Control Chart Generator

What are Control Charts?

Control charts, also known as Shewhart charts or process behavior charts, are a fundamental tool of Statistical Process Control (SPC). Invented by Walter A. Shewhart at Bell Telephone Laboratories in the 1920s, they provide a visual method for monitoring whether a process is operating in a state of statistical control over time.

A control chart plots data points in time order against a center line (CL) representing the process average and two control limits: an Upper Control Limit (UCL) and a Lower Control Limit (LCL), typically set at three standard deviations from the center line. These limits define the expected range of common cause variation — the natural, inherent variability of a stable process.

When data points fall outside the control limits or exhibit non-random patterns, this signals special cause variation — an assignable cause that has shifted or destabilized the process. The key insight of SPC is that common cause variation should be addressed by changing the system, while special cause variation should be investigated and eliminated.

Types of Control Charts

Different control chart types are designed for different data types and situations:

• X-bar & R Chart: Used for continuous (variable) data collected in subgroups of 2 to 10 measurements. The X-bar chart monitors the subgroup means, while the R chart monitors the range (spread) within each subgroup. This is the most commonly used control chart in manufacturing.
• Individuals & Moving Range (I-MR) Chart: Used for continuous data when only one measurement is taken per time period, or when subgrouping is not practical. The Individuals chart tracks each observation, while the Moving Range chart tracks the absolute difference between consecutive points.
• p Chart (Proportion Defective): Used for attribute data where each unit is classified as defective or non-defective. Plots the proportion of defective items in each sample. Appropriate when sample sizes may vary.
• np Chart (Count Defective): Similar to the p chart but plots the actual count of defective items rather than the proportion. Requires a constant sample size across all samples.

Western Electric Rules

The Western Electric rules (also known as the Western Electric Company rules or WECO rules) are a set of decision rules for detecting out-of-control conditions on a control chart. Originally published in the Statistical Quality Control Handbook by Western Electric in 1956, they supplement the basic "one point beyond 3-sigma" rule with additional pattern-based tests:

• Rule 1: Any single point falls outside the 3-sigma control limits (beyond UCL or below LCL).
• Rule 2: Two out of three consecutive points fall in the same zone beyond 2 sigma from the center line (Zone A or beyond).
• Rule 3: Four out of five consecutive points fall in the same zone beyond 1 sigma from the center line (Zone B or beyond).
• Rule 4: Eight or more consecutive points fall on the same side of the center line (a run).

These rules increase the sensitivity of the control chart to small process shifts while maintaining a reasonable false alarm rate. When any rule is violated, the process should be investigated for special cause variation.

How to Read a Control Chart

To interpret a control chart effectively, follow these steps:

• Check for out-of-control points: Look for any data points beyond the UCL or LCL. These are the most obvious signals of special cause variation and should be investigated immediately.
• Look for patterns: Even if all points are within control limits, non-random patterns like trends (steadily increasing or decreasing), cycles, or runs (many consecutive points on one side of the center line) may indicate process instability.
• Examine both charts together: For X-bar & R or I-MR charts, always analyze the range or moving range chart first. If the variability chart shows lack of control, the mean chart's control limits are unreliable.
• Assess overall stability: A process in statistical control shows a random scatter of points around the center line within the control limits, with no systematic patterns. This does not mean the process meets specifications — only that it is predictable.