KEVOS® MAKEOS · Quality
c-Chart Check (Defects per Unit, Poisson Control Limits, Counts Out of Control)
From the number of defects found on each inspection unit, what is the average count, where are the control limits, and is any unit out of control?
Counts (c) control chart from up to twelve inspection units of the same size: the average number of defects per unit, the upper and lower control limits from the Poisson model (no lower limit when it would be negative), the defect count that would signal, and which units fall outside the limits.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of units used | units | How many of the units below to use, in time order. |
| Limit width | standard deviations | How many standard deviations the limits sit from the centre line (3 is usual). |
| Defects found on each unit | ||
| Unit 1 defects | defects | Number of defects (nonconformities) counted on inspection unit 1. |
| Unit 2 defects | defects | Number of defects (nonconformities) counted on inspection unit 2. |
| Unit 3 defects | defects | Number of defects (nonconformities) counted on inspection unit 3. |
| Unit 4 defects | defects | Number of defects (nonconformities) counted on inspection unit 4. |
| Unit 5 defects | defects | Number of defects (nonconformities) counted on inspection unit 5. |
| Unit 6 defects | defects | Number of defects (nonconformities) counted on inspection unit 6. |
| Unit 7 defects | defects | Number of defects (nonconformities) counted on inspection unit 7. |
| Unit 8 defects | defects | Number of defects (nonconformities) counted on inspection unit 8. |
| Unit 9 defects | defects | Number of defects (nonconformities) counted on inspection unit 9. |
| Unit 10 defects | defects | Number of defects (nonconformities) counted on inspection unit 10. |
| Unit 11 defects | defects | Number of defects (nonconformities) counted on inspection unit 11. |
| Unit 12 defects | defects | Number of defects (nonconformities) counted on inspection unit 12. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of units used
- What it is
- How many of the inspection units listed below are used for the chart, counting from the first in time order.
- Units and format
- Enter a number in units: a count of units. The form accepts 2 units to 12 units. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Units beyond this count are ignored.
- Get it right
- Use 20 to 25 units for settled limits; twelve gives a first look.
What this means: Limit width
- What it is
- How many standard deviations the control limits sit above and below the average count.
- Units and format
- Enter a number in standard deviations: standard deviations. The form accepts 1 standard deviations to 6 standard deviations. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 standard deviations as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The limits move out in proportion to the square root of the average count.
- Get it right
- Three is usual (NIST notes k is often 3).
Defects found on each unit
What this means: Unit 1 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 1, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 14 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 1, using the same inspection unit size and method as the other units.
What this means: Unit 2 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 2, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 2, using the same inspection unit size and method as the other units.
What this means: Unit 3 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 3, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 3, using the same inspection unit size and method as the other units.
What this means: Unit 4 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 4, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 4, using the same inspection unit size and method as the other units.
What this means: Unit 5 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 5, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 5, using the same inspection unit size and method as the other units.
What this means: Unit 6 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 6, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 6, using the same inspection unit size and method as the other units.
What this means: Unit 7 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 7, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 17 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 7, using the same inspection unit size and method as the other units.
What this means: Unit 8 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 8, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 13 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 8, using the same inspection unit size and method as the other units.
What this means: Unit 9 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 9, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 19 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 9, using the same inspection unit size and method as the other units.
What this means: Unit 10 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 10, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 10, using the same inspection unit size and method as the other units.
What this means: Unit 11 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 11, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 11, using the same inspection unit size and method as the other units.
What this means: Unit 12 defects
- What it is
- The number of defects (nonconformities) counted on inspection unit 12, such as blemishes on a panel or faults on an assembly.
- Units and format
- Enter a number in defects: defects. The form accepts 0 defects to 10000000 defects. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 defects as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the average count and the limits slightly; a count above the upper limit signals a special cause.
- Get it right
- Count every defect on unit 12, using the same inspection unit size and method as the other units.
Method and formulas
- Centre line c̄ = total defects ÷ number of units.
- Control limits = c̄ ± k √c̄ (Poisson: the variance equals the mean; NIST e-Handbook 6.3.3.1); if the lower limit is negative there is no lower limit.
- A unit above the upper or below a positive lower limit signals a special cause.
- Example: average 16 defects per unit, limits 4 to 28; 0 unit(s) outside.
Limitations
- Every inspection unit must be the same size (same area, length or number of items); different sizes need a chart of defects per unit size.
- Assumes defects occur independently (Poisson); clustered defects give false signals.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Chart paint or weld defects per panel or assembly
- Check whether a bad unit is a special cause
- Set an alarm level for defects found at final inspection
Who it is for
- Quality engineers and inspectors
- Production supervisors
- Continuous improvement staff
What you get
- Average defects per unit
- Upper and lower control limits
- Defect count that signals
- Units outside the limits
Interpreting the result
- A c chart counts defects, not defective items: one unit can carry several defects. Use a p chart for the fraction of defective items.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.3.3.1 Counts Control Charts — https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc331.htm
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Are the stops random? Poisson counts and memoryless clocks
In Breakdowns and Buffers by the Numbers
What it covers: Testing a stoppage log for the randomness a Markov model assumes: Poisson counts per shift, a c chart for special causes, exponential intervals, repair time spread and wear-out parts.
Method explained here · KEVOS® original book
Charts for counts and proportions
In Control Charts by the Numbers
What it covers: Defectives and defects as binomial and Poisson random variables: p and c chart limits, why they are asymmetric, limits that change with sample size, missing lower limits, and when to use a u chart.
Method explained here · KEVOS® original book
Charting and sampling defect counts
What it covers: Charting daily defect counts with c and u charts, why clustering between parts causes false alarms and how to widen the limits, how inspection misses defects, and planning sampling of outgoing parts.
Method explained here · Library collection
Statistical process control on the shop floor: control charts, real signals and when to leave a process alone
What it covers: Control charts separate the normal noise of a process from real change. How to choose a chart, set limits, read the signals and stop well-meant adjustments that make variation worse.
KEVOS® tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the c-Chart Check (Defects per Unit, Poisson Control Limits, Counts Out of Control) calculator