RISK-BASED QUALITY AND INSPECTION
Understanding variation. Building stable processes.
A practical guide to statistical process control (SPC): recognise signals that need investigation, distinguish stability from capability, and turn process data into informed action.
OBSERVE THE PROCESS OVER TIME
What does SPC tell us?
SPC uses time-ordered data to detect changes in a process. It goes beyond asking whether each result meets a specification: it helps us understand how the system varies and when its behaviour may have changed.
Product control: does this result conform?
Compare a measurement or lot with the relevant requirements. This supports a conformity decision, but a problem may already have occurred before it is detected.
Process control: has the system changed?
Compare current behaviour with a stable historical baseline. Signals prompt investigation of possible changes in the process or the measurement system.
A stable process is not necessarily capable. It can consistently produce results outside specifications. Conversely, results may currently meet specifications while coming from an unstable process.
For lot-level decisions, see the complementary Acceptance Sampling guide.
TWO SOURCES OF VARIATION
Common causes and special causes
Common causes
The routine combination of materials, equipment, methods, environment and measurement produces the variation inherent in the current system.
- They persist as part of normal operation.
- Adjusting a single observation rarely removes them.
- Reducing them generally requires changes to the system.
Special causes
Identifiable circumstances depart from the usual pattern: a displaced sensor, an equipment fault, an ingredient change or a dosing error.
- They may produce unusual points or patterns.
- They require timely investigation.
- Removing the cause may restore stability.
Avoid tampering: adjusting the process after every common-cause fluctuation can increase variation. A signal is a reason to investigate, not proof of a particular cause.
THE STRUCTURE OF A CHART
Centre line and control limits
A control chart plots a statistic in time order. Its centre line represents the baseline level; its limits describe the expected variation of that plotted statistic under the selected model.
UCL = centre line + 3 × standard deviation of the plotted statistic
LCL = centre line − 3 × standard deviation of the plotted statistic
UCL and LCL mean upper and lower control limit. For a subgroup mean, the relevant standard deviation is its standard error—not the spread of individual units. Use chart-specific estimators and formulas; limits for counts, proportions and dispersion need their own treatment.
Control limits
Derived from process data or a justified reference model. They help detect changes and should not be set by copying product tolerances.
Specification limits
Defined by the customer, design, intended use or applicable requirements. They describe acceptability, independently of the historical process behaviour.
MATCH THE CHART TO THE DATA
Which control chart should you use?
| Data and sampling structure | Usual chart | Food-industry example |
|---|---|---|
| Continuous measurements in rational subgroups | X̄–R or X̄–S | Fill weights from several packs collected together each hour. |
| One continuous measurement per sampling interval | Individuals–moving range (I–MR) | A scheduled measurement of a process characteristic; check serial dependence. |
| Fraction of nonconforming units; constant or varying sample size | p | Proportion of packs with a sealing nonconformity. |
| Number of nonconforming units; constant sample size | np | Incorrectly labelled packs in a fixed-size sample. |
| Count of nonconformities; constant opportunity for occurrence | c | Visual packaging faults in a fixed inspection area or quantity. |
| Nonconformities per unit; varying opportunity for occurrence | u | Packaging faults per metre inspected, with different lengths examined. |
A nonconforming unit is not the same as a nonconformity: one unit can have several faults. For p and u charts, limits generally depend on the sample size or inspection opportunity.
Define sampling frequency, rational subgroups, measurement method and responsibilities before collecting data. A rational subgroup groups observations made under similar short-term conditions, so changes between subgroups can be detected. Check model assumptions: binomial for p/np, Poisson for conventional c/u charts, and the relevance of independence. Clustering, overdispersion or autocorrelation may require a different model.
ESTABLISH A BASELINE BEFORE MONITORING
Phase I and Phase II
Phase I · establish the baseline
Examine historical or initial observations, investigate signals and estimate limits that represent a stable operating state. Assess both location and dispersion, and document any exclusions.
Phase II · monitor prospectively
Use the established limits to detect subsequent shifts, trends or changes in dispersion. Review limits only for a documented reason, such as a verified process change—not to absorb an unwanted signal.
Do not remove points merely to make the chart look better. Exclusion from the baseline requires an evidenced special cause and a recorded decision. A baseline based on few observations has uncertain limits and should be treated accordingly.
MORE THAN POINTS OUTSIDE THE LIMITS
Signals that deserve investigation
An extreme point
A point outside a control limit may indicate an abrupt change, a special cause or a measurement problem.
A run or sustained shift
A long sequence on one side of the centre line may indicate that the process level has changed.
A trend or recurring pattern
Progressive increases, cycles or alternating values can reflect wear, environmental effects, shifts or repeated adjustments.
Choose a documented set of signal rules in advance. Supplementary rules increase sensitivity but also false alarms. Do not combine rule sets indiscriminately or choose rules after seeing the data.
STABILITY BEFORE CAPABILITY
Cp, Cpk and specifications
Capability indices compare the variation of a stable process with specification limits. Check stability, measurement adequacy, independence, distribution and data sufficiency before interpreting them.
Cp = (USL − LSL) / (6σ)
Cpk = min[(USL − μ) / (3σ), (μ − LSL) / (3σ)]
USL and LSL: upper and lower specification limits.
μ: process mean. σ: process standard deviation, estimated using a stated method.
Cp · potential capability
Compares the specification width with the process spread. It does not account for whether the mean is centred.
Cpk · capability allowing for off-centring
Also considers the distance from the mean to the nearer specification limit. It can be lower than Cp and does not establish capability on its own.
These conventional interpretations assume an approximately normal distribution. For non-normal data or a one-sided specification, select an appropriate method. Document the variation estimate and consider uncertainty; no single capability threshold establishes food safety or regulatory compliance.
PRACTICAL APPLICATION
Example: fill-weight monitoring
Each hour, an operator weighs five consecutive packs produced under comparable conditions. The objective is to detect changes in average fill weight and within-subgroup variation.
- Check measurement: confirm that the balance and measurement procedure are suitable.
- Define the subgroup: use the five packs as a rational subgroup; record line, product, time and relevant events.
- Select X̄–R: monitor subgroup averages and ranges together. Check dispersion before interpreting the mean chart.
- Establish Phase I limits: investigate format changes, adjustments and stoppages. Do not pool fundamentally different operating conditions.
- React in Phase II: a signal triggers the agreed response—identify potentially affected product, check the balance and filler, investigate and document.
- Assess capability after stability: compare the stable process with the appropriate fill-weight specifications.
Practical sequence: verify measurement → establish stability → assess capability → improve.
This is a monitoring example, not a legal net-content sampling or release procedure. Product disposition and any required controls remain separate decisions.
FROM DATA TO ACTION
A four-step reaction plan
01 · Detect
Confirm the signal and check for recording or measurement errors. Record when it first appeared.
02 · Contain
Identify potentially affected product and determine its status under the relevant food-safety and quality procedures.
03 · Investigate
Review changes in materials, methods, equipment, environment and personnel. Assign responsibility for follow-up.
04 · Learn
Correct the cause, verify effectiveness and update process knowledge. Document the basis for restarting or revising controls.
COMMON PITFALLS
What to avoid
- Using specification limits as control limits.
- Calculating capability for an unstable process.
- Adjusting the process after every random fluctuation.
- Combining incompatible sources of variation within subgroups.
- Ignoring the measurement system or serial dependence.
- Applying many signal rules without assessing false alarms.
- Looking only at averages and overlooking dispersion.
- Detecting signals without assigning actions and responsibilities.
SOURCES AND FURTHER READING
Technical references
- NIST/SEMATECH: Univariate and Multivariate Control Charts.
- NIST: What are Variables Control Charts? Limits, baseline considerations and signal rules.
- NIST: Shewhart X-bar, R and S Control Charts.
- NIST: What are Attributes Control Charts?.
- NIST: What is Process Capability?.
- Statistical Process Control for process control of microbiological levels (2006): AOAC contract deliverable hosted by FDA; technical background, not a current binding regulatory standard.
An educational QualiFood adaptation. SPC supports process understanding; it does not replace validated food-safety controls, applicable requirements or professional judgement.
Future development: an interactive control-chart dashboard
A planned tool will support chart selection, signal visualisation and documentation of a process-specific reaction plan. It is not available yet.