Choosing the right attribute chart
| Constant sample size | Variable sample size | |
|---|---|---|
| Defective units (pass/fail) | np chart | p chart |
| Defects (count of nonconformities) | c chart | u chart |
Formulas
- p chart:
p̄ = Σd / Σn, limitsp̄ ± 3√(p̄(1 − p̄) / nᵢ) - np chart: centre
n·p̄, limitsn·p̄ ± 3√(n·p̄(1 − p̄)) - c chart:
c̄ = Σc / k, limitsc̄ ± 3√c̄ - u chart:
ū = Σc / Σn, limitsū ± 3√(ū / nᵢ)
Tips
Collect at least 20 to 25 samples before calculating limits. Samples should be large enough to contain a few defectives on average, otherwise most points sit on zero and the chart cannot react. Attribute charts need much more data than variables charts, so when you can measure the characteristic, an X-bar R or I-MR chart is more sensitive. To decide which defect types to attack first, use a Pareto chart.
Frequently asked questions
›When do I use a p chart instead of an np chart?
Both track defective units. Use an np chart when every sample has the same size, it plots the number of defectives. Use a p chart when sample sizes vary, it plots the proportion defective and the control limits change with each sample size.
›What is the difference between a defect and a defective?
A defective is a unit that fails, counted once no matter how many problems it has (p and np charts). A defect is a single nonconformity, and one unit can have several (c and u charts).
›When do I use a c chart instead of a u chart?
Use a c chart when the inspection area or number of units is the same for every sample, for example defects per car. Use a u chart when it varies, for example defects per square metre of fabric with different roll lengths.
›Why is the lower control limit zero?
Counts cannot be negative. When the calculated lower limit is below zero it is set to zero, which is common for low defect rates. Very low rates also mean the normal approximation is weak, which the tool warns about.
›Which out-of-control rules are applied?
Points beyond 3 sigma, 9 points in a row on the same side of the centre line and 6 points in a row steadily increasing or decreasing. With variable sample sizes the rules are applied to standardised values.