How You can Use Statistics in the Food Industry - Part 3

Recap:
So far we have looked at Paredo, Histograms, Run charts, and Fishbone diagrams.  What next?  Process Capability, Gauge R&R, 6Sigma, and SPC.  Is there more than this - yes, but I think, once the above list is complete - further info would need to be part of a statistics course or a "6 Sigma (green or black belt) program".

Process Capability:

To begin a project of statistical process control, you need to start with a couple of tasks.  The first task is to construct a histogram of your test results to see if you have a normal curve and if your process falls within your upper and lower specification limits - is your process in control (this can be done visually - see part 1 of this series, or by doing a chi squared test)?  The second task is to do a process capability which can only be done if your process is in control. 

In process capability, there are two steps - The Cp and the Cpk.  Cp is a simple index that relates your processes spread to the upper and lower specification limits. 

1. If Cp is >1 you are in good control (the specification limits are wider than your variation)
2. If Cp=1 your specification limits are the same as your variation and 0.3% defect are being made. 
3. If Cp is > 1 your product variation is greater than your spec limits and you are making a lot of scrap. 

The calculation for this number is the upper spec limit minus the lower spec  limit.  The result is then divided by 6 multiplied by the "estimated process standard deviation" 

USL-LSL

6*STDDEV


The deviation is calculated by Range (or average of the ranges for all subgroups) divided by a factor called d2.  Where d2 comes from is a chart of factors for computing Central lines for X and R charts.  I have found a link (below) for this chart of factors.

http://www.dfx.nl/userfiles/file/pdf/Control%20Chart%20Constants%20and%20Formulas.pdf
 

The second task is the Cpk which not only takes into account the variation (spread) of the process but also asks "is the process centered?".  In other words is the mean of the histogram dead centre between the specification limits or is it closer to the upper or lower limit. 

1. If you are below 1, you are not centered and your processes variation is falling outside of the upper or lower specification limit. Thus producing out of spec product, as shown below:
   
2. At 1 to 1.33 you are OK but with no margin for error or drift (running the process too tight).  The process variation is right against either the upper or lower spec limit.
   
3. Above 1.33 - the higher the number the more room you have between your variation and the nearest specification limit.  You may wish to tighten-up your control limits in this case.

Once you have your data points, calculate the average (mean) and the standard deviation.  Subtract the mean from the upper spec limit and divide by 3 X standard deviation.  Do this calculation for the lower spec limit by subtracting the lower spec limit from the mean and then dividing by 3 X standard deviation.  The smaller of the two numbers will be your Cpk (also the spec limit your process is closest to). Equations;

USL-AVE

3*STDDEV

 And

AVE-LSL

3*STDDEV

 Free software at qualityadvisor.com is available as a quick and easy method of getting at this metric.  You will need to know how to select the subgroup size.  1 subgroup is one set of data from one lot and one production run.  Two subgroups would be data from two operators, two lots, etc.

For more information on the calculations, please take a look at isixsigma.com