Control Phase: Sustaining Performance

Introduction

The Control phase is the final phase of DMAIC. Its purpose is not merely to confirm that an improvement worked, but to ensure that the improved process continues to produce predictable results after the project team withdraws. A process that performs well for a few weeks and then returns to its former condition has not been sustainably improved. Control therefore converts a project solution into an operating management system.

Control links statistical evidence, process ownership, standard work, measurement systems, visual management, and disciplined responses to abnormal conditions. It also establishes how performance will be reviewed, who is authorized to act, and when the process should be re-examined. In this sense, Control is both a statistical activity and a governance activity.

A mature control system answers five questions:

1. What characteristic must be controlled?
2. How will it be measured accurately and frequently enough?
3. What constitutes normal and abnormal performance?
4. Who responds, by what method, and within what time?
5. How is learning incorporated into the process and its documentation?

Learning objectives

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

• construct a risk-based control plan;
• distinguish standard work, visual management, and response plans;
• select and interpret variable, attribute, short-run, and advanced control charts;
• calculate control limits for common Shewhart charts;
• distinguish common-cause from special-cause variation;
• design escalation and reaction procedures;
• evaluate the limitations of statistical process control (SPC) in organizational settings; and
• integrate control activities into operational governance and continuous improvement.

1. Control as a closed-loop management system

Improvement changes the process; control protects the change. The control phase begins by identifying the critical-to-quality (CTQ) characteristics and the process inputs that influence them. It then specifies operational methods, measurement rules, control limits, review frequency, and responses.

A useful closed-loop model is:

Figure: Control is a feedback loop linking operation, measurement, decision, and response.

Control does not mean eliminating all variation. Every real process varies. The objective is to make variation predictable, reduce avoidable special causes, and ensure that the remaining common-cause variation is acceptable relative to customer and business requirements.

2. The control plan

A control plan is a living document that translates the improved process design into operational controls. It should be owned by the process owner rather than treated as a project deliverable stored in isolation.

A practical control-plan structure includes:

Control plans should be risk-based. A high-severity failure with a low observed frequency may require stronger prevention and detection than a frequent but harmless deviation. Failure mode and effects analysis (FMEA), process capability, regulatory obligations, customer requirements, and historical instability should influence control intensity.

A specification limit is not the same as a control limit. Specification limits come from requirements; control limits are calculated from process data and describe expected process behavior. A stable process can be incapable of meeting specifications, while an apparently capable process may be unstable and therefore unsuitable for capability analysis.

Measurement-system prerequisites

SPC cannot compensate for unreliable measurement. Before relying on a chart, the organization should establish operational definitions, calibration status, resolution, repeatability, reproducibility, and data integrity. For continuous measurements, a measurement-system analysis may estimate variation attributable to the measurement system relative to total process variation. For attribute inspection, inspectors require consistent decision rules and representative examples.

Data must also be traceable to time, machine, operator, material lot, location, and other variables relevant to diagnosis. Excessive aggregation can conceal shifts and produce misleadingly smooth charts.

3. Standard work and process ownership

Standard work defines the current best-known method for performing a task safely, efficiently, and consistently. It normally specifies sequence, expected time or pace, work-in-process limits, critical points, quality checks, and abnormality responses. Standard work is not intended to suppress employee judgment in emergencies; it creates a stable baseline from which deviations and improvements can be recognized.

Effective standard work has three properties:

• visible: available at the point of use in understandable language;
• specific: describes observable actions and acceptance criteria; and
• change-controlled: revised when evidence supports a better method.

The process owner is accountable for sustained performance, while operators remain essential sources of process knowledge. A control system is weak when ownership is assigned only to the quality department. Quality personnel may facilitate measurement and analysis, but line management must own daily execution and response.

Layered process audits can verify whether critical controls are being performed. They should examine adherence and effectiveness, not become punitive inspections. Audit findings should be categorized, assigned, closed, and reviewed for recurring patterns.

4. Visual management and response plans

Visual management makes normal and abnormal conditions apparent without requiring extensive analysis. Examples include status boards, trend displays, color-coded locations, first-piece approval indicators, electronic alerts, andons, and defect samples. Visuals should support a decision; decoration without a defined response adds little value.

A response plan should specify:

1. the signal or threshold that triggers action;
2. immediate containment, including identification of potentially affected output;
3. notification and escalation requirements;
4. diagnostic checks and authorized adjustments;
5. disposition of nonconforming material or service;
6. verification that the process has returned to control; and
7. documentation and preventive follow-up.

The plan must distinguish adjustment from tampering. An operator who changes a stable process after every minor fluctuation may increase variation rather than reduce it. Adjustments should be based on defined evidence, such as a special-cause signal or a verified change in a controllable input.

5. Statistical process control

5.1 Common and special causes

Common-cause variation is inherent in the current process design and operating system. It is produced by many small, usually random influences. Reducing it generally requires a fundamental process change, such as redesigned equipment, improved materials, or a different method.

Special-cause variation is produced by an identifiable, non-routine influence: a broken tool, incorrect setup, unusual supplier lot, software change, or measurement failure. The first response is to investigate and remove or contain the cause. Control limits should not be recalculated merely to hide an assignable cause.

A control chart is a time-ordered display of process data with a centre line and statistically derived limits. For a stable approximately normal process, three-sigma limits provide a practical balance between sensitivity and false alarms. They are decision boundaries, not specification requirements.

5.2 Variable control charts

For individual observations, the Individuals–Moving Range (I–MR) chart is useful when rational subgroups of size one are unavoidable. For observations x₁, x₂, …, xₘ, the moving range is:

The average moving range is MR̄. Under common assumptions, an estimate of within-process standard deviation is:

where d₂ is a bias-correction constant determined by moving-range length; for a two-observation moving range, d₂ ≈ 1.128. Individuals-chart limits are:

These limits assume reasonably independent observations and a stable estimation period. Autocorrelation, trends, and changing measurement conditions can make this approach inappropriate.

For subgrouped continuous data, an X̄–R chart is commonly used for small subgroup sizes. With subgroup means x̄ᵢ and ranges Rᵢ:

where k is the number of subgroups. The limits are:

The constants A₂, D₃, and D₄ depend on subgroup size and are obtained from standard SPC tables. The range chart is examined first because unstable within-subgroup variation undermines interpretation of the X̄ chart.

For larger subgroups, an X̄–S chart uses subgroup standard deviations sᵢ. With average standard deviation [[S̄]], its usual limits are:

Again, constants depend on subgroup size and the assumptions of the charting method.

Worked example: an X̄–R chart

Suppose five subgroups of size four have means 10.2, 10.4, 10.1, 10.3, and 10.5, and ranges 0.8, 1.0, 0.6, 0.9, and 0.7. Then:

For subgroup size four, standard constants are A₂ = 0.729, D₃ = 0, and D₄ = 2.282. Therefore:

All five subgroup means and ranges are within these limits. This supports, but does not prove, statistical control; additional run-rule patterns and process knowledge must also be considered.

5.3 Attribute charts

Attribute charts apply when data are counts or classifications rather than measured values.

• p chart: fraction or proportion nonconforming, with potentially varying sample size.
• np chart: number nonconforming, with constant sample size.
• c chart: count of nonconformities per constant inspection unit.
• u chart: nonconformities per unit when the number of units inspected varies.

For a p chart, if p̄ is the average fraction nonconforming and nᵢ is the sample size at time i:

Negative lower limits are set to zero. The binomial model assumes a defined binary classification and appropriate independence. For a c chart with average count c̄, limits are:

The Poisson assumption should be examined; overdispersion may require an alternative model or an investigation of heterogeneous opportunities.

5.4 Short-run and advanced charts

Traditional charts need enough repeated observations under comparable conditions. Short-run production, high-mix manufacturing, clinical services, and project-based work often violate that condition. Suitable approaches include standardized charts, nominal-based charts, charting residuals, and EWMA or CUSUM methods.

Standardized charting converts measurements with different means and scales into comparable values, but only when the reference means and standard deviations are meaningful and stable. Nominal-based charts compare deviations from each product’s target; they require careful treatment of product-specific tolerances and measurement systems.

An EWMA chart uses a weighted average that emphasizes recent observations:

where xₜ is the current observation, zₜ is the smoothed statistic, and λ is the weighting parameter. Small λ values are sensitive to small persistent shifts but respond more slowly to large sudden changes. A CUSUM accumulates departures from a target and is also effective for detecting small sustained shifts. These methods require deliberate parameter selection and trained interpretation; more sensitivity can create more false signals if the process model is poor.

For autocorrelated data, ordinary Shewhart limits may generate misleading alarms. Time-series models, residual charts, or specialized methods may be needed. In regulated or safety-critical environments, chart choice and alarm rules should be validated and documented.

6. Interpreting signals and capability

A point outside a control limit is one signal of special cause. Other evidence includes long runs on one side of the centre line, trends, cycles, stratification, and unusual clustering. Organizations should define a consistent rule set before reviewing results. Western Electric or Nelson rules may be used, but applying many rules simultaneously increases false-alarm probability.

Capability analysis is meaningful only after stability has been demonstrated. For approximately normal data with specification limits USL and LSL:

Here μ is the process mean and σ is the relevant within-process standard deviation. Cₚ describes potential capability if centred; Cₚₖ also reflects off-centre operation. Non-normal data require an appropriate transformation or distribution-based method. Capability indices are not substitutes for control charts and do not establish causal explanations.

7. Detailed illustrative case: outpatient laboratory turnaround time

Background. A hospital laboratory promised routine chemistry results within 60 minutes. An improvement project reduced median turnaround time, but complaints returned three months later.

Problem. The original project measured only weekly averages. It did not distinguish collection delay, transport delay, analytical processing, and result verification. Ownership of the post-project controls was unclear.

Analysis. The team defined turnaround time as the elapsed time from specimen receipt in the laboratory information system to verified result release. A measurement audit found inconsistent timestamps and missing records. After the definition was standardized, daily subgroup data were collected by shift. An X̄–R chart showed a stable analytical-processing time but special-cause increases on night shifts. Stratification identified a recurring analyzer maintenance event and inadequate night-shift staffing during batch verification.

Approach. The control plan assigned the laboratory supervisor as process owner. Standard work specified specimen triage, analyzer checks, maintenance handover, and escalation. A visual board displayed the current shift’s median time, the proportion exceeding 60 minutes, pending specimens, and open abnormalities. A p chart monitored the fraction exceeding the service requirement because daily sample sizes varied. The response plan required containment of delayed specimens, notification to clinical units for urgent cases, investigation of timestamp or equipment causes, and documented release by the supervisor.

Outcome. The process remained statistically stable for the following quarter, and the proportion exceeding 60 minutes declined. More importantly, the organization could distinguish an ordinary fluctuation from a maintenance-related event and respond before service failure became widespread.

Learning points. The case demonstrates that control requires a precise operational definition, reliable data, ownership, stratification, appropriate chart selection, and a response that protects patients while root causes are investigated. It also shows that a control chart cannot repair an ambiguous process definition.

8. Governance, ethics, technology, and limitations

Control data can affect employee evaluation, supplier qualification, customer communication, and regulatory reporting. Using charts as instruments of blame encourages under-reporting, data manipulation, and concealment of abnormalities. Ethical control systems protect truthful reporting and separate process learning from unjust disciplinary action. Access controls, audit trails, retention rules, and privacy safeguards are necessary when data include patient, employee, or customer information.

Digital SPC platforms can automate data collection, calculate limits, and trigger alerts. Artificial intelligence may help identify nonlinear patterns, contextualize alarms, or prioritize investigations. However, automated detection does not establish causation. Models require validated data, monitoring for drift, explainable decision rules, cybersecurity protection, and human accountability. An AI-generated alarm should never silently change a process or disposition nonconforming product without authorized governance.

Common limitations include inadequate sample sizes, non-random sampling, autocorrelation, unstable measurement systems, changing specifications, overuse of alarm rules, and failure to distinguish product families. Control limits calculated from a mixture of unlike processes are often meaningless. Conversely, excessive controls can increase cost and encourage tampering. The appropriate response is not maximum measurement but effective, risk-proportionate measurement.

9. Best-practice implementation sequence

A practical implementation sequence is:

1. confirm the improved process and its CTQs;
2. validate the measurement system and operational definitions;
3. identify owners, stakeholders, risks, and regulatory obligations;
4. document standard work and mistake-proofing;
5. select chart types based on data type, sampling, and process structure;
6. establish a reliable baseline and calculate limits using appropriate data;
7. define visual controls and a written reaction plan;
8. train operators and supervisors using realistic abnormal scenarios;
9. audit both compliance and effectiveness;
10. review performance at defined intervals and revise the plan when evidence warrants; and
11. transfer residual opportunities to the next improvement cycle.

The final handoff should include the control plan, chart definitions, data dictionary, measurement instructions, response contacts, training records, open risks, and criteria for re-opening the project.

Chapter Summary

The Control phase sustains the gains achieved through DMAIC by converting improvements into a managed operating system. A robust control plan identifies CTQs, measurement methods, sampling, responsibilities, control techniques, and reaction procedures. Standard work provides a stable baseline; visual management makes conditions and priorities visible; and response plans ensure that abnormal signals lead to containment, investigation, recovery, and learning.

SPC separates common-cause from special-cause variation and uses appropriate charts for continuous measurements, attribute data, individual observations, short runs, and autocorrelated or small shifts. Control limits describe process behavior and must not be confused with specification limits. Capability indices should be interpreted only after stability and measurement adequacy are established. Sustainable control also depends on ownership, ethical data use, validated technology, and continual review.

Key Terms

Control phase: DMAIC phase that sustains and governs improved performance.

Control plan: Document specifying process controls, measurements, responsibilities, and responses.

Standard work: The current best-defined method for performing a process.

Visual management: Display of information so normal and abnormal conditions are readily apparent.

Reaction plan: Predefined actions following an abnormal signal.

Common cause: Variation inherent in the current process system.

Special cause: Non-routine, identifiable source of variation.

Control limit: Statistical boundary describing expected process behavior.

Specification limit: Customer, regulatory, or engineering requirement.

CTQ: Critical-to-quality characteristic important to customer or process performance.

SPC: Statistical process control using data to monitor and improve process behavior.

Rational subgroup: Data grouped so within-group variation represents short-term process variation.

Individuals–moving range chart: Chart for sequential individual measurements and their moving ranges.

X̄–R chart: Chart for subgroup means and ranges.

p chart: Chart for fraction nonconforming.

c chart: Chart for counts of nonconformities with constant opportunity.

EWMA: Exponentially weighted moving-average chart sensitive to persistent shifts.

Process capability: Ability of a stable process to meet specifications.

Cₚₖ: Capability index incorporating process centring.

Tampering: Unwarranted adjustment of a stable process in response to routine variation.

Review Questions

Short Answer Questions

1. Why are control limits different from specification limits?
2. Distinguish common-cause and special-cause variation.
3. What information should a reaction plan contain?
4. When is an X̄–R chart preferable to an Individuals–MR chart?
5. Why must measurement-system adequacy be checked before SPC implementation?

Long Answer Questions

1. Explain how a control plan, standard work, visual management, and process ownership work together to sustain Six Sigma gains.
2. Compare p, np, c, and u charts, including their data requirements and practical applications.
3. Derive and interpret the control limits of an X̄–R chart and explain why the range chart is examined first.
4. Discuss the conditions under which EWMA, CUSUM, or short-run methods are preferable to traditional Shewhart charts.
5. Critically evaluate the ethical, organizational, and technical limitations of using automated SPC systems.

Analytical / Application Questions

1. A service process has varying daily volumes and records the number of cases exceeding a response-time requirement. Select an appropriate chart, specify the data definition, and design a reaction plan.
2. A stable process has excellent Cₚ but poor Cₚₖ. Diagnose the likely condition and recommend corrective actions without confusing capability improvement with control-limit adjustment.
3. An operator adjusts a machine after every point moves slightly above or below the centre line. Use SPC principles to explain the risk and design a more appropriate decision rule.

Multiple Choice Questions with Answers

Question 1

Which statement best distinguishes a control limit from a specification limit?

A. A control limit is set by the customer, while a specification limit is calculated from process data.

B. A control limit describes expected process behavior, while a specification limit expresses a requirement.

C. Both are calculated identically from the process mean and range.

D. A specification limit is used only for attribute data.

Correct Answer: B. A control limit describes expected process behavior, while a specification limit expresses a requirement.

Question 2

Which chart is generally appropriate for the fraction nonconforming when sample size varies?

A. p chart

B. np chart

C. c chart

D. X̄–R chart

Correct Answer: A. p chart

Question 3

For five subgroup means of 10.2, 10.4, 10.1, 10.3, and 10.5, the grand mean is:

A. 10.0

B. 10.2

C. 10.3

D. 10.5

Correct Answer: C. 10.3

Question 4

What is the first priority when a control chart shows a credible special-cause signal?

A. Immediately widen the control limits

B. Contain affected output and investigate the cause

C. Delete the unusual observation

D. Increase the specification limits

Correct Answer: B. Contain affected output and investigate the cause

Question 5

Which chart is designed to give greater sensitivity to small persistent shifts?

A. c chart

B. np chart

C. EWMA chart

D. Simple tally sheet

Correct Answer: C. EWMA chart

Question 6

Why should capability indices normally be calculated only after process stability is established?

A. Capability indices require attribute data only

B. An unstable process has no reliable, consistent distribution for capability interpretation

C. Control charts cannot be used with specifications

D. Capability indices are independent of variation

Correct Answer: B. An unstable process has no reliable, consistent distribution for capability interpretation

Question 7

For an X̄–R chart with X̄̄ = 10.3, R̄ = 0.8, and A₂ = 0.729, the upper X̄ limit is approximately:

A. 9.717

B. 10.300

C. 10.583

D. 10.883

Correct Answer: D. 10.883

Question 8

What is the principal danger of tampering with a stable process?

A. It always reduces common-cause variation

B. It can increase variation by reacting to routine fluctuations

C. It converts specifications into control limits

D. It eliminates the need for standard work

Correct Answer: B. It can increase variation by reacting to routine fluctuations

Question 9

Which chart is appropriate for the number of nonconformities per unit when the number of units inspected varies?

A. u chart

B. np chart

C. X̄ chart

D. Individuals chart

Correct Answer: A. u chart

Question 10

Which practice most directly supports ethical SPC governance?

A. Using abnormal signals primarily for punishment

B. Allowing automated systems to change processes without review

C. Protecting truthful reporting and maintaining traceable data and accountability

D. Suppressing inconvenient observations from the baseline

Correct Answer: C. Protecting truthful reporting and maintaining traceable data and accountability