g(K_uVX^ + D_t + S₍    (1)

In this equation, Y₍ is the value of the controlled variable at time /, X_t_± is the value of a manipulated variable following an adjustment madę after the last lab measurement, expressed as a deviation from a reference point, Aq. g is the process gain (the change in Y resulting from a unit increase in X), and D₍ represents the current State of normal process disturbances, or what the lab measurement would be if X were held at some fixed value, and S₍ is usually equal to zero but can be used to represent the elfect of special causes not typical of usual process behavior. This model assumes that the luli effect of a change in X has taken place before the next sample is taken, an assumption which is often true if Y is a laboratory variable measured only once per several hours. For continuous process signals which can be sampled morę frequently, the relationship between Y and X usually requires a morę complicated “transfer function” model as described by Box and Jenkins (1976). In such cases, the control algorithm presented in this paper is not recommended.

The basis for using the EWMA for calculating process adjustments is that it is the statistic which minimizes the mean squared forecast error when the process disturbances can be described with an integrated moving average process of order (0,1,1). The IMA(0,1,1) is defined in Box and Jenkins (1976) by the dilference equation,

^Dt ^{= D}t-\ ⁺ a, “O -    1