Definition
A control chart is a time-series plot of process data — measurements taken in sequence — with three horizontal lines: a center line (the process average) and upper and lower control limits (UCL and LCL), calculated statistically from the data itself (typically at ±3 standard deviations from the mean).
The control chart answers a single, critical question: is this process stable, or is something unusual happening?
- Points that fall within the control limits and show no patterns indicate a stable process — variation is due to common causes inherent to the system.
- Points that fall outside the control limits, or that show non-random patterns (trends, runs, cycles), indicate special cause variation — something has changed, and the cause should be investigated.
This distinction between common cause and special cause variation is the foundation of statistical process control. It prevents two costly errors: over-adjusting a stable process (tampering) and failing to investigate an unstable process (ignoring signals).
Japanese Origin
管理図 (kanri zu) combines 管理 (kanri, “management, control, supervision”) and 図 (zu, “diagram, chart”). The word 管理 is the same term used throughout Japanese management vocabulary — 品質管理 (hinshitsu kanri, quality control), 生産管理 (seisan kanri, production control). The control chart is, literally, the “management diagram” — the tool managers use to understand whether a process is in control.
History
Walter Shewhart, 1924 — Shewhart, a physicist and statistician at Bell Telephone Laboratories, created the control chart on May 16, 1924. It was the first application of statistical methods to manufacturing process control. Shewhart’s insight was that all processes exhibit variation, and the task is not to eliminate all variation (impossible) but to distinguish between variation that is inherent to the system (common cause) and variation that signals a change (special cause).
W. Edwards Deming, 1950 — Deming, who had studied under Shewhart, brought statistical quality control methods to Japan through his JUSE lectures in 1950. Deming taught the control chart as the fundamental tool for understanding process behavior. His influence on Japanese industry was so profound that JUSE established the Deming Prize in 1951.
Kaoru Ishikawa, 1960s — Ishikawa included the control chart in the 7 QC Tools, making it part of the standard toolkit for frontline workers and QC circles. Ishikawa simplified the mathematical treatment to make control charts accessible to non-statisticians.
At Toyota — Control charts are used in Toyota’s quality management system, particularly in machining and assembly processes where dimensional precision is critical. They are also used in monitoring process parameters (temperature, pressure, torque) that affect quality. However, Toyota’s primary quality strategy is prevention (jidoka, poka-yoke) rather than statistical detection — control charts complement, rather than replace, built-in quality.
Types of Control Charts
Variables charts (for measured data — dimensions, weights, temperatures):
- X̄-R chart — plots the average (X̄) and range (R) of small samples; the most common type
- X̄-S chart — plots average and standard deviation; used for larger sample sizes
- Individual-Moving Range (I-MR) chart — plots individual values; used when each unit is measured
Attributes charts (for counted data — defects, pass/fail, go/no-go):
- p chart — proportion of defective items in a sample
- np chart — number of defective items in a fixed-size sample
- c chart — number of defects per unit
- u chart — number of defects per unit with varying sample sizes
How to Read a Control Chart
In-control process: Points scattered randomly within the control limits with no discernible patterns. This does not mean the process is meeting specification — only that it is stable and predictable. A stable process can consistently produce defects if its natural capability does not match the specification.
Out-of-control signals:
- A single point beyond the UCL or LCL
- Seven or more consecutive points on one side of the center line (run)
- Seven or more consecutive points trending consistently up or down (trend)
- Unusual patterns (two out of three points in the outer third, cyclical patterns)
The critical distinction: When an out-of-control signal appears, investigate the special cause — what changed? New material lot? Different operator? Equipment adjustment? Identify the cause, address it, and the process returns to stability. When the process is in control, do not adjust it — common cause variation can only be reduced by changing the system itself (better equipment, better materials, better methods).
Common Mistakes
Confusing control limits with specification limits. Control limits are calculated from the process data and describe what the process is doing. Specification limits describe what the process should be doing (the customer requirement). A process can be in statistical control while producing out-of-specification parts. A process can be out of statistical control while still meeting specifications (for now). The two are independent concepts.
Adjusting the process in response to common cause variation. This is Deming’s “tampering” — adjusting a stable process because a single point is closer to one limit than the other. Each adjustment introduces new variation, making the process worse. The correct response to common cause variation is to leave the process alone (or change the system fundamentally).
Not collecting enough data before calculating limits. Control limits should be based on at least 20-25 subgroups of data from a stable process. Limits calculated from 5-10 points are unreliable and may produce misleading signals.
Plotting the chart but not responding to signals. A control chart on the wall that is never reviewed, or that shows out-of-control signals with no investigation, is waste. The chart is only useful if it triggers a response: investigate the special cause, implement a countermeasure, verify the fix.
Using control charts where poka-yoke would be better. A control chart detects problems statistically after some defects have already been produced. Poka-yoke prevents defects before they occur. Where error-proofing is feasible, it is always superior to statistical detection. Toyota’s preference hierarchy: prevent → detect immediately (jidoka) → detect statistically (SPC).