SPC in Manufacturing: Control Charts and Cpk Explained

What SPC is for

Statistical process control is a way of listening to a process. Every process varies; SPC tells you whether today's variation is the normal background noise of the process (common cause) or a signal that something has changed (special cause), such as a worn tool, a new material lot or a different operator setup. Reacting to noise wastes time and often makes things worse. Ignoring signals produces scrap.

Control limits are not specification limits

Specification limits come from the customer or the drawing: what the part must be. Control limits come from the process: what it is actually doing. A process can be in control and still produce out-of-specification parts if it is centred wrongly or too variable. It can also be out of control while every part is within specification, which is an early warning worth acting on.

Building an X-bar and R chart

• Choose a characteristic that matters to fit, function or the customer.
• Decide a rational subgroup: usually 3 to 5 consecutive parts taken together, so that variation within the subgroup is short-term only.
• Collect at least 20 to 25 subgroups before calculating limits.
• Calculate the average of each subgroup (X-bar) and its range (R).
• Calculate the grand average (X-double-bar) and the average range (R-bar).
• Control limits for X-bar: X-double-bar ± A2 × R-bar. Control limits for R: D3 × R-bar and D4 × R-bar. For subgroups of 5, A2 = 0.577, D3 = 0 and D4 = 2.114.

Worked example (illustrative numbers)

A shaft diameter has a specification of 20.00 ± 0.10 mm, so LSL = 19.90 and USL = 20.10. After 25 subgroups of 5 parts, the grand average is 20.02 mm and the average range is 0.058 mm.

X-bar control limits: 20.02 ± 0.577 × 0.058 = 20.02 ± 0.033, giving UCL 20.053 and LCL 19.987. The R chart upper limit is 2.114 × 0.058 = 0.123.

Estimated short-term standard deviation: sigma = R-bar / d2, where d2 = 2.326 for subgroups of 5. So sigma = 0.058 / 2.326 = 0.0249 mm.

Cp = (USL − LSL) / 6 sigma = 0.20 / 0.150 = 1.34. Cpk = min(USL − mean, mean − LSL) / 3 sigma = min(0.08, 0.12) / 0.0748 = 1.07.

Interpretation: the process spread is capable (Cp 1.34) but it is running off-centre towards the upper limit, which pulls Cpk down to 1.07. Re-centring the process to 20.00 would bring Cpk up to about 1.34 without reducing variation at all. That is usually a cheaper fix than a new machine.

Cpk versus Ppk

Cpk uses short-term variation estimated from within subgroups. Ppk uses the overall standard deviation of all individual readings, which includes shift-to-shift and lot-to-lot drift. If Ppk is much lower than Cpk, the process is capable in the short term but drifts over time; look at setups, material lots and tool changes. Many customers ask for Cpk or Ppk of at least 1.33 on key characteristics, but always check the specific requirement in your customer's quality manual.

Rules that signal a special cause

• One point outside the control limits.
• Seven or more consecutive points on the same side of the centre line.
• Six or more consecutive points steadily increasing or decreasing.
• Two out of three consecutive points beyond two sigma on the same side.

Common mistakes

• Calculating Cpk on an unstable process. Capability numbers only mean something when the chart is in control.
• Recalculating control limits every week, which hides gradual drift.
• Using specification limits as control limits on the chart.
• Measuring with an uncalibrated or inadequate gauge. Check gauge resolution and measurement system variation first.
• Charting everything. Focus on a small number of critical characteristics.

Choosing what to chart

Start with characteristics flagged as critical or significant on the drawing or control plan, then add any characteristic that has caused customer complaints or internal scrap in the past year. For each one, confirm that the measurement system can resolve the tolerance: as a rule of thumb, the gauge should discriminate to at least one tenth of the tolerance band. Review the list quarterly and stop charting characteristics that have been stable and highly capable for a long time; replace them with verification checks so effort goes where risk is.

Doing SPC without the spreadsheet

In QCIN, measurements captured during digital inspections feed X-bar and R charts automatically, with Cpk, Ppk and Pareto analysis on the live dashboard, so the chart is current while the shift is still running.