C Chart and U Chart: When to Use Each and How They Work

Not all quality problems show up as measurements.

Sometimes what matters is not how long a shaft is or how heavy a component is — it is how many defects were found on a circuit board, how many errors appeared in a document, or how many paint blemishes were recorded on a finished panel. These are counts. And when you need to monitor counts of defects over time to determine whether your process is stable, you need an attribute control chart.

The c chart and the u chart are the two attribute control charts designed specifically for counting defects. They are closely related — both are built on the same statistical distribution, both track defect counts rather than defective units, and both answer the same fundamental question: is the number of defects in my process behaving predictably, or has something changed?

The difference between them comes down to one practical condition: whether your sample size stays the same from subgroup to subgroup.

This article explains what c charts and u charts are, the critical distinction between defects and defectives, the formulas for both charts, when to use each, step-by-step instructions for building them, and where they fit in a Six Sigma DMAIC project.

Defects vs. Defectives: The Foundation of Chart Selection

Before choosing between a c chart and a u chart — or between any attribute control charts — you need to be clear on whether you are counting defects or defectives. These are different things, and they require different charts.

A defective is a unit that fails. The entire unit either passes or fails. A part is either conforming or nonconforming. One unit, one outcome. Charts for defectives are the p chart (proportion defective) and the np chart (count of defective units).

A defect is a nonconformity — a single flaw, error, or problem found on or within a unit. A single unit can have multiple defects. A circuit board can have six soldering defects and still function. A printed page can have three typographical errors. A painted panel can have two blemishes in one corner and one scratch elsewhere. Each of those individual problems is a defect, and you can count them.

C charts and u charts are for counting defects. If a unit either passes or fails with no middle ground, use a p or np chart instead.

What Is a C Chart?

A c chart (count chart) monitors the total number of defects found in a series of inspection units, where each inspection unit is the same size.

“Same size” is the key requirement. The inspection unit must remain constant from sample to sample — the same number of products inspected, the same physical area examined, the same length of material reviewed. When that condition holds, the raw count of defects is directly comparable from one data point to the next, and the c chart gives you a valid way to monitor whether that count is stable over time.

The c chart assumes the defect counts follow a Poisson distribution — a statistical distribution commonly used to model the number of events occurring in a fixed interval of space or time, where each event is independent and the average rate is constant. In a Poisson distribution, the variance equals the mean, which is why the standard deviation used in c chart control limits is the square root of the average defect count.

C Chart Formula

The control limits for a c chart are:

Centerline: c̄ (c-bar) = Total defects / Number of subgroups

UCL = c̄ + 3√c̄

LCL = c̄ − 3√c̄ (if negative, set LCL = 0)

Where c̄ is the average number of defects per subgroup, calculated from the historical data used to establish the chart.

The absence of a separately calculated sigma is intentional. Because the Poisson distribution has variance equal to its mean, the standard deviation is simply the square root of the mean — no additional calculation is needed.

Also Read: Measles Chart: Six Sigma Tool for Defect Tracking

C Chart Example

A team monitors soldering defects on printed circuit boards. Each day, exactly 20 boards are inspected. Over 15 days, the total defects found are 90. The average daily defect count is:

c̄ = 90 / 15 = 6.0 defects per day

UCL = 6.0 + 3√6.0 = 6.0 + 3(2.449) = 6.0 + 7.35 = 13.35

LCL = 6.0 − 7.35 = −1.35 → set to 0

Any daily defect count above 13 signals a potential special cause and warrants investigation. A count of zero would also merit attention — not as a problem, but as a potential signal of genuine improvement or a measurement issue worth confirming.

What Is a U Chart?

A u chart (defects-per-unit chart) monitors the average number of defects per inspection unit, where the sample size can vary from subgroup to subgroup.

The u chart solves the practical limitation of the c chart. In many real-world processes, inspecting exactly the same number of units each period is not possible — production volumes fluctuate, rolls of material vary in length, documents differ in page count, or inspection resources are not always consistent. When sample size varies, a raw defect count is not a fair comparison across periods: 12 defects from inspecting 100 units is very different from 12 defects from inspecting 200 units.

The u chart adjusts for this by dividing each subgroup’s defect count by its sample size — converting raw counts into a defects-per-unit rate. This rate is what gets plotted and compared. It is a more honest measure when sample sizes differ.

Like the c chart, the u chart is based on the Poisson distribution. Because sample size varies, the control limits are recalculated for each subgroup individually — which means the upper and lower control limit lines on a u chart step up and down based on the sample size at each point.

U Chart Formula

Centerline: ū (u-bar) = Total defects / Total units inspected = Σc / Σn

For each subgroup i with sample size nᵢ:

UCL_i = ū + 3√(ū / nᵢ)

LCL_i = ū − 3√(ū / nᵢ) (if negative, set LCL = 0)

Where nᵢ is the number of inspection units in subgroup i. When sample sizes are unequal, each subgroup gets its own pair of control limits.

U Chart Example

A team monitors errors in invoices processed each week. The number of invoices processed varies. Over four weeks, the data is:

Week	Invoices (n)	Errors (c)	u = c/n
1	120	18	0.150
2	95	11	0.116
3	140	22	0.157
4	108	14	0.130
Total	463	65

ū = 65 / 463 = 0.140 errors per invoice

Control limits for Week 1 (n = 120):

• UCL = 0.140 + 3√(0.140/120) = 0.140 + 3(0.0342) = 0.140 + 0.103 = 0.243
• LCL = 0.140 − 0.103 = 0.037

Control limits for Week 2 (n = 95):

• UCL = 0.140 + 3√(0.140/95) = 0.140 + 3(0.0384) = 0.140 + 0.115 = 0.255
• LCL = 0.140 − 0.115 = 0.025

Notice that the smaller the sample size, the wider the control limits — a direct consequence of greater uncertainty in smaller samples. This stepping behavior is a normal and expected feature of u charts with variable sample sizes.

C Chart vs. U Chart: How to Choose

The decision rule is straightforward.

Use a c chart when:

The sample size (area of opportunity) is constant from subgroup to subgroup. Every inspection covers exactly the same number of units, the same physical area, or the same production volume. When this condition holds, the c chart is simpler to construct and interpret because the control limits are fixed rather than variable.

Typical c chart applications: circuit boards inspected per shift (constant batch size), fabric panels of fixed dimensions, glass sheets cut to the same area, molded parts inspected in fixed lots.

Use a u chart when:

The sample size varies from subgroup to subgroup. Different quantities are inspected at different intervals, or the inspection area changes with production volume. The u chart accommodates this variation by expressing results as defects per unit rather than raw defect counts.

Typical u chart applications: invoices processed per day (variable volume), documents of varying length, hospital admissions per week, material rolls of varying length, software code reviews with different line counts.

The quick test: Ask whether inspecting twice as many units in one period would double the expected defect count for purely proportional reasons. If yes, and sample size varies, use the u chart.

One practical shortcut: if sample sizes are nearly constant but vary by less than 25%, some practitioners use a c chart with the average sample size as a simplification. When variation in sample size is larger than that, the u chart’s variable control limits are worth the additional calculation complexity.

Also Read: What is Run Chart?

C and U Charts in the Context of All Four Attribute Charts

Knowing where c and u charts sit among all attribute charts helps you select the right chart for any situation. The four attribute charts are:

p chart: Proportion of defective units. Sample size can vary. Underlying distribution: binomial. Use when each unit is classified as pass or fail and sample size varies.

np chart: Count of defective units. Sample size must be constant. Underlying distribution: binomial. Use when each unit is pass/fail and sample size is fixed.

c chart: Count of defects per unit. Sample size must be constant. Underlying distribution: Poisson. Use when units can have multiple defects and sample size is fixed.

u chart: Average defects per unit. Sample size can vary. Underlying distribution: Poisson. Use when units can have multiple defects and sample size varies.

The two-by-two structure is clean: defectives vs. defects on one axis, constant vs. variable sample size on the other. Once you know which category your data falls into, the chart selection is unambiguous.

Step-by-Step: Building a C Chart

Step 1 — Verify constant sample size. Confirm that each subgroup covers the same number of inspection units. If sample size is not constant, switch to a u chart.

Step 2 — Collect and record defect counts. For each subgroup (time period, batch, shift), record the total number of defects found. Collect at least 20 to 25 subgroups before establishing control limits to ensure reliable estimates.

Step 3 — Calculate the centerline. c̄ = Total defects across all subgroups / Number of subgroups

Step 4 — Calculate UCL and LCL. UCL = c̄ + 3√c̄ LCL = c̄ − 3√c̄ (set to 0 if negative)

Step 5 — Plot the chart. Plot the defect count for each subgroup on the y-axis against time or subgroup number on the x-axis. Draw the centerline and control limits.

Step 6 — Interpret. Points beyond the control limits signal potential special causes. Non-random patterns — runs of 8 or more points on one side of the centerline, consistent trends, or cyclical behavior — also indicate non-random variation even if no individual point exceeds the limits.

Step-by-Step: Building a U Chart

Step 1 — Record defect counts and sample sizes. For each subgroup, record both the number of defects found (c) and the number of units inspected (n). Collect at least 20 to 25 subgroups.

Step 2 — Calculate the u value for each subgroup. u = c / n (defects per unit for that subgroup)

Step 3 — Calculate the centerline. ū = Total defects / Total units inspected = Σc / Σn

Step 4 — Calculate control limits for each subgroup. UCL_i = ū + 3√(ū / nᵢ) LCL_i = ū − 3√(ū / nᵢ) (set to 0 if negative)

Because sample sizes vary, each subgroup has its own UCL and LCL. Wider limits appear where sample sizes were smaller; narrower limits appear where sample sizes were larger.

Step 5 — Plot the chart. Plot the u value (defects per unit) for each subgroup. Draw the centerline and the variable control limit lines.

Step 6 — Interpret. Apply the same rules as the c chart — points beyond variable control limits, runs, and trends all signal non-random behavior worth investigating.

Running C and U Charts in Minitab

In Minitab, c charts and u charts are located under:

Stat > Control Charts > Attributes Charts > C (for c charts) Stat > Control Charts > Attributes Charts > U (for u charts)

For a c chart: select your defect count column, specify the subgroup size (constant), and run.

For a u chart: select your defect count column, specify the subgroup size column (variable), and run. Minitab automatically calculates the variable control limits for each subgroup.

Minitab also applies the standard out-of-control test rules automatically, flagging violations in the chart output. Both charts support historical baseline data and real-time monitoring modes.

Common Mistakes When Using C and U Charts

Using a c chart with variable sample sizes. This is the most frequent error. When sample sizes differ and a c chart is used anyway, the control limits are wrong for every subgroup that deviates from the assumed constant size. Some subgroups will appear in control when they are not; others will appear out of control when they are not. Use a u chart whenever sample size varies.

Confusing defects with defectives. Choosing a c or u chart for data where each unit is simply classified as pass or fail applies the wrong statistical model. Defective unit data requires a p or np chart, which is based on the binomial distribution, not the Poisson distribution.

Ignoring a negative LCL. When c̄ or ū is small, the LCL formula can produce a negative value. A negative number of defects is impossible, so the LCL is set to zero. This is a standard adjustment, not an error, but it means there is no lower control limit in practice — only an upper one. Keep this in mind when interpreting the chart.

Using too few subgroups to establish limits. Control limits calculated from fewer than 20 subgroups are unreliable. Fewer data points produce wider uncertainty in the c̄ or ū estimate, resulting in control limits that may be meaninglessly wide or misleadingly tight.

Treating a point below the LCL as automatically good news. A defect count lower than the lower control limit is statistically unusual and warrants investigation — just like a point above the UCL. The cause might be a genuine process improvement worth understanding and standardizing. Or it might reflect a measurement or recording error. Either way, it is a signal, not just a bonus.

C and U Charts in DMAIC

Both charts appear across multiple DMAIC phases, with their primary value in the Measure and Control phases.

Measure phase: When establishing baseline process performance for a defect count metric, a c or u chart confirms whether the process is in statistical control before capability analysis is attempted. A process showing special cause variation on an attribute chart should have those causes identified and removed before a meaningful baseline is established.

Analyze phase: Comparing attribute charts from different time periods, shifts, machines, or operators can reveal patterns that point toward root causes. A c chart that shows consistently higher defect counts on one shift compared to others provides evidence for a shift-related root cause investigation.

Improve phase: After implementing process changes, a new c or u chart built from post-improvement data shows whether the change produced a statistically significant reduction in the defect rate — a lower centerline, narrower control limits, or both.

Control phase: The c or u chart becomes part of the control plan for ongoing monitoring. Operators use the chart to distinguish normal variation in defect counts (common cause) from unusual spikes or trends (special cause) that require investigation. This is the primary value in the long term: keeping the process at its improved level by catching special causes early, before they produce significant defect volumes.

Learn Attribute Control Charts in Our Training Programs

C charts, u charts, and the full attribute control chart toolkit are covered in our Lean Six Sigma Green Belt and Black Belt programs. You will not just learn the formulas — you will work through chart selection, construction, and interpretation using real data, in software, and in the context of a complete DMAIC project.

At Six Sigma Development Solutions, statistical process control is taught as a practical skill set, not a theoretical exercise:

• Onsite training at your facility, using your processes and your defect data
• Live virtual classroom with a live instructor, real-time Q&A, and software exercises
• Online self-paced certification you can complete on your own schedule

Our Green Belt program covers the full control chart selection framework, attribute and variable chart construction and interpretation, and control plan development. Our Black Belt program adds advanced SPC methods, measurement system analysis, and process capability for attribute data.

Lean Six Sigma Green Belt Training Brochure

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