Control Chart — Statistical Process Monitoring with Shewhart Charts
Statistical Control Chart (Shewhart Chart) · Also known as: Shewhart chart, process-behavior chart, SPC chart, quality control chart
A control chart is a time-series graph with statistically derived upper and lower control limits that separates the natural, random variation of a process (common cause) from unusual, assignable variation (special cause). Invented by Walter Shewhart at Bell Labs in 1924, control charts remain the foundational tool of Statistical Process Control and are used across manufacturing, healthcare, software, and service industries to monitor whether a process remains stable and predictable over time.
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When to use it
Use a control chart whenever you need to determine whether a process is in statistical control — producing output whose variation is driven only by common causes — and to detect shifts or trends as they occur, before they generate a large volume of defects. It is the right tool for ongoing process monitoring in production, clinical, or service environments where outputs are measured repeatedly over time. Do not use a control chart as a substitute for process capability analysis (which answers whether a stable process meets specifications) or as an acceptance sampling tool. Avoid control charts when you have only a handful of historical observations, when measurements are not independent across time, or when you need to detect very small shifts quickly — in that case, CUSUM or EWMA charts are more sensitive alternatives.
Strengths & limitations
- Provides a rigorous, statistically founded rule for distinguishing real process changes from random noise, preventing over-adjustment.
- Detects shifts, trends, and other non-random patterns in near-real time, enabling prompt corrective action before defects accumulate.
- Universally applicable — the same conceptual framework covers continuous measurements, counts, and proportions across all industries.
- Generates a permanent, auditable time-series record of process performance, valuable for regulatory compliance and continuous improvement.
- Simple enough for operators on the production floor to maintain and interpret without advanced statistical training.
- Control limits are not specification limits — a process can be in statistical control yet still produce out-of-specification output if its inherent variation is too wide.
- Standard Shewhart charts are relatively insensitive to small, sustained shifts (less than about 1.5 sigma); CUSUM or EWMA charts are needed in such cases.
- Requires an adequate baseline sample (20–30 subgroups) to estimate control limits reliably; with fewer data the limits are imprecise and signals are unreliable.
- Assumes process observations are approximately independent; strong autocorrelation inflates apparent out-of-control signals and requires special chart variants.
Frequently asked
What is the difference between control limits and specification limits?
Control limits (UCL and LCL) are calculated from the process data itself and describe the range of variation the process naturally produces when only common causes are present. Specification limits are set by the customer or engineer and define what is acceptable. A process can be in control (stable) but out of specification (incapable), or in specification but out of control (unpredictable). Process capability indices such as Cp and Cpk relate the two.
How many subgroups do I need before the chart is reliable?
The standard guidance is 20–30 rational subgroups of 4–5 observations each (for X-bar and R charts) to obtain stable estimates of the center line and control limits. With fewer subgroups the limits have wide confidence intervals and the chart is prone to both false alarms and missed signals. For Individuals charts, 30 or more individual observations are preferable.
When should I use an Individuals (I-MR) chart instead of an X-bar/R chart?
Use an I-MR chart when it is impractical or impossible to collect subgroups — for example, when each batch takes hours to produce, when measurements are destructive, or when the process produces one unit at a time. X-bar/R charts are preferred when rational subgroups of 2–10 observations can be formed, because subgroup averaging makes the chart more sensitive to small shifts.
What do I do when a point falls outside the control limits?
Do not automatically adjust the process — first confirm the signal is real (not a measurement error or data-entry mistake). Then investigate the assignable cause using process logs, operator input, or root-cause tools. Identify and remove the cause, document the corrective action, and if appropriate remove the out-of-control point from the baseline data and recalculate the limits. Adjusting the process without finding the cause often increases, not decreases, variation.
Can control charts handle non-normal data?
Standard Shewhart charts are reasonably robust to mild non-normality because the three-sigma limits still capture approximately 99% of the distribution for many common process distributions. For highly skewed data (e.g., rare-event counts), use the appropriate attribute chart (c-chart, u-chart) or apply a data transformation before charting. For very non-normal continuous data, distribution-specific control charts or Box-Cox transformations are documented alternatives.
Sources
- Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. Van Nostrand. link ↗
- Montgomery, D. C. (2009). Introduction to Statistical Quality Control (6th ed.). Wiley. ISBN: 978-0470169926
How to cite this page
ScholarGate. (2026, June 3). Statistical Control Chart (Shewhart Chart). ScholarGate. https://scholargate.app/en/experimental-design/control-chart
Which method?
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