Control Charts

Lesson 4

The following data has been reported on a process of interest:

This data represents any type of situation under study.  It can be characteristic, quality, business, or social data, and in this case it represents something where a higher value is better.  Higher is better data includes things like personal income, machine output, survival rates and efficiency.  There are, also, lower is better data like cost, scrap rates, mortality and time to complete tasks.  The same thinking applies to data where lower is better, however, in this example we will use the higher is better type.  The time period could be days, months, years or any other period, though here it is shown as years. 

We often see data presented like this as part of any effort to monitor and evaluate the success of various improvement efforts.  Data like this is often presented, noting how the trend is upward or downward, improves from period to period, or changes thru all five periods as evidence of a successful effort or expenditure.  Specifically, this data has increases for the periods from 0.1 to 1.8, and a total of 4.9 thru all of the periods.  The percentage increase for period to period is from 0.3% to 5.7%, and a  total of 16.3% thru all of the periods.  Most observers would conclude, using standard reasoning and experience, that this data shows a real increase.  

Some presenters may show only 2 periods for interpretation, showing how one period is up over the last period.  We have shown 5 periods here for better understanding.

However, we should ask about the significance of this change.  Is it like man bites dog or dog bites man, as discussed in Lesson 2?   Is it like 6 heads or 10 heads, as discussed in Lesson 3?  Is the change a real signal, or is it just noise?  If it is a real signal, maybe our actions caused it and should be continued.  If, on the other hand, the change in the data is noise and not a real trend, we need to know so we can better select our future actions.

The control chart, developed by Dr. Walter A. Shewhart and widely promoted by Dr. W. Edwards Deming, is the proper way to determine if this variation is real.  In other words, is the variation a signal of real change or just noise?  The control chart shown below makes use of all the data for the 25 year period.  In the table above, due the difficulty of showing all the data, it is shown in 5 year increments, as is typical of many presentations.  

The data from above is reproduced here to help make easier comparisons to the control chart.

The Shewhart control chart above shows the data over the entire period, with control limits.  Control limits, shown as long dashed lines, are the natural boundaries of variation or noise.  Control limits, often referred to as the 'voice of the process,' are calculated from the data itself, not the specification, not desire, and not folklore.  This data is in statistical control, since the data stays within the control limits and is free of other patterns for the entire time period on both the individual and moving range charts.  Therefore, there are no real changes for the whole period of this data  There is no signal and only noise.  Further, it is expectable for this process to continue this amount of variation as predicted by the control limits.

And maybe most importantly, the efforts made for the entire period did not really change the situation in this study.  The control chart has very important business and social application to help understand whether a change in a situation is signal or only noise.

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