SPC
Control charts that speak up
A control chart has one job: to tell you, as early as possible, that your process has changed - before the parts go out of specification, before the customer finds out, before anyone has to write an NCR. Most control charts in the wild never get the chance, because they are drawn weekly in a spreadsheet, glanced at, and filed. A chart that nobody reads in real time is a history lesson, not a control.
The good news: the statistics you need to run SPC well fit in one article. This one.
Control limits are not specification limits
The single most important idea in SPC, and the most commonly fumbled. Specification limits are what the customer needs - they come from the drawing. Control limits are what the process does - they are calculated from your own data, at roughly three standard deviations either side of the process mean. The process neither knows nor cares about your drawing.
Specification limits describe the parts you are allowed to make. Control limits describe the parts your process actually makes when nothing unusual is happening. Confuse them and you will either tamper with a healthy process or sleep through a sick one.
A point outside a control limit does not mean "out of spec". It means "something changed" - a special cause has entered: a tool has worn, a material lot is different, a setting has drifted. That is precisely the information you want at the earliest possible moment.
Which chart: X-bar & R or I-MR?
For measured (variable) data, the choice comes down to how your data arrives:
X-bar & R - subgrouped data
- You can grab small samples (2-5 consecutive parts) at intervals
- The X-bar chart tracks between-sample drift; the R chart tracks within-sample scatter
- Averaging makes it more sensitive to small shifts than individual points
- The standard choice for reasonably fast, repetitive production
I-MR - individual readings
- Each measurement stands alone: slow processes, batch values, destructive tests, one reading per lot
- The I chart tracks the readings; the MR chart tracks the jump between consecutive readings
- Less sensitive than X-bar & R, but honest when subgrouping is impossible or artificial
In both cases the limits come from published constants (A2, D3, D4 by subgroup size for X-bar & R; E2 = 2.660 for individuals) applied to your average range. The constants are not folklore - they are the bridge between the range and an estimate of the process standard deviation - and applying the right constant for the right subgroup size is exactly the detail cheap templates get wrong.
Run rules: catching the drift that never breaches a limit
A process can go wrong politely - drifting slowly, never quite crossing a limit. That is what the run rules are for. The three that catch most real-world trouble:
- Beyond limits - any point outside a control limit. The classic special cause.
- Run of 7 - seven consecutive points on the same side of the centre line. The odds of that from a centred process are below 1%: the mean has shifted, even though no limit was breached.
- Trend of 7 - seven consecutive points steadily rising or falling. The signature of tool wear, temperature creep and slow drift.
These should be formulas, not eyeballing. A rule that depends on a busy human noticing a subtle pattern across seven points is a rule that fires late. When a signal does fire, the response is investigation and adjustment of the process - and crucially, no adjustment when there is no signal. Tampering with an in-control process (chasing every wiggle back to nominal) adds variation; Deming demonstrated it with a funnel decades ago and production lines re-demonstrate it daily.
Control first, capability second
Cp and Cpk - the capability indices that compare your process spread and centring to the specification - are only meaningful for a process in statistical control. An out-of-control process has no single "spread" to compare; whatever number you compute today will be a different number next week. The order of operations is fixed: prove the gauge (Gauge R&R), get the chart stable, then read Cp/Cpk against the 1.33 threshold most customers expect. Capability claimed from an unstable chart is a number wearing a lab coat.
And connect the chart to the paperwork: SPC as the control method on a characteristic is exactly what your control plan's Control Method column is for, with the reaction plan saying what happens when a rule fires.
SPC that flags special causes itself
X-bar & R (subgroup 2-5) and I-MR charts with auto limits from the correct constants, automatic Beyond limits / Run of 7 / Trend of 7 flags, and a Cp/Cpk tab with a colour-coded verdict.