9. Advanced Statistical Process Monitoring

Introduction and context

Statistical process control (SPC) is most effective when the monitoring method reflects the nature of the process, the size of change that matters, the speed with which a signal is required, and the consequences of delayed detection. The traditional Shewhart chart remains valuable for detecting relatively large and sudden departures from a stable process. However, many contemporary processes do not conform to this simple situation. A small but persistent shift in a mean may create substantial quality loss before a Shewhart chart signals. Data may be autocorrelated, seasonal, sparse, short-run, highly dimensional, or generated by rare-event mechanisms. In such settings, advanced monitoring methods are not optional refinements; they are necessary extensions of statistical reasoning.

This chapter examines cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts, short-run and rare-event monitoring, time-weighted methods, multivariate charts, and methods for processes affected by autocorrelation and seasonality. It also compares classical SPC with broader change-detection approaches used in analytics and industrial intelligence. The central principle is that a control chart is a decision system, not merely a graph. Its design must connect statistical evidence with process knowledge, operational response, and governance.

Learning objectives

By the end of this chapter, the learner should be able to:

1. Explain why advanced monitoring methods are required beyond Shewhart charts.

2. Construct and interpret CUSUM and EWMA charts for detecting small process shifts.

3. Select suitable methods for short-run, rare-event, time-weighted, and high-mix processes.

4. Diagnose the effects of autocorrelation and seasonality on control-chart performance.

5. Explain the logic of multivariate monitoring and distinguish major multivariate charts.

6. Compare classical SPC with statistical and machine-learning change-detection methods.

7. Design a monitoring strategy that links chart signals to investigation and corrective action.

8. Evaluate limitations, risks, ethical issues, and implementation requirements in advanced SPC.

From pointwise alarms to accumulated evidence

A Shewhart chart evaluates each observation, or a subgroup statistic, against fixed control limits. This makes it sensitive to a large one-time disturbance, but relatively insensitive to a small shift distributed across many observations. Advanced charts improve sensitivity by retaining information from previous observations. They therefore introduce a memory of the process into the monitoring rule.

Suppose measurements are standardized as

\[

Z_t=(X_t-\mu_0)/\sigma,

\]

where \(\mu_0\) and \(\sigma\) are the in-control mean and standard deviation. A shift of only 0.5 standard deviations may be operationally important but may not immediately cross a Shewhart limit. A memory-based chart accumulates evidence that the process has moved, while also controlling the tendency of random variation to produce a false alarm.

The design of any monitoring scheme involves several related quantities:

• In-control average run length (ARL0): the expected number of observations before a false signal when the process is stable.
• Out-of-control average run length (ARL1): the expected number of observations until a signal after a specified change.
• Detection delay: the time between the change and its detection.
• False-alarm probability: the likelihood that ordinary variation is interpreted as a special cause.
• Reference or allowance value: a parameter that prevents small random deviations from accumulating excessively.

No chart is uniformly best. Increasing sensitivity to small shifts often increases false alarms unless the limits and decision rules are carefully calibrated. Chart selection is therefore an economic and operational decision as well as a statistical one.

CUSUM: evidence accumulated sequentially

The cumulative sum chart is designed to detect sustained changes in a process parameter. For a standardized observation, a two-sided CUSUM can be written as

\[

C_t^+=\max[0,C_{t-1}^+ + Z_t-k],

\]

\[

C_t^- =\max[0,C_{t-1}^- - Z_t-k],

\]

where \(k\) is the reference value. An alarm is produced when either statistic exceeds a decision interval \(h\). The upper statistic accumulates evidence of an upward shift; the lower statistic accumulates evidence of a downward shift.

The reference value is often selected in relation to the shift of interest. If a standardized shift of magnitude \(\delta\) is important, a common design principle is to set \(k\) near half that shift, subject to the chosen ARL and sampling scheme. The decision interval controls the balance between sensitivity and false alarms. These parameters should not be selected mechanically: the desired shift, sampling frequency, process capability, and cost of investigation must be considered together.

CUSUM is particularly useful when the process is expected to move gradually or when a small persistent deterioration is more important than a single extreme observation. It is also useful in process adjustment, where the chart can indicate the direction and approximate onset of a shift. A tabular CUSUM is often convenient for implementation because only the previous cumulative value and current observation are required.

A CUSUM signal does not prove that a particular assignable cause exists. It indicates that the recent sequence is less consistent with the in-control model than the decision rule permits. The investigator must then examine equipment settings, materials, operators, environmental conditions, measurement systems, and recent process changes.

EWMA: continuously weighted memory

The exponentially weighted moving average chart assigns greatest weight to the latest observation while retaining diminishing weights from earlier observations. Its statistic is

\[

S_t=\lambda X_t+(1-\lambda)S_{t-1},\quad 0<\lambda\leq1,

\]

where \(S_0\) is usually set to the target mean. A small \(\lambda\) gives substantial memory and is effective for small, sustained shifts; a large \(\lambda\) responds more rapidly to recent changes. For independent observations with stable variance, the approximate steady-state limits are

\[

\mu_0\pm L\sigma\sqrt{\frac{\lambda}{2-\lambda}}.

\]

The limits are narrower than Shewhart limits because the EWMA statistic is less variable than an individual observation. During start-up, however, the variance of the statistic is smaller than its long-run variance. Accurate implementation may therefore use time-varying limits, especially when early observations matter.

CUSUM and EWMA are similar in purpose but differ in form. CUSUM accumulates deviations after subtracting a reference value and can be interpreted through likelihood-ratio logic. EWMA smooths observations through a weighted average and is often easier to explain to users familiar with moving averages. CUSUM can provide sharper design control for a specified shift, whereas EWMA offers flexible smoothing and a visually intuitive trajectory. Both methods can be combined with a Shewhart rule to detect either abrupt or gradual changes.

Choosing between Shewhart, CUSUM, and EWMA

A practical choice begins with the change that must be detected. If a sudden, large deviation is dangerous—for example, a major calibration failure—a Shewhart component is essential. If the concern is a gradual drift of 0.25 to 1 standard deviation, CUSUM or EWMA is generally more appropriate. If both situations are possible, a combined chart can be used, provided that its overall false-alarm behaviour is evaluated rather than assuming independent alarm rates.

Sampling frequency also matters. A highly sensitive chart applied to every tiny measurement may generate operationally excessive signals. Conversely, monitoring too infrequently creates unavoidable detection delay. The chart should be designed around the time scale of the process and the time available to prevent nonconforming output.

Short-run and high-mix processes

Classical control charts often assume a long production run of one product made under relatively constant conditions. High-mix manufacturing, laboratories, maintenance operations, healthcare services, and customized production violate this assumption. A product may be produced only a few times before the process changes to another product or setup.

Short-run SPC seeks to separate common process behaviour from product-specific effects while retaining information across related products. One approach is to standardize measurements using product-specific targets and tolerances:

\[

Z_{it}=\frac{X_{it}-T_i}{s_i},

\]

where \(T_i\) and \(s_i\) represent the target and an appropriate scale for product or characteristic \(i\). The standardized values can then be plotted on a common chart. This is valid only when the targets, scales, and measurement systems are credible and comparable.

Other approaches include standardized control charts, deviation-from-target charts, charting within-product performance, and hierarchical or mixed-effects models. The latter distinguish variation attributable to product family, machine, operator, and time. A useful operational strategy is to maintain product-family baselines and use a common monitoring layer for standardized residuals.

Short-run charts require disciplined identification of setup effects. A changeover may legitimately alter the mean, but an avoidable setup error should not be absorbed into a new baseline. Engineers must distinguish a planned change in product specification from an unplanned process shift. Control limits should not be recalculated after every signal, because doing so can conceal deterioration.

Rare-event and attribute monitoring

Some defects are so infrequent that conventional fraction-nonconforming charts become inefficient. A p-chart may display long sequences of zeros, followed by an apparently dramatic but statistically ambiguous change. Rare-event charts are designed for situations in which the probability of an event is very small and the monitoring objective is to detect a meaningful increase quickly.

Examples include safety incidents, contamination, field failures, fraud indicators, serious medical events, and defects in highly reliable products. Suitable methods include geometric or waiting-time charts, g-charts for the number of opportunities between events, and t-charts for the time between events. A g-chart may monitor the number of conforming units or opportunities between successive failures; a t-chart monitors elapsed time between events.

The underlying assumptions must be examined carefully. If opportunities differ in exposure, a simple event count is misleading. A rate model with an offset, such as a Poisson or negative-binomial model, may be more appropriate. If events cluster because of common causes, independence assumptions fail. A rare event may also be underreported, making apparent improvement a measurement or reporting phenomenon rather than a real quality gain.

Zero-defect observations do not demonstrate that the process is risk-free. They may reflect limited exposure, weak detection, or insufficient sample size. Governance systems should therefore combine rare-event charts with audits, near-miss information, reliability analysis, and engineering controls.

Time-weighted and adaptive monitoring

Time-weighted charts give different importance to observations according to their temporal position or persistence. CUSUM and EWMA are the principal time-weighted methods, but the broader idea includes moving-window statistics, weighted likelihood ratios, adaptive limits, and change-point procedures. The objective is to respond to sustained evidence without treating every observation as independent and equally informative.

A moving-window chart calculates a statistic over the latest \(w\) observations. A short window reacts quickly but is noisy; a long window is stable but may delay detection. Adaptive methods alter the window, smoothing parameter, or threshold in response to process conditions. Such flexibility can be valuable but increases the risk of opaque decision rules and inflated false-alarm rates.

Time-weighted methods require a clearly defined reset policy. After a confirmed assignable cause is removed, should the statistic be reset to zero, restarted at the target, or retained to reflect residual uncertainty? The answer depends on whether the process has genuinely returned to the original state. Resetting without verification can erase evidence of continuing instability.

Autocorrelation and seasonality

Many industrial and service measurements are serially dependent. Temperature, chemical concentration, energy demand, cycle time, and financial or transactional measures often depend on recent values. Applying ordinary control limits to autocorrelated data can produce excessive false alarms or mask changes, because the assumed independent-noise model is incorrect.

A useful approach is model-based monitoring. First, estimate the expected structure using a time-series model—for example, an autoregressive model, a regression model with operational covariates, or a seasonal model. Then monitor the residuals, provided that the residuals are approximately independent and stable. The workflow is therefore:

1. Specify the process mean using engineering and time-related predictors.

2. Model serial dependence and seasonal patterns using suitable historical data.

3. Check residual independence, variance stability, and parameter adequacy.

4. Apply Shewhart, CUSUM, or EWMA charts to residuals.

5. Investigate both residual signals and changes in the underlying model.

Seasonality must not be confused with special-cause variation. A weekly demand pattern, shift-related temperature effect, or monthly workload cycle may be predictable and should be modelled rather than treated as instability. However, a seasonal pattern that changes amplitude or timing may itself signal a process problem.

Prewhitening can remove predictable autocorrelation before charting, but poor models can create misleading residuals. Model selection should therefore use process knowledge, diagnostics, and validation—not merely the model with the best historical fit. Forecast-error monitoring is another practical option: a large unexpected forecast error may be charted, while the forecast system is periodically revalidated.

Multivariate statistical process monitoring

Modern processes frequently produce several correlated quality characteristics. Monitoring each variable separately creates two problems: correlation is ignored, and the overall false-alarm rate increases as the number of charts grows. A process can also move in a direction that is not extreme on any single variable but is unusual in combination.

The classical Hotelling \(T^2\) statistic for a vector of measurements \(\mathbf{x}\) is

\[

T^2=(\mathbf{x}-\boldsymbol{\mu})'\mathbf{S}^{-1}(\mathbf{x}-\boldsymbol{\mu}),

\]

where \(\mathbf{S}\) is the covariance matrix. It measures the multivariate distance from the in-control mean while accounting for correlation. A large value indicates that the overall vector is unusual, but it does not automatically identify the responsible variable. Contribution plots, conditional analysis, and engineering review are needed for diagnosis.

Multivariate EWMA and multivariate CUSUM extend memory-based monitoring to vector observations. They are useful for small sustained changes in correlated characteristics. Principal component analysis (PCA) can reduce a high-dimensional measurement system to a smaller set of latent dimensions. Scores may represent normal process variation, while residual or squared-prediction-error statistics may identify departures not captured by the main components.

Multivariate methods face important challenges. Covariance matrices become unstable when the number of variables approaches the number of observations. Missing data, changing sensors, non-normality, and multiple operating modes further complicate analysis. Regularized covariance estimation, robust methods, dimension reduction, and mode-specific models may be necessary. A statistically significant multivariate signal must still be translated into an actionable physical cause.

Classical SPC and change-detection methods

Classical SPC generally assumes a defined in-control process, rational sampling, interpretable parameters, and a stable distinction between common and special causes. Change-detection methods use a broader family of sequential techniques to identify shifts, changes in distribution, or changes in dependence. Examples include likelihood-ratio procedures, Bayesian change-point methods, sequential probability ratio tests, kernel-based detectors, and machine-learning methods for data streams.

The distinction is not absolute. CUSUM itself can be derived as a sequential likelihood-ratio method, and modern change detection often uses SPC principles such as false-alarm control, run length, and out-of-control detection delay. The practical difference lies in emphasis. SPC focuses on process control, parameter stability, and corrective action; change detection may focus on identifying any distributional change, including changes that have no immediate engineering interpretation.

Machine-learning detectors can identify nonlinear patterns or complex multivariate behaviour, but they require representative training data and careful control of concept drift. Black-box scores may be difficult to explain to operators or auditors. A strong architecture often combines methods: interpretable SPC for critical quality variables, model-based residual monitoring for predictable dynamics, and anomaly detection as a supplementary screening layer. Automated alerts should not bypass human review when decisions affect safety, employment, customers, or regulatory compliance.

An illustrative case: monitoring a high-mix precision machining cell

Background

A precision machining cell produces several families of components on a shared group of computer numerical control machines. Each order is small, changeovers occur several times per shift, and quality characteristics include diameter, surface roughness, and positional error. Historical data show that tool wear causes gradual drift, while coolant temperature follows a predictable shift pattern.

Situation and problem

The existing practice uses separate Shewhart charts for each characteristic and product. Operators report two difficulties: charts rarely signal before a sizeable amount of material is affected, and frequent product changes make many limits statistically weak. Management wants earlier detection without creating an unmanageable number of alarms.

Analysis

The quality team first verifies the measurement system and separates data by product family, machine, and tool condition. Product-specific values are standardized relative to validated targets and scales. A regression model includes coolant temperature and product family; residual diagnostics reveal moderate serial correlation during long runs. The residual model is improved with an autoregressive term.

The team then designs an EWMA chart for standardized diameter residuals, with a small smoothing parameter because gradual tool wear is the primary concern. A Shewhart limit is retained for abrupt tool breakage or major setup errors. A multivariate \(T^2\) chart monitors diameter, roughness, and positional error together after removing predictable temperature effects. For rare catastrophic defects, a time-between-events chart is maintained separately.

Approach and solution

The monitoring system is implemented in layers. The operator dashboard displays current product and machine context, the EWMA trajectory, immediate Shewhart status, and multivariate status. A signal starts a structured investigation rather than an automatic product rejection. The response procedure requires checking tool life, offsets, coolant condition, fixture seating, and recent changeover records. A confirmed tool-wear signal triggers planned replacement; an unexplained multivariate signal triggers engineering review and temporary increased sampling.

Limits are estimated from verified stable periods and are not recalculated after every signal. The team evaluates the design using simulated shifts and historical replay, comparing false alarms, detection delay, and affected units. Operators receive training on the difference between a warning, an alarm, and a confirmed nonconformance.

Outcome

The system improves early recognition of gradual drift while preserving rapid detection of large disturbances. More importantly, signals become more actionable because the chart is linked to product family, machine state, and a defined response plan. The organization does not treat the statistical signal as a substitute for process knowledge; it uses the signal to focus investigation.

Learning points

The case illustrates five principles: standardization is essential in high-mix production; autocorrelation should be modelled before charting; one chart rarely serves every detection objective; multivariate alarms require diagnostic follow-up; and the value of SPC depends on the quality of the response system.

Implementation risks and professional responsibilities

Advanced monitoring can fail even when the formulas are correct. Common mistakes include estimating limits from unstable data, ignoring changes in measurement systems, applying independent-data limits to autocorrelated observations, using too many charts without adjusting alarm expectations, and treating every signal as proof of operator error. Repeatedly widening limits to reduce alarms is another form of concealment rather than improvement.

Data quality and traceability are central governance requirements. Time stamps, product identity, machine state, operator actions, missing values, overrides, and chart-parameter changes should be auditable. Cybersecurity matters when charts are connected to manufacturing execution systems or automated control loops. A false alarm may cause unnecessary adjustment, while a missed alarm may release unsafe or nonconforming output; both risks should be assessed.

Ethically, monitoring data should not be used carelessly to rank individuals when variation is primarily systemic. Personnel need fair notice about how data are used, and investigations should distinguish process conditions from individual performance. In regulated industries, validation, electronic records, change control, and documented approval of algorithms may be required. Any AI-assisted detector should be explainable to the extent needed for the decision, tested for drift, and subject to human accountability.

Best-practice design framework

A robust advanced-SPC project follows a sequence adapted to the process rather than a fixed software menu:

1. Define the quality risk, critical characteristics, and action time available.

2. Verify the measurement system, data lineage, sampling plan, and operating context.

3. Establish a credible in-control reference period, excluding known special causes only with documented justification.

4. Diagnose distributional form, autocorrelation, seasonality, stratification, and product or mode effects.

5. Select a chart according to the change of interest: Shewhart for large shifts, CUSUM or EWMA for persistent small shifts, rare-event charts for sparse outcomes, and multivariate methods for correlated characteristics.

6. Set limits using ARL, detection delay, economic consequences, and practical investigation capacity.

7. Define warning and action responses, including escalation, containment, root-cause analysis, and reset rules.

8. Validate the chart by historical replay, simulation, and review with process experts.

9. Monitor chart performance itself: false alarms, missed events, delay, overrides, and response completion.

10. Revalidate after changes in equipment, products, sensors, specifications, or operating conditions.

Current developments

Advanced SPC is increasingly integrated with streaming data platforms, edge computing, digital twins, and manufacturing execution systems. These technologies permit near-real-time monitoring and context-aware analysis, but they also increase the volume and speed of decisions. Automated feature extraction from images, vibration, acoustic signals, and sensor networks can support early detection, while dimensionality reduction and anomaly scoring help organize complex data.

The emerging direction is not the replacement of SPC by artificial intelligence. Rather, organizations are combining interpretable statistical rules with richer predictive models. Research and practice continue to address concept drift, distributed sensing, online covariance estimation, robust monitoring under non-normality, and human-centred alert design. The enduring requirement remains unchanged: a monitoring method must produce trustworthy evidence that leads to an appropriate process decision.

Chapter Summary

Advanced statistical process monitoring extends SPC to situations in which changes are small, data are dependent, events are rare, production is short-run or high-mix, and quality characteristics are correlated. CUSUM accumulates deviations relative to a reference value, while EWMA applies declining weights to past observations. Shewhart charts remain important for abrupt shifts, and combined schemes may address both abrupt and gradual changes.

Short-run methods require standardization or hierarchical modelling; rare-event charts focus on event counts or waiting times; and time-weighted methods improve sensitivity to persistent change. Autocorrelation and seasonality should generally be modelled before residual monitoring. Hotelling’s T-squared, multivariate CUSUM, multivariate EWMA, and PCA-based methods address correlated measurements but require careful covariance estimation and diagnosis. Change-detection and machine-learning methods can complement classical SPC, yet interpretability, false alarms, governance, and human accountability remain essential. Effective monitoring is therefore a designed socio-technical system linking data, statistical evidence, expertise, and action.

Key Terms

Advanced SPC: Statistical monitoring methods designed for complex, dependent, sparse, multivariate, or nonstandard processes.

ARL0: Expected number of observations before a false signal under in-control conditions.

ARL1: Expected number of observations until a signal after a specified process change.

CUSUM: A chart that accumulates deviations from a target or reference value.

Reference value: Allowance parameter in CUSUM that limits accumulation from small deviations.

Decision interval: Threshold that a cumulative statistic must exceed to signal.

EWMA: A recursively calculated weighted average giving greatest weight to recent observations.

Short-run SPC: Monitoring designed for limited production runs and frequent product or setup changes.

High-mix process: A process producing many product types or variants with relatively few observations of each.

Rare-event chart: A chart designed for very infrequent defects or incidents.

g-chart: A chart monitoring the number of opportunities or units between rare events.

t-chart: A chart monitoring elapsed time between rare events.

Autocorrelation: Dependence between observations at different time lags.

Seasonality: A repeating time-related pattern in process behaviour.

Residual monitoring: Charting deviations left after predictable effects are modelled.

Hotelling’s T-squared: A multivariate distance statistic accounting for covariance among variables.

PCA: Principal component analysis, a method for representing correlated variables through fewer latent dimensions.

Change detection: Sequential identification of a change in a process distribution, parameter, or dependence structure.

Detection delay: Time between the occurrence of a process change and its statistical signal.

Review Questions

Short Answer Questions

1. Why are CUSUM and EWMA generally more sensitive than Shewhart charts to small sustained shifts?

2. What roles do the reference value and decision interval play in a CUSUM chart?

3. Why can ordinary control limits be misleading for autocorrelated data?

4. What is the purpose of standardization in short-run or high-mix SPC?

5. Distinguish a g-chart from a t-chart.

Long Answer Questions

1. Explain the construction, interpretation, and design considerations of a two-sided CUSUM chart.

2. Compare Shewhart, CUSUM, and EWMA charts for abrupt, gradual, and persistent process changes.

3. Describe a model-based monitoring procedure for a seasonal and autocorrelated process.

4. Explain how Hotelling’s T-squared and PCA-based monitoring address multivariate quality data.

5. Discuss the governance, ethical, and implementation risks of automated advanced-SPC systems.

Analytical / Application Questions

1. A process has a stable standard deviation but experiences a gradual mean drift of 0.4 standard deviations over several hours. Select and justify a monitoring design, including how you would control false alarms.

2. A hospital records very few serious adverse events, but reporting intensity varies by department. Propose a rare-event monitoring approach and identify the assumptions that must be checked.

3. A high-mix production cell has three correlated quality characteristics, strong weekly seasonality, and frequent changeovers. Design an integrated monitoring architecture and explain how signals would be investigated.

22. Multiple Choice Questions with Answers

Question 1

Which monitoring method is most specifically designed to accumulate evidence of a small, sustained shift in a process mean?

A. A basic p-chart

B. A CUSUM chart

C. A simple histogram

D. A one-time acceptance test

Correct Answer: B. A CUSUM chart

Question 2

In a two-sided CUSUM, the reference value primarily serves to:

A. Convert all observations into percentages

B. Prevent small deviations from accumulating too readily

C. Estimate the covariance matrix

D. Remove seasonal variation automatically

Correct Answer: B. Prevent small deviations from accumulating too readily

Question 3

A small EWMA smoothing parameter generally produces a chart that:

A. Places greater effective weight on historical observations

B. Responds only to the most recent observation

C. Cannot detect persistent shifts

D. Requires independent product specifications

Correct Answer: A. Places greater effective weight on historical observations

Question 4

Which situation most strongly supports the use of a rare-event chart?

A. A process with frequent continuous measurements

B. A process in which defects occur very infrequently

C. A process with perfectly known seasonality only

D. A process with no recorded outcomes

Correct Answer: B. A process in which defects occur very infrequently

Question 5

Why should autocorrelated observations generally not be monitored using ordinary independent-data limits without adjustment?

A. Autocorrelation changes product specifications

B. Dependence can distort false-alarm rates and detection performance

C. Autocorrelation eliminates all process variation

D. Independent-data limits always produce wider limits

Correct Answer: B. Dependence can distort false-alarm rates and detection performance

Question 6

Which statistic explicitly accounts for covariance among several quality characteristics?

A. Hotelling’s T-squared

B. A univariate moving range

C. A simple defect count

D. A single-product target value

Correct Answer: A. Hotelling’s T-squared

Question 7

In a high-mix process, standardizing measurements primarily helps to:

A. Remove the need for a measurement system study

B. Place observations from different products on a comparable scale

C. Guarantee that all products have identical specifications

D. Eliminate all setup effects automatically

Correct Answer: B. Place observations from different products on a comparable scale

Question 8

A residual chart for a seasonal process is appropriate when the residuals:

A. Retain strong unmodelled seasonality

B. Are produced after predictable structure has been adequately modelled

C. Are calculated without reference to time

D. Are deliberately mixed across incompatible products

Correct Answer: B. Are produced after predictable structure has been adequately modelled

Question 9

What is a major practical limitation of a multivariate alarm?

A. It can never detect a combined shift

B. It automatically identifies the physical root cause

C. It may indicate unusual joint behaviour without identifying the responsible variable

D. It does not require stable covariance estimates

Correct Answer: C. It may indicate unusual joint behaviour without identifying the responsible variable

Question 10

Which statement best distinguishes classical SPC from many black-box anomaly detectors?

A. Classical SPC links defined process behaviour to interpretable control decisions

B. Classical SPC cannot monitor sequential data

C. Black-box methods always have lower false-alarm rates

D. SPC does not use statistical models

Correct Answer: A. Classical SPC links defined process behaviour to interpretable control decisions