A particular process makes parts of diameter D. There are 10 parts produced per batch. The batches are sampled periodically and the diameter of all the parts from the sampled batch is measured. Data, representing deviation from the target, for the first 6 sampled batches is shown in Table 1. The graph of the data is shown in Figure 1. Positive numbers indicate the measured diameter was larger than the target while negative numbers indicate the measured diameter was smaller than the target. The upper and lower specification limits for acceptable deviation are given as +/- 3.
The most recent batch, sample batch number six, shows one of the 10 parts having a diameter smaller than the lower specification limit. As such, it is a nonconforming part.
The discovery of a nonconforming product triggers two parallel activities: i) figuring out what to do with the nonconforming product, and ii) addressing the cause of the nonconforming product to inhibit the nonconformance from occurring again.
Nonconforming product may be repaired or reworked when possible, but it can always be scrapped. Each one of these three options has its own set of complications and cost.
Repairing a nonconforming product involves additional steps beyond what are usually needed to make the product. This additional processing has the potential to create previously unknown weaknesses in the product e.g. stress concentrations. So repaired product will need to be subjected to testing that verifies it still satisfies its intended use. For this particular case, repairing is not possible. The diameter is smaller than the target. Repair would have been possible if the diameter had been larger than the target.
Reworking a nonconforming product involves undoing the results of the previous process steps, then sending the product through the standard process steps a second time. Undoing the results of the previous process steps involves additional process steps just as were required to repair a nonconforming product. This additional processing has the potential to create previously unknown weaknesses in the product. Reworked product will need to be subjected to testing that verifies it still satisfies its intended use. For this particular case, reworking is not possible.
Scrapping a nonconforming product means to destroy it so that it cannot be accidentally used. For this particular case, scrapping the nonconforming part is the only option available.
ADDRESSING THE CAUSE
In order to determine the cause of the nonconformity we have to first determine the state of the process i.e. whether the process is stable or not. The type of action we take depends on it.
A control chart provides a straightforward way to answer this question. Figure 2. shows an Xbar-R chart for this process. Neither the Xbar chart (top), nor the R chart (bottom) show uncontrolled variation. There is no indication of a special cause affecting the process. This is a stable process in the threshold state. While it is operating on target i.e. its mean is approximately the same as the target, its within-batch variation is more than we would like. Therefore, there is no point trying to hunt down a specific cause for the nonconforming part identified above. It is most likely the product of chance variation that affects this process; a result of the process’s present design.
In fact, the process was left alone to collect more data (Figure 3.). The Xbar-R charts do not show any unusual variation that would indicate external disturbances affecting the process. Its behavior is predictable.
But, even though the process is stable, it does produce nonconforming parts from time to time. Figure 4. shows that a nonconforming part was produced in sampled batch number 22 and one in sampled batch number 23. Still, it would be wasted effort to hunt down specific causes for the creation of these nonconforming parts. They are the result of chance variation that is a property of the present process design.
Because this process is stable, we can estimate the mean and standard deviation of the distribution of individual parts. They were calculated to be -0.0114 and 0.9281. Assuming that the individual parts are normally distributed, we can estimate that this process will produce about 0.12% nonconforming product if left to run as is. Some of these parts will be smaller than the lower specification limit for the diameter. Others will be larger than the upper specification limit for the diameter. That is, about 12 nonconforming pieces will be created per 10,000 parts produced. Is this acceptable?
If the calculated nonconforming rate is not acceptable, then this process must be modified in some fundamental way. This would involves some sort of structured experimentation using methods from design of experiments to reduce variation. New settings for factors like RPM or blade type among others will need to be determined.
This rarely happens. So rarely that I don’t remember the last time, if ever, I had a clean drive to my destination. You know, the drive where you not only hit every single green light, but cars shift out of your lane so you don’t have to compensate for their slowness. Ah! It was most satisfying.
Putting that obviously aberrant experience aside, most times I drive I seem to hit every traffic light and inevitably get stuck behind morons that can’t drive. This is woefully true when I am running late for an appointment. “C’mon dude! Can’t be lettin’ everyone in!” I feel as if the Fates were mocking me and laughing harder with each curse word I would let loose. (You’ll have to trust me that I am a defensive driver. I promise.)
But, is it really so? Are there alway special causes? Would it all be okay if ‘this guy’ or ‘that girl’ would just drive better — like me? I decided to check. Everyday I’ve been logging my commute time to and from work. They are shown in the charts below.
Sure, the average (solid red line) commute to work (~35 minutes) is less than the average commute from work (~43 minutes). And, yes, the variation about the average commute to work is a lot less than that about the average commute from work. But, all points are within my control limits (dashed red lines)! That means, all the variation about the average is from common causes! There are no special causes.
If there were special causes, as would have been highlighted by points outside the limits, I could do something about them. If I ran out of gas during my trip which then added to my commute, I could start my future trips with a full tank of gas. If my tires ran flat because they were bald and delayed me, then before all future trips I would make sure my tires were okay. If there was an accident, then I have a legitimate excuse for being late.
Thing is I have no control over common causes for variation like traffic signals changing to red or getting stuck behind some random slow driver or rain or fog. Sometimes, all these things and others combine in a ‘perfect storm’ to make the commute unusually long… or unusually fast. What the charts tell me is, by and large, the time it takes me to get to work will be between 26 – 45 minutes, and the time it takes me to get home from work will be between 27 – 59 minutes. No amount of frustration is going to change that.