Can you identify the Truncation Effect on your incomming inspection?

A friend of mine, Jon Glommen, was asked to review a chart similar to this during an interview for a quality position.

Incoming Inspection Data for Large Number of Parts

The histogram showed the incoming inspection data for a  large number of parts from a supplier (100% inspection).  The curve was supposed to illustrate how each part was built to spec and show that the supplier had no quality issues.  Mr. Glommen then informed the interviewer that the curve was only showing half of the picture and that the supplier was actually producing a large number of nonconforming parts which were scrapped and these costs were being passed on to the customer.

Jon noticed that the curve represented only a portion of a normal distribution.  The supplier was measuring each part at final inspection and only shipping the parts that met the required dimensions.  The remaining parts were either reworked or scrapped, both of which increased costs and delayed delivery.  Removing nonconforming data points and only showing the data that meets the specification is called the Truncation Effect.

The curve in the above picture was generated using a random set of data with a mean of 100 and standard deviation of 5.  In this theoretical example, I have set the lower spec limit at 92 and upper spec limit at 108.  This is the same as removing approximately the lower 5.4% and upper 5.4% of the curve.   In other words, the supplier would have to produce 111 parts in order to ship 100 parts.  This increases both the lead time and cost by 11%.

The histogram below is another view of the same set of data adding back the parts that the supplier had removed.

Histogram including truncated parts

This chart clearly shows the long flat tails that are typical of a normal distribution.  Using a statistical software application (JMP), I have added the theoretical normal distribution curve.  In this case, the mean is 100 and the calculated standard deviation is 4.97.  Notice how the curve closely matches the data set in this example.

Next, I calculated the distribution for the incoming inspection excluding the truncated data points.  The stats software calculated the same mean of 100 but a lower standard deviation of 3.88.  Below is the calculated normal distribution curve overlaid on the incoming inspection data.

Calculated Normal Distribution overlaid on data with the Truncation Effect

Notice that the center of the calculated curve is higher than the center points and that the edges of the curve are lower than the data points.

One method to check for the Truncation Effect is to use Process Capability Analysis.  Here is a quick overview of Process Capability Analysis.  The standard formula for Process Capability is Cp = (USL - LSL)/(6* sigma).  The Cp for the truncated data = (108-92)/(6*3.88) =0.68 which is less than 1.  This tells us that the spec width is smaller than the process width and that the supplier is producing nonconforming parts.

Why is it important to look for the Truncation Effect?
If all of your parts pass incoming inspection, you may believe that your supplier is producing high quality parts.  However when you use a histogram or Process Capability Analysis on the data you may find that your supplier is achieving the high quality by removing the non-conforming parts.

Next Steps
First, if you have observed that inspection and/or test has resulted in rework or scrap, or the distribution of incoming material indicates that truncation is occurring, then it is important to work with your supplier to identify why parts are being reworked or scrapped and to help your supplier eliminate this waste.

Second, an accurate test is needed to determine if there is evidence of truncation.  One test might measure the number of points above 10% of the lower spec limit.  If you see a large percentage of points near the cutoff, it may indicate that there is hidden waste. If you have a large amount of data, if truncation is occurring it should be pretty obvious.

Third, a method is needed to estimate the true mean and standard deviation of the population in the presence of truncation. To get this information we need to have the supplier report first time yield and final yield. In addition we need to know the test or inspection results (i.e., measurement results not just pass/fail) of all units which were sampled.

In conclusion, incoming inspection of parts from a supplier may only show that the supplier only delivers parts that meet your requirements.  Further analysis is needed to determine if your supplier has hidden waste that they are containing internally.  By working with your supplier to help minimize this internal waste, you will speed up delivery and reduce costs the of your parts because the overall yield of the supplier's process will increase.

Note: For further reading, learn about Process Capability Analysis http://www.qimacros.com/qiwizard/process-capability.html