Statistical process control (SPC): normal variation or a signal?

Values creeping towards the limit

A dimension has been stable for weeks. During one shift the values move slowly towards the upper tolerance limit, but every part is still accepted. The operator wonders whether to adjust. Quality wonders whether the process has changed. Production wonders whether a tool change should be planned.

Without a way to tell normal variation from a real change, the answer is a feeling. Statistical process control gives everyone the same basis for the decision. In everyday speech it is often just called process control.

Common causes and special causes

Variation comes in two kinds. Common causes are the many small factors that are always present: slight differences in material, temperature, set-up and measurement. Together they give a spread that is stable and predictable. Special causes are specific events that change the process, such as a worn tool, a new batch of material or a changed setting.

A process affected only by common causes is called stable, or in statistical control. You can predict how it will behave. Adjusting a stable process because of normal variation, chasing every value, tends to make the spread larger, not smaller.

The control chart

The tool for telling the two apart is the control chart. Small subgroups are measured at regular intervals and plotted in time order, together with a centre line and control limits calculated from the process’s own data, typically three standard deviations from the centre line.

The most common charts are:

• X̄-R: subgroup means and ranges, for subgroups of a few parts, for example five parts every hour.
• X̄-s: as X̄-R but with the standard deviation, for larger subgroups.
• Individuals and moving range (I-MR): when each measurement is its own subgroup, for example when testing is expensive or production slow.
• Attribute charts (p, np, c, u): for the proportion or count of defects, when the result is pass or fail rather than a measured value.

Control limits are not tolerance limits. A process can give a signal while every part is good, and it can be stable while producing parts outside tolerance. The first is an early warning. The second means the process needs improving or the requirement needs reviewing; adjusting will not fix it.

Rules for signals

The most familiar signal is a point outside a control limit. But a process can change without any single point crossing a limit, so additional rules look for patterns that are unlikely under common-cause variation alone. A widely used set, originally from Western Electric, includes:

• one point beyond three standard deviations from the centre line
• two out of three consecutive points beyond two standard deviations on the same side
• four out of five consecutive points beyond one standard deviation on the same side
• eight consecutive points on the same side of the centre line

Lloyd Nelson’s set of eight rules adds others, for example six points in a row steadily increasing or decreasing, which catches gradual drift such as tool wear.

More rules find changes sooner but also give more false alarms. Choose a set that fits the process and use it consistently.

A signal is a question, not an answer

A signal means: look for the cause. The response belongs in a reaction plan written before it is needed. Who checks what, when to stop, when to adjust. Write down what was found and done, so the next person can see the history on the chart.

Before you start

• Know your measurement system. If the gauge contributes a large share of the variation, the chart shows measurement noise. Measurement system analysis answers that question.
• Choose rational subgroups. Parts in a subgroup should be made under the same conditions, so that differences between subgroups show change over time.
• Base limits on a stable period with enough data, typically at least 20 to 25 subgroups.

When the process is stable, it makes sense to ask whether it can meet the requirement in the long run. That is process capability.

In short

SPC is a way of listening to the process. It tells you when something has changed so that you can find out why, and it tells you when nothing has changed so that you can leave the process alone.