Control Chart Theory is a fundamental statistical tool used in the Control Phase of Lean Six Sigma to monitor process performance and maintain improvements over time. Developed by Walter Shewhart in the 1920s, control charts help distinguish between common cause variation (natural, inherent process…Control Chart Theory is a fundamental statistical tool used in the Control Phase of Lean Six Sigma to monitor process performance and maintain improvements over time. Developed by Walter Shewhart in the 1920s, control charts help distinguish between common cause variation (natural, inherent process variation) and special cause variation (unusual, assignable factors requiring investigation).
A control chart consists of three key elements: a center line representing the process mean, an Upper Control Limit (UCL), and a Lower Control Limit (LCL). These limits are typically set at three standard deviations (±3σ) from the mean, capturing approximately 99.73% of data points when the process is stable.
The theory operates on the principle that all processes exhibit variation. When data points fall within the control limits and display random patterns, the process is considered "in statistical control." When points fall outside the limits or show non-random patterns, this signals special cause variation that requires corrective action.
Common types of control charts include X-bar and R charts for continuous data with subgroups, Individual and Moving Range (I-MR) charts for individual measurements, and p-charts and c-charts for attribute data such as defect counts or proportions.
Key rules for identifying out-of-control conditions include: a single point beyond control limits, seven consecutive points on one side of the center line, six consecutive points trending upward or downward, and two out of three consecutive points beyond two standard deviations.
In the Control Phase, control charts serve as an early warning system, enabling teams to detect process shifts before they result in defects or customer dissatisfaction. They provide objective evidence of process stability and capability, support data-driven decision making, and create documentation for sustained process improvement. Regular monitoring using control charts ensures that gains achieved during the Improve Phase are maintained long-term.
Control Chart Theory: A Comprehensive Guide for Six Sigma Green Belt
Why Control Chart Theory is Important
Control charts are the backbone of Statistical Process Control (SPC) and are essential tools for monitoring process performance over time. For Six Sigma Green Belt practitioners, understanding control chart theory is critical because it enables you to:
• Distinguish between common cause and special cause variation • Maintain process stability after improvements are implemented • Make data-driven decisions about when to intervene in a process • Prevent overreaction to natural process variation • Ensure sustained quality improvements during the Control phase
What is Control Chart Theory?
Control chart theory is based on the statistical principle that all processes exhibit variation, and this variation can be categorized into two types:
Common Cause Variation: Natural, inherent variation that exists in every process. This variation is random, predictable within limits, and can only be reduced through fundamental process changes.
Special Cause Variation: Unusual variation caused by specific, identifiable factors that are not part of the normal process. These causes are assignable and should be investigated and eliminated.
A control chart plots process data over time with three key lines: • Center Line (CL): Represents the process average • Upper Control Limit (UCL): Typically set at +3 standard deviations from the mean • Lower Control Limit (LCL): Typically set at -3 standard deviations from the mean
How Control Charts Work
Control charts function by establishing baseline performance and then monitoring data points against statistical limits:
1. Data Collection: Collect samples from the process at regular intervals
2. Calculate Statistics: Compute the appropriate statistic (mean, range, proportion, etc.) for each sample
3. Establish Control Limits: Calculate UCL and LCL using formulas specific to the chart type. The 3-sigma limits capture approximately 99.73% of data when the process is stable.
4. Plot and Monitor: Plot each new data point and analyze patterns
5. Interpret Results: Apply rules to detect out-of-control conditions
Types of Control Charts:
Variable Data Charts: • X-bar and R Chart (for subgroup averages and ranges) • X-bar and S Chart (for larger subgroups, using standard deviation) • Individual and Moving Range (I-MR) Chart (for individual measurements)
Attribute Data Charts: • p-Chart (proportion defective) • np-Chart (number defective with constant sample size) • c-Chart (count of defects with constant opportunity) • u-Chart (defects per unit with variable sample size)
Out-of-Control Signals (Western Electric Rules):
• One point beyond 3 sigma from the center line • Nine consecutive points on one side of the center line • Six consecutive points steadily increasing or decreasing • Fourteen consecutive points alternating up and down • Two out of three consecutive points beyond 2 sigma on the same side • Four out of five consecutive points beyond 1 sigma on the same side
Exam Tips: Answering Questions on Control Chart Theory
1. Know Your Chart Selection: Memorize which chart to use based on data type and sample characteristics. Variable data with subgroups uses X-bar charts; attribute data counting defectives uses p or np charts; counting defects uses c or u charts.
2. Understand Control Limits vs. Specification Limits: Control limits are calculated from process data and indicate what the process IS doing. Specification limits are set by customer requirements and indicate what the process SHOULD do. Never confuse these on exam questions.
3. Remember the 3-Sigma Concept: Control limits are typically set at ±3 standard deviations, capturing 99.73% of variation. This means approximately 0.27% of points may fall outside limits due to chance alone in a stable process.
4. Recognize Pattern Questions: Many exam questions show control charts with various patterns. Practice identifying runs, trends, cycles, and points outside control limits. Know the Western Electric Rules thoroughly.
5. Process Stability First: Remember that a process must be in statistical control before calculating process capability. Questions may test this sequence.
6. Common Calculation Questions: Be prepared to calculate control limits using provided formulas and control chart constants (A2, D3, D4, etc.). Practice these calculations before the exam.
7. Rational Subgrouping: Understand that subgroups should be selected to maximize variation between subgroups and minimize variation within subgroups. This concept appears frequently in exam scenarios.
8. Action Based on Chart Signals: When a point is out of control, the correct response is to investigate and identify the special cause. When the process is in control with only common cause variation, process improvement requires fundamental changes to the system.