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Statistical quality control (SQC) uses data to make quality decisions, but its methods answer different questions. Control charts monitor whether a process is behaving consistently over time; capability analysis compares a stable process with product specifications; acceptance sampling helps decide whether to accept or reject a particular lot. None of these methods, by itself, proves that every item is conforming.
What is statistical quality control?
Statistical quality control is the use of statistical methods to understand and manage quality. In practice, the term can refer broadly to methods for both process monitoring and product acceptance, so it helps to name the decision being made.
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The NIST/SEMATECH Engineering Statistics Handbook gives this definition: “Statistical Quality Control is the process of inspecting enough product from given lots to probabilistically ensure a specified quality level.” That wording describes the acceptance-sampling aspect of SQC; it is not a definition of all process-monitoring methods. NIST/SEMATECH Handbook: Process Control Techniques
| Method | Decision it supports | What the result means |
|---|---|---|
| Statistical process control (SPC) | Is the process behaving consistently over time? | A chart signal prompts investigation; it does not identify a cause on its own. |
| Process capability analysis | Can a stable process fit within its specification limits? | Capability indices compare process variation and centering with customer or engineering requirements. |
| Acceptance sampling | Should this particular lot be accepted or rejected? | A sample-based decision carries risks; accepting a lot does not certify every unit. |
NIST distinguishes process control from product acceptance, while the American Society for Quality (ASQ) describes SPC as a way to monitor and control a process through statistical methods. The terms overlap in general quality writing, but process monitoring and lot disposition should not be treated as interchangeable decisions. NIST/SEMATECH Handbook: Process Control Techniques · ASQ: Statistical Process Control
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What do control charts show?
A control chart plots a measured quality characteristic or count in time order. It typically has a center line and upper and lower control limits, calculated to reflect the process behavior being monitored. A point outside a limit is a signal to investigate, and a sequence of nonrandom patterns can also be informative even when every point falls within the limits. NIST/SEMATECH Handbook: Control Charts
Control limits are not specification limits
Control limits are statistical boundaries for interpreting the process. Specification limits express requirements for the product or service, such as an acceptable range set by an engineering design or customer. A process may be stable but produce output outside specifications; conversely, a process can appear to meet specifications while still showing an unstable pattern that needs attention. NIST/SEMATECH Handbook: Control Charts
How limits are established and used
NIST describes a two-phase approach. In Phase I, historical data are reviewed to set initial limits and investigate unusual observations. Once suitable limits have been established, Phase II uses them to monitor new observations in real time. Limits should not be confused with targets or specifications, and a signal is evidence to investigate rather than proof of a particular cause. NIST/SEMATECH Handbook: Process Control Techniques
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Under a normal-distribution model, NIST/SEMATECH reports that three-sigma limits correspond to approximately 0.27% of observations falling outside either limit. That probability is conditional on the model and those limits; it is not a universal false-alarm rate for every chart, process, or combination of signal rules. NIST/SEMATECH Handbook: Control Charts
Choose a chart for the data and detection need
Chart choice depends on what is measured, how observations are grouped, how many characteristics are monitored, and the size and speed of shifts that matter. Shewhart-style charts are a common choice for straightforward monitoring and larger shifts. CUSUM charts accumulate deviations from a target, while EWMA charts calculate weighted averages that give more weight to recent observations; these approaches can help reveal smaller or more persistent changes. Multivariate charts address multiple characteristics. No chart is best for every process, and additional detection rules can increase false alarms. NIST/SEMATECH Engineering Statistics Handbook, Chapter 6 · ASQ: Statistical Process Control
Other quality tools help organize or explore evidence rather than replace time-ordered monitoring. ASQ lists check sheets, Pareto charts, cause-and-effect diagrams, histograms, and scatter diagrams among common quality tools. They can help document observations, prioritize issues, explore possible relationships, or inspect a distribution; a control chart addresses whether behavior changes over time. ASQ: Statistical Process Control
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What should you do when a chart signals a problem?
A signal is a reason to follow a documented out-of-control action plan, investigate the process, and record what was found. It does not establish that a specific machine, operator, material, or other factor caused the change. Avoid adjusting a process automatically without evidence: unnecessary adjustment can add variation instead of fixing a real cause. NIST/SEMATECH Handbook: Out-of-Control Action Plans
- Confirm the signal. Check the chart, data, timing, and applicable signal rules for errors or unusual patterns.
- Investigate in context. Use the action plan to examine relevant process changes and evidence rather than assuming a cause.
- Document the finding and response. Record what was checked, what was supported by evidence, and what action was taken.
- Resume monitoring as defined by the plan. Do not silently revise limits or treat a changed process as though its earlier baseline necessarily still applies.
The investigation is meant to distinguish a meaningful change from routine process variation. The appropriate response depends on the process and the organization’s action plan; a chart alone cannot prescribe a corrective action. NIST/SEMATECH Handbook: Out-of-Control Action Plans
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1Scan for outdated or missing drivers - takes under a minute2Clear out junk files and repair common Windows errors3Fix the driver behind crashes, sound loss and screen glitchesWhat is process capability?
Process capability compares the output of an in-control process with its specification limits. Establish stability first: capability estimates are difficult to interpret if the process is changing, because the data may combine different operating conditions. A stable process is not automatically capable; its output can be consistent yet too variable or poorly centered to meet requirements. NIST/SEMATECH Handbook: Process Capability
How Cp and Cpk differ
In their common formulations, Cp compares the specification width with the process spread, while Cpk also accounts for how close the process is to the nearer specification limit. In notation, Cp = (USL − LSL) / 6σ; Cpk = min(USL − μ, μ − LSL) / 3σ, where USL and LSL are the upper and lower specification limits, μ is the process mean, and σ is the process standard deviation. A centered process can have a Cp that reflects its spread but a lower Cpk if it is shifted toward one specification boundary. These common indices rely on normally distributed process data; check whether the distribution and other assumptions suit the application before interpreting them. NIST/SEMATECH Handbook: Process Capability
Use enough suitable data, not just a rule-of-thumb count
NIST/SEMATECH says that about 50 independent values is generally thought of as “large enough” for many capability-index estimates, while noting that capability studies often need larger samples. This is source-specific guidance, not a universal minimum or a guarantee of a reliable estimate. Sample design, process stability, dependence among observations, distribution, and uncertainty all affect whether an estimate is useful. NIST/SEMATECH Handbook: Process Capability
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What is acceptance sampling?
Acceptance sampling randomly selects units from a lot and uses the sample results to decide whether to accept or reject that lot. It can be a practical middle path between no inspection and inspecting every unit, especially when testing is destructive, inspection is expensive, or a full inspection would take too long. Its main purpose is lot disposition, not a precise estimate of the lot’s quality. NIST/SEMATECH Handbook: Acceptance Sampling
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A sampling plan sets decision rules and reflects risks for both the producer and the consumer. Because only part of the lot is inspected, a rejected lot may contain acceptable units and an accepted lot may still contain nonconforming units. Acceptance is a probabilistic decision under the plan, not a guarantee that all units conform. NIST/SEMATECH Handbook: Acceptance Sampling
How to choose the right SQC method
- Need to detect process change over time? Use an appropriate control chart and define what data it monitors, how observations are grouped, and what signal will trigger investigation.
- Need to know whether a stable process fits requirements? Use capability analysis only after establishing stability, and assess the assumptions behind the selected index.
- Need a decision on a specific lot? Use an acceptance-sampling plan when inspection constraints justify a sample-based disposition and its associated risks are understood.
- Need to inspect several kinds of evidence? Combine appropriate charts and supporting quality tools rather than expecting one statistic to explain every problem.
For organizations validating SPC software, ASQ lists ISO/TR 11462-3:2020 as guidance with example datasets and test results for validating selected methods from ISO 7870 and ISO 22514. The listed scope includes sample statistics, capability indices, control limits, chart visualization, and out-of-control detection. It is a specialist software-validation resource, not a substitute for understanding the statistical method or checking current standards requirements. ASQ listing: ISO/TR 11462-3:2020
For a broader reference, ASQ lists Mark L. Crossley’s The Desk Reference of Statistical Quality Methods, Second Edition (2007), covering acceptance sampling, control charts, capability analysis, and other statistical quality methods. ASQ product page
Conclusion
Use control charts to monitor process behavior, capability indices to compare a stable process with specifications, and acceptance sampling to make a risk-based decision about a lot. Keeping those questions separate prevents a stable process from being mistaken for a capable one, or a sampled lot’s acceptance from being mistaken for proof about every unit.
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