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

How to Eat Less

Do you finish all of the food on your plate or are you able to stop eating even if there is still food left?  Chances are, many people will not stop eating until all the food is gone no matter how much is on the plate.  This action is logical in some cases.  Many people who grew up during the depression did not know when they would receive their next meal therefore they would eat all the food on their plate.  Other people are members of the Clean Plate Club because as children, their parents spoke of the starving people in other countries.  Luckily, food scarcity is less of a problem these day and restaurants will often serve more food than the average person should eat in a typical sitting.  So why do you still finish all the food even if you know when the next meal is coming from and how do you limit your eating to prevent weight gain?

The answer may lie in a behavioral bias called the Endowment Effect which causes people to place a higher value on things that they posses.  The Endowment Effect states that people will demand more for an object that own than they are willing to pay for that same object.  In other words, if I gave you a mug as a present, you would only be willing to sell that mug for a higher price than you would be willing to buy it for.

In the case of eating, it may be, that people are unwilling to give up the food on their plate because they feel it is theirs even when they know that they should not eat all of the food.

To break this cycle, you need to be willing to give up some food on your plate.  Of course it would be impolite to take food off of your plate and put it someplace else on the table.  However the following plate design would serve a similar purpose.

To eat less, just push some food on your plate into the "For Later" section.

At some point in your meal, simply push some food into the portion of the plate that says “For Later”.  The phrase can be interpreted different ways.  For some people, it could mean that they want to bring the extra food home in a doggy bag for a snack at home.  For others it could mean that the food they do not eat today does not increase their weight later.  Another way to view it is to give your body a chance to digest the food that you are currently eating before eating more.  Often times, the feeling of satiation or fullness takes a while to kick-in after a meal.  Pausing during the meal gives your body time to register the food you have eaten and you will find that you are really not that hungry for the remaining portion.  Either way, by pushing the food away from you, you are overcoming the Endowment Effect thereby gaining control over how much you eat.

The amount of food that you push away is not important.  In the beginning, it feels very strange, but with time, it becomes second nature.  When using this technique, you will find that you leave the table with a feeling of lightness rather than heaviness.  See a related post on ways to make you feel better after eating: http://latentvalue.blogspot.com/2010/11/how-restaurants-can-increase-value-of.html.

By designating a portion of the plate for later, people would more comfortable not eating all of the food on their plate creating a healthier balance between caloric intake and caloric needs.

Note:  There can also be other variations on what is written on the plate.  You could show a cute monsters mouth or say something like “Feed your Willpower”.