Calculate c-chart control limits for defect count data. Monitor the number of defects per inspection unit using Poisson-based SPC limits.
The c-chart is an attribute control chart that monitors the count of defects per inspection unit. Unlike the p-chart, which tracks whether units are defective or not, the c-chart counts how many defects occur on each unit. A single circuit board could have 0, 1, 2, or more solder defects — the c-chart monitors this count.
The c-chart assumes defect counts follow a Poisson distribution, which is valid when defects are relatively rare and the inspection area or opportunity is constant across samples. Control limits are calculated from c-bar (the average defect count) using the Poisson standard deviation √c-bar.
This calculator computes c-bar and control limits from total defects observed and number of samples inspected, providing ready-to-use limits for your c-chart.
Quantifying this parameter enables systematic comparison across time periods, shifts, and production lines, revealing patterns that might otherwise go unnoticed in routine operations. This analytical approach aligns with lean manufacturing principles by replacing waste-generating guesswork with efficient, fact-based processes that directly support value creation and cost reduction.
When defects can occur multiple times per unit (scratches, solder defects, paint blemishes), the c-chart is the right SPC tool. It tracks defect count trends and detects process deterioration before defect levels become critical. Data-driven tracking enables proactive decision-making rather than reactive problem-solving, ultimately saving time, materials, and labor costs in production operations.
c̄ = Total Defects / Number of Samples UCL = c̄ + 3 × √c̄ LCL = max(0, c̄ − 3 × √c̄)
Result: c̄ = 6.0, UCL = 13.35, LCL = 0
c̄ = 180 / 30 = 6.0 defects per unit. UCL = 6 + 3 × √6 = 6 + 7.35 = 13.35. LCL = 6 − 7.35 = −1.35, set to 0. Any unit with more than 13 defects signals a process change.
Common applications include: solder defects on PCBs, paint defects per car body panel, weaving flaws per meter of fabric, scratches per glass panel, and documentation errors per report. Any countable, relatively rare occurrence on a fixed inspection unit qualifies.
Some practitioners consider using an individuals (I-MR) chart for defect count data. While this works in some cases, the c-chart's Poisson-based limits are more appropriate for count data and avoid the normality assumption required by I-MR charts.
A declining c̄ over time confirms that process improvements are reducing defects. Set new, tighter control limits after achieving a sustained reduction. This ratcheting approach prevents backsliding and codifies gains.
Use a c-chart when the inspection area (unit of inspection) is the same for every sample. Use a u-chart when sample sizes or inspection areas vary, as it normalizes defects per unit of measurement.
A defect is a single nonconformity (e.g., one scratch). A defective is an entire unit judged as nonconforming. One defective unit may contain multiple defects. The c-chart counts defects; the p-chart counts defectives.
The c-chart assumes a Poisson distribution for defect counts. For a Poisson distribution, the variance equals the mean, so the standard deviation is √c̄. Control limits at ±3 standard deviations use 3√c̄.
Yes, but if c̄ is very small (below 1–2), the Poisson approximation may be poor, and the lower limit will be zero with a very wide upper limit. Consider accumulating data over larger inspection units.
At least 20–25 samples are recommended for reliable control limit estimates. Fewer samples increase uncertainty in c̄ and the resulting limits.
Investigate the specific defect types that contributed to the high count. Use tools like 5 Whys or fishbone diagrams to identify root causes. Implement corrective actions and verify with subsequent data.