Concept Architecture
Concept
Theoretically, Statistical Process Control (SPC) is a quantitative methodology for monitoring, controlling and improving process performance through the application of statistical techniques. It is founded on probability theory and statistical inference and distinguishes between common cause variation, which is inherent in a stable process, and special cause variation, which arises from identifiable external influences. SPC provides the theoretical basis for determining whether a process is operating in a state of statistical control.
Mathematically, Statistical Process Control is implemented using control charts, in which process statistics are plotted over time against statistically derived control limits. These limits are typically based on the process mean and standard deviation, allowing statistically significant departures from expected variation to be identified. Numerous chart types exist, including X?, R, S, p, np, c and u charts, each designed for specific forms of continuous or attribute data.
In practice, Statistical Process Control is widely applied in healthcare quality improvement, pharmaceutical manufacturing, laboratory medicine and health service operations. Health economists use SPC to evaluate quality improvement initiatives, monitor clinical performance indicators, assess operational efficiency and estimate the economic consequences of process variation and system improvement.
Purpose
Used to monitor process performance, distinguish common cause from special cause variation, detect process changes, support continuous quality improvement and inform operational and health economic decision-making.
Mathematical Formulae
Primary Formula
Upper Control Limit (UCL) = ? + 3�
Centre Line (CL) = ?
Lower Control Limit (LCL) = ? ? 3�
where:
- ? = process mean
- � = process standard deviation
Supporting Formulae
Sample Mean
X? = �x? � n
Standard Deviation
� = �[�(x? ? ?)� � N]
Process Capability
Cp = (USL ? LSL) � 6�
Related Mathematical Methods
- Control charts
- Process capability analysis
- Six Sigma
- Shewhart charts
- Moving range analysis
- Statistical quality control
Example
A laboratory monitors the daily turnaround time for diagnostic tests.
- Mean turnaround time = 48 hours
- Standard deviation = 4 hours
Upper Control Limit
UCL = 48 + (3 ? 4)
= 60 hours
Lower Control Limit
LCL = 48 ? (3 ? 4)
= 36 hours
Any observation outside 36?60 hours suggests special cause variation requiring investigation.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(A2:A101) | Calculate the process mean. |
| STDEV.S | =STDEV.S(A2:A101) | Calculate the process standard deviation. |
| Formula | =B2+(3*C2) | Calculate the Upper Control Limit. |
| Formula | =B2-(3*C2) | Calculate the Lower Control Limit. |
| IF | =IF(OR(A2>UCL,A2<LCL),"Special Cause","Common Cause") | Identify observations outside statistical control limits. |
VBA (Optional)
Automate generation of control charts, calculation of control limits, detection of out-of-control observations and production of quality monitoring dashboards across healthcare performance indicators.
Sources
- Shewhart WA. Economic Control of Quality of Manufactured Product.
- Montgomery DC. Introduction to Statistical Quality Control.
- Wheeler DJ. Understanding Statistical Process Control.
- Benneyan JC, Lloyd RC, Plsek PE. Statistical Process Control as a Tool for Research and Healthcare Improvement.
- ISO 7870. Control Charts.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Health at a Glance 2023: OECD Indicators — Organisation for Economic Co-operation and Development, 2023 Edition ed., 2023 (OECD Publishing)
OECD’s comprehensive biennial compendium of comparative indicators on population health and health-system performance across member and partner countries — health status, risk factors, access, quality, resources and spending — the standard cross-country benchmarking reference.
Frequently Asked Questions (6)
What is statistical process control?
A quality management method using statistical techniques to monitor a process, distinguishing normal variation from a genuine, significant change requiring action.
Source: Shewhart 1931
What statistical techniques does statistical process control use?
Statistical process control is a quality management method that uses statistical techniques to monitor a process. It uses those techniques, such as control charts and calculated limits, to watch how a process behaves over time. It distinguishes normal variation from a genuine, significant change requiring action, so routine noise is not mistaken for a real shift. It is a quality management method, a disciplined approach to keeping a process in control. It relies on a control chart, the central tool through which it monitors and judges a process. Watching a process statistically to catch real change is what it does. Shewhart (1931) set this out.
Source: Shewhart 1931
What does statistical process control use?
Statistical process control uses statistical techniques to monitor a process, so it applies statistical methods to watch a process, distinguishing normal variation from a genuine, significant change requiring action. This use of statistical techniques defines it. So statistical process control is a quality management method using statistical techniques to monitor a process, distinguishing normal variation from a genuine, significant change requiring action This distinction of normal variation from a real change is what statistical process control is used to make for a process.
Source: Shewhart 1931
What does statistical process control distinguish?
Statistical process control distinguishes normal variation from a genuine, significant change requiring action, so it separates the ordinary variation of a process from a real, meaningful shift that calls for action. This distinction defines its purpose. So statistical process control is a quality management method using statistical techniques to monitor a process, distinguishing normal variation from a genuine, significant change requiring action This status as a quality management method is what places statistical process control among the tools for managing quality.
Source: Shewhart 1931
What kind of method is statistical process control?
Statistical process control is a quality management method, so it is a method used in quality management, applying statistical techniques to monitor a process and distinguish normal variation from a genuine, significant change requiring action. This status as a quality management method defines it. So statistical process control is a quality management method using statistical techniques to monitor a process, distinguishing normal variation from a genuine, significant change requiring action.
Source: Shewhart 1931
How does statistical process control relate to a control chart?
Statistical process control relates to a control chart as the method to a core tool of it: statistical process control uses statistical techniques to monitor a process and distinguish normal variation from a genuine change, and a control chart is a statistical tool monitoring a process over time using control limits to make that distinction. So a control chart is a central tool of statistical process control, connected as the method and the chart it relies on.
Source: Shewhart 1931
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 27 Mar 2026
Content version: 1.0.0
Canonical Identity
- Term code
- HS-NHS-HQ-077
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