c Chart

A c chart monitors nonconformity counts, often called defects, in constant inspection units.
It is an attribute chart based on a Poisson count model.^[1]

Prerequisites

Prerequisites: Poisson distribution and control chart basics.

Process Context

Use a c chart when the opportunity for defects is essentially constant from sample to sample: same area, same length, same form, same number of units, or same inspection effort.

Definition

The plotted value $c_i$ is the count of nonconformities in inspection unit $i$ . A unit can have more than one nonconformity.

Assumptions / Requirements

• Constant inspection unit size.
• Defects are countable events.
• Events are approximately independent and rare over many opportunities.
• The stable defect rate is constant unless a special cause occurs.

Notation

Control Limits / Formula

Interpretation Rules

• A high point means more defects than expected from stable Poisson variation.
• Low points can indicate improvement or changed inspection methods.
• If inspection unit size changes, use a u chart.

Worked Example

Five equal-area panels have defect counts $3,5,2,4,6$ . Then $\overline{c}=4$ .

All five counts are inside the limits.

Common Mistakes

• Using a c chart for defective units instead of defects.
• Using a c chart when inspection area or opportunity changes.
• Treating each defect as equally severe without checking whether stratification is needed.
• Forgetting that the LCL is zero when the formula is negative.

Connections

References