SPC and process capability

Two numbers get confused more often than any others in manufacturing: the limits that come from the process and the limits that come from the drawing. They arrive from opposite directions, they answer different questions, and putting them on the same chart is how a good control tool becomes a source of unnecessary adjustment.

An X-bar and range control chart on a clipboard at a grinding machine, partly filled in by hand, with plotted points and calculated control limits drawn as dashed lines, a bore gauge and a master ring on the bench beside it, and a capability report showing a histogram on a monitor in the background. — Hand plotted, at the machine, by the person who can act on it. That is still the arrangement that works best.

Control limits are not specification limits

A diagram contrasting control limits with specification limits. At the top, an X-bar control chart is drawn with a centre line and upper and lower control limits as dashed lines, labelled as calculated from the process data and describing what the process does. Below it the same chart is redrawn with specification limits added as heavy solid lines further out, labelled as coming from the design and describing what is required, with a warning symbol and a note that plotting specification limits on a control chart invites reaction to points that are not signals. To the right, four cases are shown as distribution curves against a tolerance band: in control and capable, in control but not capable, out of control but appearing capable, and neither, with a note that only the first can be predicted. At the bottom, a tampering sequence shows a stable process where each small random deviation is corrected, producing a plotted output whose spread is visibly wider than the original. — Four combinations, and only one of them lets you say anything about tomorrow. The strip at the bottom is what over-adjustment costs.

	Comes from	Answers
Control limits	The process data	What does this process do?
Specification limits	The design	What is required?

Neither answers the other’s question. A process can be beautifully in control and entirely incapable, and it can be out of control while most parts happen to conform.

Common cause, special cause, and tampering

Variation	Nature	Response
Common cause	Inherent, always present	Change the process
Special cause	An identifiable disturbance	Investigate and eliminate

Rational subgroups

A subgroup should be chosen so that variation within it is common cause only. Consecutive parts usually achieve this, because very little can change in that interval, and shifts then show up as variation between subgroups, which is what the chart is built to detect.

Sample across two machines into one subgroup and the within-subgroup variation inflates, the control limits widen, and the chart stops signalling anything. A chart that never signals looks reassuring and is worthless.

Reading more than the limits

Watching only for points outside the limits throws away most of the chart’s sensitivity. A sustained mean shift can occur with no point crossing a limit at all.

Pattern	Suggests
Point beyond a control limit	A distinct event
Eight points one side of the centre line	A shift in the mean
Six points steadily rising or falling	Tool wear, thermal drift
Alternating sawtooth	Two streams mixed, or over-adjustment
Points hugging the centre line	Subgrouping or plotting problem

The four indices

A diagram explaining the four capability indices. On the left, two distribution curves are drawn against the same tolerance band. The first is narrow and centred, annotated with a high Cp and a high Cpk. The second is equally narrow but shifted towards the upper specification limit, annotated with the same high Cp but a much lower Cpk, illustrating that Cp ignores centring. On the right, a long sequence of subgroups is drawn over time, each individually narrow but with the subgroup means stepping up and down between setups and tool changes. A bracket over one subgroup is labelled within subgroup variation giving Cp and Cpk, and a bracket over the whole sequence is labelled total variation giving Pp and Ppk, with the visible gap between the two annotated as shifts and drifts between subgroups. A note states that Cpk can never exceed Cp, and that a large gap between Cpk and Ppk points at setup, tool change and material lot effects rather than inherent spread. — Same spread, different centring, on the left. Same spread, different time horizon, on the right.

Index	Uses	Accounts for centring
Cp	Within-subgroup (short-term)	No
Cpk	Within-subgroup (short-term)	Yes
Pp	Total (long-term)	No
Ppk	Total (long-term)	Yes

Two relationships carry most of the diagnostic value:

Cpk can never exceed Cp. A big difference between them means the process is off centre — and centring is usually the cheapest improvement available.
A big gap between Cpk and Ppk means the process is capable moment to moment but not held over time. That points squarely at setup, tool change and material lot effects rather than inherent spread.

Variable beats attribute, when you can afford it

A variable chart shows the mean walking towards a limit while every part still conforms — which is the entire window in which prevention is possible.

An attribute chart shows nothing until parts start failing, because a pass or fail result throws away the information about how close to the limit the part was. By the time it signals, the opportunity has been spent.

Which characteristics get charted, at what frequency and with what response, is recorded in the control plan; what happens when a chart signals a real problem belongs to problem solving and 8D.

What to take away

Control limits describe the process; specification limits state the requirement.
Never plot specification limits on a control chart.
Common cause needs a process change; special cause needs an investigation.
Tampering measurably widens the output spread. React to signals, not points.
Rational subgroups — consecutive parts, so shifts appear between subgroups.
Poor subgrouping widens the limits and produces a chart that never signals.
Use the run and trend rules; a mean can shift with no point out of limits.
Recalculate limits only after a verified deliberate change.
Cpk ≤ Cp always; the gap is an off-centre process.
A Cpk-to-Ppk gap means setup, tool change and lot effects, not spread.
Capability requires stability first, and a capable measurement system before that.
Attribute charts signal late — variable data buys you the prevention window.