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Which control chart should I use?

Picking the right control chart comes down to two questions: what kind of data do you have, and how is it grouped?

Step 1: measured or counted?

Measured (continuous) data means things like a diameter, weight, temperature or time. Use a variables chart.
Counted (attribute) data means things like the number of defective parts, or the number of scratches on a panel. Use an attributes chart.

Step 2: pick the chart

Your data	Chart
Measurements, one reading at a time (e.g. one batch per day)	I-MR (individuals and moving range)
Measurements in subgroups of 2–9	X̄-R
Measurements in subgroups of 10 or more	X̄-S
Defective units (pass/fail), sample size varies	p chart (proportion defective)
Defective units, sample size constant	np chart (number defective) or p chart
Defects (counts of flaws), same area or amount inspected each time	c chart
Defects, the inspected area or amount varies	u chart (defects per unit)

Defective or defect? A defective is a whole unit that fails (counted with p or np). A defect is a single flaw, and one unit can have several (counted with c or u).

Worked example: p chart

Each day you inspect 200 parts and record how many are defective. Over 20 days you inspect 4,000 parts and find 120 defectives.

p̄ = 120 / 4000 = 0.030 σ of p = √( p̄(1 − p̄) / n ) = √( 0.03 × 0.97 / 200 ) = 0.01206 UCL = p̄ + 3σ = 0.030 + 3 × 0.01206 = 0.0662 (6.62%) LCL = p̄ − 3σ = 0.030 − 0.0362 = −0.0062 → 0 (a proportion can't be negative)

So a day with 14 defectives out of 200 (7.0%) is above the UCL. That is a signal to investigate. A day with 10 defectives (5.0%) is within normal variation.

Common exam traps

Mixing up p and c charts. Pass/fail units go on p or np charts. Counts of flaws go on c or u charts.
Using a c chart when the inspection area changes. If the amount inspected varies, use a u chart (defects per unit).
Using X̄-R for large subgroups. Once n reaches about 10, the range wastes information. Use X̄-S.
Negative lower limits. When the LCL formula gives a negative number for a count or proportion, set the LCL to 0.
Confusing control limits with spec limits. Control limits come from the process data and show what the process does. Spec limits come from the customer and show what is acceptable. Never draw spec limits on an X̄ chart.

Need A₂, D₄, d₂ or c₄ for your subgroup size? See the free control chart constants table (n = 2–25) with an X̄-R / X̄-S limits calculator.

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