What is SPC?

Statistical Process Control uses the behaviour of a process’s own output to tell you whether it is behaving consistently — which is a different question from whether its parts pass.

The idea that makes it work

Every process varies. The insight, which is a century old and still routinely missed, is that variation comes in two kinds.

Common cause variation is inherent — the accumulated noise of a process running normally. It is stable and predictable, and you cannot remove it by reacting to individual readings.

Special cause variation is something new: a tool wearing, a material batch change, a different operator, a machine drifting. It is not part of normal behaviour, and it is what you want to detect.

SPC separates the two. That matters because reacting to common cause variation as though it were special — adjusting the machine because one reading looked high — measurably makes a process worse. This is called tampering, and it is one of the most common ways well-intentioned operators increase variation.

Control limits are not tolerance limits

The single most important point on this page.

Tolerance limits come from the drawing. They say what the customer will accept.

Control limits are calculated from the process’s own observed variation. They say what the process normally does.

They are unrelated numbers, and confusing them destroys the value of the technique. A process can be perfectly in control and still produce scrap, if its natural variation is wider than the tolerance. And a process can be drifting badly out of control while every part still passes — which is the case SPC is for, because it gives you hours of warning before the first bad part.

Practical consequence: never draw tolerance limits on a control chart and treat them as control limits. It is a common spreadsheet error and it makes the chart blind to exactly what it exists to detect.

Reading an X̄–R chart

The most common pair for measured data. Take small subgroups — typically four or five consecutive parts — and plot two things: the average of each subgroup, and its range.

The X̄ chart tracks whether the process centre is moving. The R chart tracks whether its spread is changing. Both matter, and the R chart is read first: if the spread is unstable, the limits on the average chart are calculated from unstable variation and cannot be trusted.

Subgrouping is not arbitrary. The point is to capture only common cause variation within each subgroup, so that anything special shows up between subgroups. Consecutive parts achieve that; five parts sampled across a shift do not, and will produce limits so wide the chart never signals.

Out-of-control signals

A point beyond a control limit is the obvious signal, and the least interesting one. The valuable signals are patterns, because they appear earlier:

• A run of points on one side of the centre line — the process has shifted.
• A steady trend up or down — something is progressively changing, such as tool wear.
• Points hugging the centre line too closely — often a sign the data is not what it appears to be, or the subgrouping is wrong.
• Alternating high-low patterns — frequently two machines or two fixtures being charted as one.

These are codified as the Nelson rules. Applying them by eye across dozens of characteristics is not realistic, which is the honest argument for software here: the rules are simple, and checking them consistently is not.

Cp, Cpk, Pp, Ppk

Capability indices compare what the process does to what the tolerance allows.

Cp compares the process spread to the tolerance width. It measures tightness and ignores position entirely. Cpk also accounts for centring, so a tight process aimed off-target has a good Cp and a poor Cpk. Report both: the gap between them is a statement about setup rather than capability, and it is usually the cheaper thing to fix.

Cp and Cpk use within-subgroup variation, describing short-term capability — what the process can do when behaving. Pp and Ppk use total variation across the whole study, describing actual long-term performance. A large gap between the pairs means the process is shifting between subgroups: capable in the short term, not held there over time.

One caveat that matters more than any index value: capability numbers from an out-of-control process are meaningless. They describe a distribution that is not stable, and predicting from them is unsound. Establish control first, then measure capability. Reversing that order is the most common misuse of these statistics in manufacturing.