Six Sigma and Beyond: Statistical Process Control, Volume IV

Traditional SPC requires a long continuous run of the same part number. Short run requires short runs of many different part numbers . A short run is any situation in which there are insufficient subgroup data for a given part number to allow calculation of traditional Shewhart control limits in a timely manner. This occurs when

1. The lot size is extremely small (1 to 15 pieces).

   Even with n = 1, not enough plot points are generated to calculate traditional control limits, where the number of plotted subgroups ( k ) is recommended to be at least 20.

   Small lot sizes are very typical in companies using short-run manufacturing systems (also in job shops ).

2. The lot size is large (more than 100 pieces), but few subgroups are collected.

   For example, a stamping operation running a certain part number may produce over 10,000 pieces per hour, with a subgroup taken every half hour . But if this part number is run for only 2 hours, only four plot points are generated ”not enough to calculate traditional control limits. (The problem, of course, is that with this small sample, we cannot really figure out the true variation of the process.)

So what is one supposed to do? Previous attempts at monitoring short runs have been tried. These include

• First/Last piece inspection (risky). Many companies measure only the first piece that is run from a new setup. If this piece is acceptable, the remainder is run with no more checks being made. This practice is risky because many process changes occur over time (tool wear, temperature changes, coolant deterioration, operator fatigue).

  Sometimes, the last piece off is also measured, but if this one is good, all that is really known is that two good pieces were made. What if this last piece is bad? When did the process change? How many bad pieces were produced? It is too late after the run is over to discover that there was a problem.

• 100% inspection (costly). Instead of checking only the first and last pieces of a run, all pieces could be measured. This is usually a costly alternative and, in cases where destructive testing is required, not practical. Even if the measurement is inexpensive and nondestructive, 100% inspection is not totally effective ”some say that it is only about 79% effective. This means that if a defective part is made, there is a 21 % chance that it will get through the 100% inspection check and end up in the hands of the customer. (We are talking about human inspection here, not automatic computer vision systems or process controllers on the machine. Those systems are as accurate as designed.)

• Traditional control charts (messy). Separate charts are needed because the control limits of traditional SPC charts depend on Xdouble bar and Rbar as shown in the following formula. If either Xdouble bar or Rbar changes from one part number to the next , then the limits change, requiring a different chart:

Quite a few companies initially try this option of implementing SPC in their job shop operations but find that it is a futile battle, and before too long they abandon the SPC with the now-famous comment, "SPC does not apply here." What they have failed to understand is that the SPC, as applied in their environment, was the wrong approach. This could be substantiated by a simple walking exercise through the plant. What one finds or notices in such situations is a filing cabinet next to every machine. The filing cabinets are necessary to hold the hundreds of control charts required for each operation ”one for every different part number ”but they are, in fact, worthless.

In addition to the unwieldy number of charts, there is usually an insufficient number of subgroups plotted on each one to calculate control limits ( k should be at least 20). It may require several runs of a part number to accumulate enough data for this calculation, which could take months (if not years ). Time- related process changes are difficult to detect because the data are divided among numerous separate charts.

To be sure, the intent was to identify the variation in the process, but with all the above tries , there was a great inefficiency and cumbersomeness associated with studying a process of small runs. To eliminate this problem and facilitate the studying of any process with small runs, there are two approaches that may be used to optimize the process, even when it generates a sample of one ( n = 1).

1. Treat ALL the data with a coding scheme and use the traditional charts as described in Chapters 8, 9, and 10, including their interpretation.

2. Use target values for each characteristic and plot the values on a ±3 sigma basis.

Both these methods are effective and will identify the variation in the process. Let us examine these methods with both variable and attribute data.