A C Chart, also known as a Count Chart, is a type of control chart used in the Lean Six Sigma Control Phase to monitor the number of defects or nonconformities in a process when the sample size remains constant. This statistical tool is essential for maintaining process stability after improvements…A C Chart, also known as a Count Chart, is a type of control chart used in the Lean Six Sigma Control Phase to monitor the number of defects or nonconformities in a process when the sample size remains constant. This statistical tool is essential for maintaining process stability after improvements have been implemented during the DMAIC methodology.
The C Chart is specifically designed for attribute data where you are counting discrete events, such as the number of scratches on a painted surface, the number of errors in a document, or the number of customer complaints per week. The key requirement is that the opportunity for defects must remain constant across all samples being measured.
The chart consists of three critical lines: the Center Line (CL), which represents the average number of defects; the Upper Control Limit (UCL); and the Lower Control Limit (LCL). The center line is calculated as the mean of all defect counts (c-bar). The control limits are typically set at three standard deviations from the center line, calculated using the formula UCL = c-bar + 3√c-bar and LCL = c-bar - 3√c-bar. If the LCL calculates to a negative value, it is set to zero.
During the Control Phase, practitioners plot individual defect counts over time and analyze patterns. Points falling outside the control limits signal special cause variation requiring investigation. Additionally, non-random patterns such as trends, cycles, or runs indicate the process may be out of statistical control.
The C Chart helps teams sustain improvements by providing early warning signals when a process begins to drift from its improved state. By continuously monitoring defect counts, organizations can take corrective action before quality deteriorates significantly, ensuring long-term process stability and customer satisfaction. This makes the C Chart an invaluable tool for ongoing quality management and continuous improvement efforts.
C Chart: Complete Guide for Six Sigma Green Belt Control Phase
What is a C Chart?
A C Chart, also known as a Count Chart, is a type of attribute control chart used to monitor the number of defects (or nonconformities) in a sample of constant size. The 'C' stands for 'count' of defects. Unlike a P Chart which tracks the proportion of defective units, a C Chart tracks the actual count of individual defects found in each sample unit.
Why is the C Chart Important?
The C Chart is essential in Six Sigma for several reasons:
• Process Monitoring: It helps teams track process stability when counting defects over time • Early Detection: Identifies when a process shifts out of statistical control before quality deteriorates significantly • Data-Driven Decisions: Provides objective evidence for process improvement initiatives • Cost Reduction: Helps reduce scrap, rework, and customer complaints by maintaining process control • Simplicity: Works well when defects can be counted but the opportunity for defects is large or unknown
When to Use a C Chart
Use a C Chart when: • You are counting the number of defects (not defective units) • The sample size or inspection unit remains constant • Defects are relatively rare compared to opportunities • The data follows a Poisson distribution • Examples include: scratches on a painted surface, errors per invoice, flaws per roll of fabric
How the C Chart Works
Key Formulas:
• Center Line (c-bar): c̄ = Total number of defects / Number of samples
• Upper Control Limit (UCL): UCL = c̄ + 3√c̄
• Lower Control Limit (LCL): LCL = c̄ - 3√c̄
Note: If LCL calculates to a negative value, set it to zero since you cannot have negative defects.
Steps to Create a C Chart:
1. Collect data on the number of defects for each sample unit (sample size must be constant) 2. Calculate the average number of defects (c-bar) 3. Calculate the control limits using the formulas above 4. Plot each data point on the chart 5. Draw the center line and control limits 6. Analyze for out-of-control conditions
Interpreting the C Chart
A process is considered out of control when: • A point falls above the UCL or below the LCL • Seven or more consecutive points on one side of the center line (run) • Seven consecutive points trending up or down • Two out of three consecutive points in the outer third of the control limits • Other non-random patterns appear
C Chart vs U Chart
A common exam topic is distinguishing between C and U Charts: • C Chart: Constant sample size, counts defects per unit • U Chart: Variable sample size, measures defects per unit (rate)
Exam Tips: Answering Questions on C Chart
1. Identify the Chart Type: If the question mentions constant sample size and counting defects (not defective units), think C Chart
2. Remember the Square Root: The standard deviation for a C Chart is √c̄, which is different from other control charts
3. Watch for Negative LCL: Always check if your calculated LCL is negative; if so, report it as zero
4. Distinguish Defects vs Defectives: C Charts count defects (one unit can have multiple defects), while NP Charts count defective units
5. Know the Distribution: C Charts assume data follows a Poisson distribution
6. Sample Size Trap: If the question states variable sample sizes, the answer is likely U Chart, not C Chart
7. Practice Calculations: Be comfortable calculating c-bar and control limits quickly
8. Interpret Patterns: Know the Western Electric rules for identifying out-of-control conditions
9. Real-World Context: Questions often present scenarios; focus on whether defects are being counted in equal-sized samples
10. Control Phase Connection: Remember that control charts are used in the Control Phase to sustain improvements and monitor ongoing process performance