Statistical process control: time order and special causes

Why it matters

Measurements coming from a process are not expected to be equal to one another. Small variations arise even when the work definition is kept. Statistical process control evaluates this variation along the time axis. The question is not only whether the mean is close to the target; it is also whether the variation comes from the same process behavior. A control chart compares new observations with a reference setup calculated from earlier observations. A point going outside the limits is a sign to investigate. The cause of a signal is not read directly from the chart. Explanations such as setup, material, measurement or recording error must be tested with evidence from the time of the event. The chart does not name the cause; it shows where investigation is needed.

Product specification limits state at which values the product will be accepted. Control limits, on the other hand, are calculated from the variability of the monitored process and the chosen chart structure. Their source and purpose are different. A signal of change can arise in the process while all products stay within specification. Conversely, while the process looks statistically stable, part of the distribution can lie outside the acceptance range. For this reason the phrase "in control" is not used to mean "all products are conforming". For the product decision, the specification and a valid measurement are needed; for process behavior, the time order and a suitable control chart are examined. The two decisions are justified under separate headings in the same report.

A subgroup is measurements taken together under similar short-term conditions. Here each subgroup has five product measurements taken consecutively. The order among subgroups preserves production time. The group mean helps monitor change in location, and the range helps monitor spread within the group. The range is the smallest value subtracted from the largest. Sorting the measurements from smallest to largest and then grouping them rewrites the conditions that occurred in the process. Even if the calculations of such groups are done correctly, the chart does not represent the real time behavior. Which sampling plan the groups came from matters as much as the choice of coefficients.

The reliability of a control chart does not depend on the calculated lines looking neat. The measurement definition, sampling frequency, data recording and response plan must be set up together. When a signal appears, a decision to protect the product may be needed; but adjusting the setup at every fluctuation can add extra variation to the process. Investigation rules defined in advance are therefore necessary. Choosing, after seeing the data, only the rule that gives the wanted result is not correct. In this lesson the range chart is examined first, then the mean chart. A limit violation and a time sequence are evaluated together; the absence of a signal gives no certainty that no problem will arise in the future.

Formula