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Attribute control chart template (p, np, c and u charts)

An attribute control chart follows counts over time instead of measurements: defective units on a p or np chart, or defects on a c or u chart. Control limits worked out from the process's own counts show how much the count varies when nothing unusual is happening, so a point beyond a limit, or a long run on one side of the center line, points to a special cause. The p and u charts allow the number inspected to change from one subgroup to the next, which is why their limits are worked out for every subgroup and step up and down with n. Page 1 of the PDF is a paper chart for any of the four: header fields, 25 subgroups with the units inspected, the count, the plotted value and both limits, and a grid lined up under them. Page 2 has a two-question flow for choosing the chart, the formulas, the sample size rules, the signals and a reaction log. Page 3 has four worked examples with their charts, and the common mistakes. The Excel version picks the chart from two answers, checks whether the sample is big enough, takes 30 subgroups on each of four chart sheets, works out the center line and the limits for each subgroup (never below 0), flags points beyond a limit and runs of 7, 8 or 9 on one side, draws the chart with step limits, and has an example sheet for each chart and a reaction log.

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Page 1 of the attribute control chartFields for process, what counts as defective and inspection method, a key for the p, np, c and u charts, a table for 25 subgroups with units inspected, count, plotted value, UCL and LCL, and a blank grid lined up under the subgroups.
Chart selectorp, np, c and u chartsLimits for each subgroupSample size checkLimit and run flagsFour worked examplesReaction log

When to use it

When to use an attribute control chart

  • When the result is pass or fail (visual inspection, a go/no-go gauge, an end-of-line test) and the question is whether the defect rate is stable.
  • When you count defects on a unit or an area: weld defects per frame, paint defects per body, solder defects per board.
  • When the number inspected changes every day, for example 100% inspection of a varying output. The p and u charts give each day its own limits.
  • After a change to a material, a fixture or a method, to see whether the rate really moved, up or down.
  • Not for measurements (use the X-bar and R chart) or for counts with no fixed area of opportunity, such as complaints or breakdowns, where an individuals chart of the rate usually works better.

How to fill it in

  1. 1

    Decide what you count

    Write down what makes a unit defective, or which defects are counted, and keep it fixed. A unit with three scratches is one defective unit and three defects.

  2. 2

    Pick the chart

    Defective units: np if the number inspected is the same every time, p if it varies. Defects: c if the area inspected is the same every time, u if it varies.

  3. 3

    Check the sample size

    The expected count per subgroup (n × p̄, or c̄) should be at least 0.5, and above 9 for a lower limit that can show an improvement. For a p chart that means n above 9(1 − p̄) ÷ p̄: about 290 units at 3% defective.

  4. 4

    Collect 20 to 25 subgroups

    In time order, with the date or shift and the number inspected each time. The center line is the total count ÷ the total inspected, not the average of the daily percentages.

  5. 5

    Set the limits

    Center line ± 3 standard deviations, using each subgroup's own n on the p and u charts. A negative lower limit is set to 0.

  6. 6

    React, then freeze the limits

    Find the cause of every point beyond a limit and every run of 8 on one side, and log it. Keep the limits; recalculate only after a deliberate change, and leave out only points whose cause was found and fixed.

Formulas

The four attribute charts and their limits

3-sigma limits. n is the number of units inspected in the subgroup; a lower limit that comes out negative is set to 0. Sources: NIST/SEMATECH e-Handbook 6.3.3.1 and 6.3.3.2, Minitab's methods and formulas for each chart.

  • p

    What you count
    Defective units
    Sample
    Can vary
    Plotted
    p = d ÷ n
    Center line
    p̄ = Σd ÷ Σn
    Control limits
    p̄ ± 3√(p̄(1 − p̄) ÷ n), per subgroup
  • np

    What you count
    Defective units
    Sample
    Same n every time
    Plotted
    d
    Center line
    n p̄
    Control limits
    n p̄ ± 3√(n p̄(1 − p̄))
  • c

    What you count
    Defects
    Sample
    Same area every time
    Plotted
    c
    Center line
    c̄ = Σc ÷ number of subgroups
    Control limits
    c̄ ± 3√c̄
  • u

    What you count
    Defects
    Sample
    Can vary
    Plotted
    u = c ÷ n
    Center line
    ū = Σc ÷ Σn
    Control limits
    ū ± 3√(ū ÷ n), per subgroup

A filled-in example

Illustrative, not a benchmark

An example: four illustrative data sets, one per chart, the same as the Excel version's example sheets.

Two of the example charts: a p chart and a c chart

p chart: share of housings defective, by day

p chart limits for each day: p̄ ± 3 × √(p̄ (1 − p̄) ÷ n)

Day 17 sits between its own UCL and the one an average n would give, too close to see on the chart.

  1. Day 17 =28 ÷ 540= 5.19%
  2. Its own UCL, n = 540 =2.83% + 3 × √(p̄ (1 − p̄) ÷ 540)= 4.98%: a signal
  3. UCL for one average n =2.83% + 3 × √(p̄ (1 − p̄) ÷ 427.6)= 5.24%: no signal

c chart: weld defects on one frame, by shift

p chart of 25 days of molded housings, 303 defective in 10,690: p-bar 2.83 percent, with limits that step with each day's sample size. Day 17, 28 of 540 or 5.19 percent, is above its own UCL of 4.98 percent, but below the 5.24 percent one average sample size of 427.6 would give. c chart of 25 shifts, one welded frame each: c-bar 10.88, UCL 20.78, LCL 0.98; shift 19, with 26 defects, is above the UCL.

Limits worked out for each day's own n caught day 17; with one average n it would look normal. Shift 19 on the c chart was a worn wire liner.
  • p chart: molded housings, 100% visual inspection, 298 to 540 parts a day for 25 days. 303 defective in 10,690 gives p̄ = 0.02834 (2.83%). Day 17, 28 of 540 = 5.19%, is above its own UCL of 4.98%.
  • With one average n of 427.6 the UCL would be 5.24% and day 17 would look normal. Limits for each subgroup's n caught it.
  • np chart: 200 valves leak-tested a day, limits from days 1 to 16: n p̄ = 7.5, UCL 15.56, no LCL. After a new press-fit fixture on day 17 every day was below 7.5, and day 24 was the 8th in a row.
  • c chart: one welded frame audited per shift. c̄ = 10.88, UCL 20.78, LCL 0.98. Shift 19 had 26 defects, above the UCL: a worn wire liner.
  • u chart: 36 to 72 boards a day, ū = 0.2952 defects per board. Day 21, 36 defects on 59 boards = 0.610, is above its UCL of 0.507.

Three special causes found and one improvement confirmed by the run rule. With the causes fixed and those points left out, p̄ falls to 2.71% and the c chart limits become UCL 19.85 and LCL 0.65 around c̄ = 10.25.

Common mistakes

  • Using one average sample size

    A p chart with limits from the average n hides some signals and invents others. In the example, day 17 is outside its own limit but inside the average-n limit.

  • Averaging the daily percentages

    When n varies, p̄ is the total defective ÷ the total inspected. The mean of the daily percentages gives small days too much weight.

  • Subgroups too small to judge

    With an expected count under 0.5 per subgroup, false alarms climb past 10% (Minitab's study of attribute charts). Inspect more per subgroup, or chart weekly instead of daily.

  • Huge subgroups with every point out

    With thousands of units per subgroup the limits shrink until normal day-to-day change looks like a signal (overdispersion). Use an individuals chart of the rate or a Laney p′ chart.

  • Recalculating the limits every week

    Limits that follow the data absorb every shift. Freeze them after 20 to 25 subgroups and recalculate after a deliberate change.

  • Mixing defect types and streams

    One chart for three machines or ten defect types blurs them all. Stratify: a Pareto of defect types first, then one chart per stream for the ones that matter.

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FAQ

Attribute control chart template (p, np, c and u charts): common questions

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