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Multiple Steam Processes

by George Runger,  Ph.D.

A multiple stream process (MSP) consists of several identical process streams. At a sample time, measurements are obtained from each stream (or a subset of the streams). The measurements are in the same units and often they have the same target value and variance.

MSPs are quite common:

• thickness measurements across a web or sheet (as seen in paper production, galvanizing steel, and magnetic tape manufacturing);
• diameter measurements at different radii or heights;
• measurements of identical features on a single part such as the vanes on a compressor or impeller;
• measurements from several identical production tools such as filling heads, cavities in injection molds, or different spindles;
• measurements from identical test instruments;
• and measurements from different locations on a wafer or disk such as in run-to-run process control in semiconductor manufacturing.

With control charts for a MSP, it is important to detect and distinguish between assignable causes that affect all streams and assignable causes that affect one or a few streams. Typically, these two types of assignable causes have different root causes, and the distinction facilitates the identification of the problem and the solution.

Figure 1. A single stream deviates from the others.

A separate control chart for each stream might be used in some cases, but it is not sensitive to the type of assignable cause shown in Figure 1. Measurements from Stream 1 are not unusual by themselves, but they are very unusual in relation to the other process streams. The power of control charts for a MSP is to detect this type of assignable cause.

Group Control Chart Disadvantages

A classical SPC method for a MSP is the group control chart. The chart simultaneously monitors the data to detect (1) an assignable cause that shifts the mean level of all of the streams over time (called an overall assignable cause) and (2) an assignable cause that changes the mean of one or more streams relative to the remainder (called a relative assignable cause). The group control chart uses a decision rule based on runs to check for a relative assignable cause that is not affected by (that is, it is not sensitive to nor degraded by) the presence of an overall assignable cause. If a particular stream generates the highest (or lowest) reading for r consecutive samples, then the stream is signaled to be off-target. The value selected for r is a trade-off between the number of false alarms produced by the chart and the time to detect an assignable cause. Consequently, the group control chart facilitates a parallel attack on both types of assignable causes that can expedite process improvements in a MSP.

However, Mortell and Runger (1995) described major disadvantages of the group control chart. For example, an out-of-control decision is based on consecutive high (or low) readings from a single stream. Consequently, if more than one stream shifts, and if the shifts are even approximately of the same magnitude, a single stream does not dominate and the detection of this assignable cause is poor. In the modern industrial environment, with automated data acquisition systems, a dozen to even 100’s of stream may be monitored simultaneously. Consequently, improvements to the group control chart were needed.

Recommended Control Charts for MSPs

Runger and Mortell (1995) recommended the simultaneous use of two control charts. One plots the average measurement from all the streams over time. The other chart plots some measure of uniformity of the streams. The range (or the standard deviation) of the measurements from each stream at a sample time is an obvious choice. The chart of means is sensitive to overall assignable causes, while the range (or standard deviation) chart is sensitive to relative assignable causes. These two can usefully replace a battery of charts generated as one for each stream, and improve the information.

The control limits for the range (or standard deviation) chart can be computed by the standard method. However, a strong warning is needed for the chart of averages. The control limits should be calculated as if each point was an individual (and the moving range method might be used). This is because the control limits should be based on variation over time (not the variation from stream to stream).

Advanced Methods

Runger and Fowler (1998) and Runger, Alt, and Montgomery (1996) considered the highly automated environment with dozens to 100’s of streams. If your factory is not there yet, you might be surprised how many are, and how soon you might be collect that type of data. They showed how some additional control charts could be used to supplement the two recommended and simple charts mentioned previously. Control charts based on the Analysis of Variance (ANOVA) and orthogonal contrasts can be used to partition the data into a hierarchy of effective control charts. And exponentially weighted moving averages (EWMAs) can be applied for even better process control. Just ask me about our current work.

Mortell, R. and G.C. Runger (1995). "Process Control for Multiple Stream Processes", J. of Quality Technology 27(1), pp. 1-12.

Runger, G.C. and Fowler, J.W. (1998). "Run-to-Run Control Charts with Contrasts", Quality and Reliability Engineering International 14, pp. 261-272.

Runger, G.C., F.B. Alt, and D.C. Montgomery (1996). "Controlling Multiple Stream Processes With Principal Components", International Journal of Production Research, 34(11), pp. 2991-2999.