**Categories:**Six Sigma Improvement Strategy

# Paths of Variation Part 2

**Review**

In my last post I introduced you to a concept known as *paths of variation. *The term paths of variation is used to describe the potential number of pathways a part can take from beginning to end of a process when multiple machines are used to produce identical products. A true case study that I was part of in a manufacturing company in Southern France. Pinions were produced on a machine that had two sides with each side having the same process steps. Because parts were free to move from side to side of this machine based on availability of the next step, the number of paths of variation was quite high. In today’s post, I will present the second of three posts on this subject and will demonstrate the actual number of paths of variation on this machine configuration. As a reminder, the actual process flow was as follows:

**Paths of Variation**

As described in my last post, the company first received metal blanks from an outside supplier and then passed them through a series of turning, drilling, hobbing, etc. process steps to finally achieve the finished product. Because of this configuration, the number of possible combinations of individual process steps, or paths of variation, used to make these pinions was very high.

The process for this particular pinion was automated with two basic process paths, one on each side of this piece of equipment. There was an automated gating operation that directed each pinion to the next available process step as it traversed the entire process which consisted of 14 steps. It was not unusual for a pinion to start its path on one side of the machine, move to the other side and back again which meant that the pinion being produced was free to move from side to side in random fashion. Because of this configuration, the number of possible combinations of machines used to make the pinion, or paths of variation, was very high. Let’s take a look now at the number of paths of variation that existed on this machine as seen in the following figure.

The first step in the process for making this style pinion was an exterior turning operation with two exterior turning machines available to perform this function (labeled A1 on one side of the machine and A2 on the other side of the machine as shown in the figure above). This purpose of this first step, like the others to follow, was to shave metal off of the blank to ultimately achieve its final shape and critical dimensions.

The next step in the process is referred to as interior turning and, again, there are two interior turning machines labeled B1 and B2, one on each side. In the third step there were two possible choices for drilling, C1 and C2. After the pinion was automatically inspected for cracks (with one, common automated gage), it then progressed to one of two hobbing machines, D1 and D2. The parts were then collected in storage bins and sent as large batches to an outside vendor for heat treatment. Upon return from heat treatment the pinions then proceeded to hard hobbing, E1 and E2 and then on through the remainder of the process as indicated in the above figure.

The boxes to the right in the above figure represent the possible paths that the pinion could take as it makes its way through the process. For example, for the first two process steps, there are four (4) possible paths, A1B1, A1B2, A2B1, and A2B2. The parts then move to the third step, drilling where you now see there are eight possible paths of variation which are listed on the right side of the above drawing.

As you can see, as the part continues on, the possible paths continue on until all 32 potential paths are seen. Do you think that the pinions produced through these multiple paths will be the same dimensions or will you have multiple distributions? What if we were able to reduce the number of paths of variation from 32 down to 2, do you believe the overall variation would be less and how many distributions would you have now? Or another way of saying it, do you believe the part to part consistency would be much better when there are only two paths of variation?

**Next Time**

In my next post, I will answer these questions and demonstrate how we can decrease the number of paths of variation from thirty-two down to two and what happens to our part variation. As always, if you have any questions or comments about any of my posts, leave me a message and I will respond.

Until next time.

Bob Sproull

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