In my previous column I discussed the role of specification limits in manufacturing, which led to thoughts about process control limits.

Walter Shewhart invented the process control chart while working for Western Electric in the 1920s. He created the basis for the process control chart and the concept of a state of statistical control through the use of natural process limits via designed experiments.

The basic idea of control limits is to periodically sample the process, measure a quality characteristic on a few selected product units, then plot these results (generally average and range) in a time series. After sufficient process history has been taken, upper and lower control limits (sometimes called natural process limits) are established at ±3 standard deviations from the average of readings (not the specification center line).

Any data points outside these ‘natural’ process control limits give an indication the process is not behaving as desired; thereby indicating the process is out of statistical control. When there are data points falling outside the control limits, there is an indication of a special-cause event, so the process should be discontinued until the issue’s root cause has been found and resolved which will then return the process to a state of statistical control.

This is a relatively simple concept and just one reason the methodology has become popular and so extensively applied. With that said, however, it seems that effective implementation of process control charts remains elusive to many.

One reason may be confusion with the concept of rational subgroups. If the proper sampling strategy isn’t employed the control charts becomes less effective, so care must be taken to choose an appropriate selection strategy. Frequently a sampling strategy is determined by logistics within an organization’s facility and manufacturing process. Often the logistics will not produce desired rational subgroups. If this is the case, control charts can give false signals and lead to improper conclusions.

Preferably, rational subgroups will be groups of product that capture or include virtually the entire inherent natural, or what Shewhart termed common cause, variation for any specific quality feature that has been targeted for control.

A colleague mentioned his frustration with a process that had very tight limits resulting in over-control due to false signals which should only happen occasionally if the proper sampling technique, from a stable process, is deployed. He worked in the semiconductor industry where the product unit is a chip that is produced on wafers within lots comprised of a specific number of wafers. The production process had many potential sources of inherent variation.

Most sampling was performed by measuring several chips on a specific wafer within a specific lot, with the resultant wafer average being used as the control statistic. While this is a logistically and seemingly an economically appropriate sampling approach, it failed to produce the rational subgroups needed for common control chart applications. There will still be inherent, common cause variation across sample groups.

Simply using a common estimate of within-group variation produced an underestimate, and sometimes a gross underestimate, of the true inherent variation in the process. This generated control limits that were too tight and resulted in over control. Ultimately there were so many false out-of-control data points that all signals began to be ignored.

The eventual success story is that the certified quality engineer over this process realized what was happening. A team was formed and a decision was made to conduct an experimental design. An analysis of variance (ANOVA) was performed to extract valid estimates of the relevant process variance components required to effectively estimate common-cause process variation. Once this was done the appropriate rational subgroup methodology was revised and the problem was resolved.

The point is that control limits provide information about process behavior and have no intrinsic relationship to engineering specifications. In practice, the process mean may not, and typically doesn’t, coincide with the specified engineering target of the quality characteristic because most manufacturing processes simply cannot deliver the process characteristic at the desired level.

Control charts shouldn’t be used without first performing process capability studies to determine the relationship between natural process limits and engineering specification. When capability is known the purpose of control chart limits is to permit simple detection events that are indicative of actual process change. When significant change (special cause variation) is detected the culprit must be identified and eliminated with affected data points eliminated from control chart limit calculation.

Bottom line, after the process capability study has been conducted, engineering specification limits are infrequently consulted by the manufacturing process personnel.