Statistical Process Control is used to detect when a significant change has taken place in a process.
All processes have variation as observed in any of their metrics but not all variation is significant from the statistical point of view.
When we want to control a process by adjusting some process parameter we can make two mistakes:
- Over-react by adjusting when we shouldn't
- Under-react by failing to adjust when we should
A case of over-reaction is illustrated by the following example:
Someone is shooting at a target and based on the deviation of the impacts he adjusts the gun site after each shot.
The end result will be an increase of the dispersion of the impacts, therefore the adjustments will make the process worse.
The correct way is, of course, to fire 5 or 6 shots without adjustments and then decide if adjustment is required based on the center of the impacts.
This is an example of under-reaction:
If you drop a live frog in boiling water it will immediately jump out to save its life.
But if you put it in a pot of cold water and heat it the frog will eventually pass out without any reaction.
Many companies have fallen into this trap:
- A big disaster generates a quick and effective reaction and the company recovers
- A slow degradation of their KPIs such as customer sat pass undetected until it is too late
Statistical Process Control
To avoid these two mistakes we can use SPC to control a metric to find out if the observed changes are SIGNIFICANT from the statistical point of view.
We will illustrate this with the use of an example: control your own weight to check if your diet is leading to your weight target or not.
You can download this example Excel file and replace the data in columns A and B with your own data:
You can decide the frequency of your data collection. In this example I have collected it daily.
It is important to collect it at the same moment (more or less) each day.
You can either have your Excel file in your smartphone or in the cloud (Google Drive or Microsoft's One Drive)
I am assuming our target is to reduce weight, therefore a downward trend will put the numbers in green and an upward trend will put them in red.
SPC uses some rules, developed by the Western Electric company, to detect symptoms of SIGNIFICANT trends . They are shown below with a screen of Minitab SPC for individuals:
The center line is the average of all values and the standard deviation is also estimated by all the values.
In our Excel file upward trend symptoms are in red and downward in green.
The Excel file applies rules 1, 2, 3, 5, and 6 of this list.
Weight data interpretation
On 2/4/2018 weight 78.8 is in red and we see the explanation with a number 2 in column N which means that two values (1/4/2018 and 2/4/2018) with 78.8 Kg are 2 σ above the average. This is passed data. What really interests us is the data we have just collected.
The numbers start getting green on 8/4 with 78 kg and the reason is that out of the 5 last numbers the last 4 are 1 σ below the average. This is interpreted as a SIGNIFICANT downward trend. This trend continues the following days.
Statistically significant trend doesn't mean that this reduction is acceptable but at least we are moving in the right direction.
Results analysis with Minitab
In our Excel file there is no graphic: we just want to alert of significant trends
Looking at this same data in Minitab we can see an SPC chart:
The red dots indicate trends. looking at the graph we notice the first two are upward and the last three downward so the overall trend is downward.
There is a common misconception about the meaning of process stability
For instance some might call the process characterized by the following data unstable:
But if we look at our SPC:
It doesn't give us any alert of unstability
This is a STABLE process consisting simply of throwing dice. Since we have always thrown dice the same way SPC is telling us that this is a stable process: no SIGNIFICANT change has been detected.
Stability is not always a good thing. In the case of our weight control stability would mean that there is no improvement.
We want stability when the process is OK. If we improve this will show with SPC alerts in the right direction.
Use for other processes
This Excel file can be used to control a variable other than weight at work. For instance:
In this case we are doing an hourly control of our process yield. In this case Yield increase is good so Red is Good.
At 20:00 we have enough evidence of a Yield increase although the change seems to have taken place at 16:00.
SPC enables the right detection of process change.
High process intrinsic variation can lead to over-reaction (adjust when you shouldn't) or under-reaction (not reacting when you should)