c‑Chart Count Defects Calculator

Enter Samples

This chart assumes a Poisson model where the sample size is constant and the count of defects per unit is monitored.

Summary

Samples n: 20
∑ Defects: 47
c̄ (mean): 2.350
σ = √c̄: 1.533

UCL (3σ): 6.949
CL: 2.350
LCL (3σ): 0.000

Data & Diagnostics

#	Defects	Zone	Status
1	3.000	Zone C (≤1σ)	In control
2	0.000	Zone A (2–3σ)	In control
3	2.000	Zone C (≤1σ)	In control
4	1.000	Zone C (≤1σ)	In control
5	4.000	Zone B (1–2σ)	In control
6	2.000	Zone C (≤1σ)	In control
7	3.000	Zone C (≤1σ)	In control
8	5.000	Zone B (1–2σ)	In control
9	1.000	Zone C (≤1σ)	In control
10	2.000	Zone C (≤1σ)	In control
11	3.000	Zone C (≤1σ)	In control
12	0.000	Zone A (2–3σ)	In control
13	6.000	Zone A (2–3σ)	In control
14	2.000	Zone C (≤1σ)	In control
15	1.000	Zone C (≤1σ)	In control
16	4.000	Zone B (1–2σ)	In control
17	3.000	Zone C (≤1σ)	In control
18	2.000	Zone C (≤1σ)	In control
19	1.000	Zone C (≤1σ)	In control
20	2.000	Zone C (≤1σ)	In control

Rules Check

Rule 1: One point beyond 3σ: No violations detected.
Rule 2: Eight consecutive on the same side of CL: No violations detected.
Rule 3: Six points trending up or down: No violations detected.
Rule 4: Two of three in Zone A on same side: No violations detected.

How calculations work

For a c‑Chart, the center line is the average number of defects per unit: c̄ = (∑ defects) / n. Sigma is σ = √c̄. Three‑sigma limits are UCL = c̄ + 3σ and LCL = max(0, c̄ − 3σ). Optional zone lines at 1σ and 2σ support supplemental runs rules.

Use a c‑Chart when the opportunity area or inspection unit size is constant and you are counting defects, not defectives.

FAQs

1) When should I use a c‑Chart instead of a u‑Chart?

Use a c‑Chart when the sample size or area of opportunity is constant across observations. If sample sizes vary, use a u‑Chart for defects per unit.

2) What assumptions underlie this calculator?

The model assumes counts follow a Poisson distribution, samples are independent, and each sample represents the same inspection opportunity. Large overdispersion suggests investigating special causes or using alternatives.

3) What do negative lower limits mean?

If the computed LCL is negative, it is set to zero by convention. Very low LCLs are common when average defect counts are small.

4) How are runs rules applied here?

We flag points beyond 3σ, eight in a row on one side of the center line, six monotonically increasing or decreasing, and two of three in Zone A on the same side.

5) Can I detect gradual drift without limit violations?

Yes. Eight on one side of the center line and six‑point trends help detect small sustained shifts that may not cross the control limits.

6) How many samples do I need?

More is better for stable limits. A common guideline is at least 20 to 25 subgroups to estimate a reliable average and standard deviation proxy.

7) Can I export and share my analysis?

Use the CSV and chart download buttons. You can also save the page after entering your samples to preserve results locally.

This tool is for educational and operational guidance. Always confirm results with your internal quality procedures.