The economics of SPC in manufacturing

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by Andrew Milivojevich

Statistical process control (SPC) is a decision tool developed in the 1920’s by Walter Shewhart. Walter was a physicist and the father of modern day SPC. His work was motivated by a simple question, “how do we know when a process is behaving abnormally?”

This ultimately led to his book called, “The Economic Control of Manufactured Product.” This famous book provided the foundation upon which the critical features of a manufactured product could be measured and the data plotted in the order it was collected and interpreted to determine if the process was manufacturing products abnormally.

Prior to SPC, when the critical feature of a product exceeded its tolerance specification, the manufacturing process was halted and an investigation ensued as to why it was behaving abnormally. By this time, much product scrap was produced along with lost productivity while engineers conducted their investigation. To avoid these costly events, Walter argued what was needed was a way to detect the start of an abnormal manufacturing event before a critical product feature was made out of tolerance specification.

Using SPC, Walter provided a set of “rules” that when applied by production personnel, could identify the “time” an abnormal production event occurred before a critical product feature exceeded its tolerance specification. These personnel could then observe the process and investigate the potential root cause while the process continued to operate. Using these “rules” , production scrap and lost productivity could be avoided. Today, abnormal production events are referred to as “special cause events.” When the process is behaving normally, it is behaving under the influence of “common causes” .

Walter defined eight special cause events that provide an early warning of abnormal production. My experience shows many manufacturing companies can reap huge benefits applying only three. I refer to these special cause events as an instantaneous shift, sustained shift, and trend. The rules for each of these special cause events are shown in table below.

SPC is a valuable management decision tool when understood and applied properly. It can monitor any business system, either administrative or manufacturing, that generates data that must be interpreted to render decisions. To illustrate the power of this tool, I will demonstrate its ability to facilitate investment decisions in the Canadian stock market. The following example examines Canadian GDP data as a means of deciding when to invest and sell one position in the Canadian stock market. The data used is shown in the following table.

The following SPC control limits (UCL, LCL red line) and average GDP (green line) level were developed by removing abnormal GDP data. All the data were then reapplied to the following SPC chart. Using this chart, abnormal GDP growth could be identified. Examining the SPC chart, notice the first four quarters of GDP growth violate rule one and suggest an over-producing economy. The 5th and 6th quarters show the economic growth behaving as expected. However, a rule three violation occurred in the 6th quarter verifying a downward trend in economic output. This trend continued until the 7th quarter when GDP growth was lower than normally expected. This quarter of economic slowdown provides a signal of an investment opportunity in the Canadian stock market. Going forward, the economic output increases until the 19th quarter when GDP growth exceeds the UCL and is thus larger than expected compared to average GDP growth. By the 26th and 27th quarter, a rule two violation is signaled. A sustained shift in economic output was realized when nine quarters of economic output exceeded the average level of GDP growth. Economic output then slows and behaves as expected until June 2008 when the Canadian economy shows evidence of a rule one violation. In Dec 2008, a rule three violation occurred as six consecutive quarters of declining GDP growth was realized. Counting backwards, the decline in GDP growth started in September 2008.

In the stock market, buy low and sell high is the goal. By identifying special cause events using–the three rules–I identified a buying opportunity in September 2001. A sell opportunity was identified in September 2006 and June 2008. These times corresponded to GDP growth that was higher and lower than average GDP growth. Note the downwards trend in GDP growth that started in September 2007 was not known until December 2008. 

The following table summarizes the TSE Index. In Sept 2001, a buy and selling opportunity occurred in September 2001 and June 2008. Between these two periods, the TSE increased by 102 per cent. Several months later the TSE Index suffered a severe decline as economic fear gripped the marketplace.

TSE INDEX SUMMARY – 2001 to 2008

Much buying and selling in the stock market is driven by emotions. I am sure you will agree with me that emotional decisions often have disastrous consequences. Using SPC substantially improves our capacity to render objective decisions.

The SPC chart in the example above is a time series chart with control limits. This type of chart is called an Individuals chart. To implement this type of chart, collect data at a frequency that can detect potential special cause events. For example, if you believe your process exhibits special causes weekly, than collect data daily. Collect enough data to span an appropriate amount of time. Analyze the data and remove any special cause data. The remaining common cause data are then used to compute the process average and upper and lower control limits. The chart is now ready to be used. Any violation of the three rules becomes an opportunity to identify a root cause, improve a process and realize higher levels of product quality and productivity.

Andrew Milivojevich is the President of “The Knowledge Management Group” and a leading source for information on Revenue Canada’s Scientific Research and Experimental Development (SRED) tax incentive program.


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