Designing an SPC System

Introduction

Statistical Process Control (SPC) is not simply the practice of placing control limits on a chart. It is a management and engineering system for understanding process behaviour, separating routine variation from unusual variation, and using evidence to improve and control performance. A technically correct control chart can still be ineffective if it is based on an incorrectly defined process, an irrelevant quality characteristic, inappropriate sampling, or subgroups that conceal important variation.

Designing an SPC system therefore begins before data are collected. The organisation must understand the process, identify the characteristics that matter to customers and regulators, determine how and when measurements will be taken, and establish rules for interpreting signals. This chapter develops a systematic approach to those decisions. Particular attention is given to process mapping, critical-to-quality (CTQ) characteristics, sampling strategies, rational subgroups, sampling frequency, and the distinction between Phase I retrospective analysis and Phase II prospective monitoring.

Learning objectives

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

1. Define the process boundary, customers, inputs, outputs, and sources of variation relevant to an SPC system.
2. Translate customer, engineering, regulatory, and business requirements into measurable CTQ characteristics.
3. Select suitable measurement methods and sampling strategies for different process conditions.
4. Construct rational subgroups that reflect the source and timing of variation.
5. Determine a defensible sampling frequency using process dynamics, risk, cost, and information value.
6. Distinguish Phase I retrospective analysis from Phase II ongoing monitoring.
7. Design an SPC implementation that includes governance, reaction plans, measurement-system evaluation, and continual review.

1. SPC as a designed socio-technical system

An SPC system has at least six connected elements:

• Process definition: what operation, service, or transaction is being studied.
• Quality characteristics: what is measured and why it matters.
• Measurement system: instruments, methods, operators, software, and data controls.
• Sampling design: which units are observed, when, where, and in what groupings.
• Statistical method: the chart or analytical technique used to detect change.
• Response system: the actions taken when evidence indicates a special cause or unacceptable performance.

These elements must be aligned. For example, an individual-values chart may be appropriate when production is slow and observations are naturally separated, whereas an X̄ chart with a range or standard-deviation chart may be appropriate when several consecutive units are produced under essentially common conditions. Neither chart is universally superior; suitability depends on the process and sampling design.

SPC also differs from inspection. Inspection often asks whether an individual product conforms to a specification. SPC asks whether the process is stable and predictable and whether its variation is changing. A stable process can produce some nonconforming units if its natural variation is wide relative to specifications; conversely, an unstable process may temporarily produce conforming output while remaining unsafe to operate.

2. Begin with process understanding

2.1 Define the process boundary

The process boundary identifies where the SPC study begins and ends. It should specify:

• the trigger or starting condition;
• the transformation performed;
• the output delivered;
• the internal or external customer;
• interfaces with preceding and succeeding processes; and
• the decisions that the SPC information will support.

A boundary that is too broad produces ambiguous data and multiple sources of variation. A boundary that is too narrow may omit upstream causes that explain the observed behaviour. The practical question is: what process can the responsible team influence, and what evidence is required to manage it?

2.2 Identify customers and requirements

Customers include end users, internal departments, regulators, auditors, and downstream processes. Their requirements may concern dimensions, reliability, delivery time, safety, completeness, cost, security, or user experience. Requirements should be translated into operational measures rather than remaining as general statements such as “high quality” or “fast service.”

A useful requirements chain is:

Customer need → measurable requirement → quality characteristic → measurement method → decision rule.

For example:

Customer need: a medication order is available when promised.

Measurable requirement: percentage of orders available within the stated time.

Quality characteristic: order-cycle time in minutes, or an on-time indicator.

Measurement method: timestamped electronic transaction data.

Decision rule: monitor the distribution and the proportion late, with escalation for sustained deterioration.

2.3 Map the process

Process mapping should reveal where variation can enter, where it can be detected, and where control is possible. A useful map normally includes suppliers, inputs, activities, decisions, outputs, customers, measurement points, and feedback loops. Depending on the application, the map may be a high-level SIPOC diagram, a cross-functional flowchart, a value-stream map, or a detailed process model.

The map should distinguish:

• value-adding steps from delays, rework, and inspection;
• sequential flow from parallel paths;
• normal operating conditions from exceptions;
• common inputs from special batches or suppliers; and
• measurement locations from the locations where corrective action is possible.

A process map is not merely documentation. It is a sampling and stratification tool. If two product families use different settings, tooling, or materials, combining them in one chart may create apparent instability. If an output is measured only after rework, the chart may conceal the original process performance.

2.4 Identify sources of variation

Potential sources should be considered using categories such as machine, method, material, measurement, manpower, environment, and management. The purpose is not to produce an exhaustive list without evidence, but to develop hypotheses about which factors can create shifts, trends, cycles, or excess dispersion.

A useful distinction is:

• Common causes: effects arising from the ordinary system of materials, equipment, methods, environment, and management. They form the process’s current pattern of behaviour.
• Special causes: identifiable, unusual, or assignable influences that are not part of the process’s ordinary pattern.

The distinction is operational rather than metaphysical. A cause may be special for one process and common for another. For example, operator-to-operator variation may be special during a one-time training event but common if the work method routinely differs among shifts.

3. From requirements to CTQ characteristics

3.1 What makes a characteristic critical to quality?

A CTQ characteristic is a measurable property whose variation has important consequences for customer satisfaction, safety, compliance, process performance, or financial results. CTQs should be selected on the basis of impact and controllability, not simply because they are easy to measure.

Typical CTQ classes include:

• Continuous characteristics: length, mass, temperature, response time, concentration, voltage.
• Count characteristics: number of defects, errors, failures, or incidents.
• Binary or categorical characteristics: pass/fail, correct/incorrect, present/absent.
• Time-to-event characteristics: time until failure, complaint, recovery, or completion.
• Functional outcomes: yield, throughput, service level, or customer rating.

A unit may have several defects, so “defects” and “defective units” must not be treated as equivalent. A defective unit fails at least one requirement; defects are individual nonconformities. The choice affects the appropriate chart and the interpretation of performance.

3.2 CTQ deployment

CTQ selection can be structured through quality-function deployment, failure mode and effects analysis (FMEA), regulatory risk analysis, process capability studies, or customer-journey analysis. A practical prioritisation score may consider severity, occurrence, detectability, and strategic importance. Formal risk scores should not replace judgement, particularly when a low-frequency event has catastrophic consequences.

For every proposed CTQ, document:

3.3 Specifications are not control limits

Specification limits are externally or internally defined requirements. Control limits are calculated from process data and describe expected process behaviour under the chosen conditions. Specifications may be asymmetric, nonlinear, or absent; control limits are statistical boundaries used to detect evidence of a change.

A process can be stable but incapable of meeting specifications. Conversely, a process can be unstable even when every observed item meets specifications. Therefore, capability analysis should generally follow a credible stability analysis rather than substitute for it.

For a stable process with approximately normal output and lower and upper specification limits LSL and USL, common capability indices are:

Here, μ is the process mean and σ is the within-process standard deviation under the stated conditions. These indices assume meaningful specification limits, a stable process, and a standard-deviation estimate appropriate to the intended capability interpretation. C_p reflects potential capability if centred; C_pk also reflects displacement from the specification centre. They are not substitutes for an SPC design.

4. Measurement-system readiness

An SPC system is only as credible as its measurement system. Before interpreting process variation, evaluate whether observed differences represent product or process differences rather than measurement error.

Important properties include:

• Validity: does the method measure the intended characteristic?
• Resolution: can it distinguish changes relevant to decisions?
• Bias: is the average measurement offset from a reference value?
• Repeatability: how much variation occurs when the same appraiser measures the same item repeatedly?
• Reproducibility: how much variation occurs among appraisers, devices, or conditions?
• Stability: does measurement performance remain consistent over time?

For a continuous measurement system, a gauge repeatability and reproducibility study may partition observed variation into repeatability, reproducibility, and part-to-part components. The precise study design should reflect the instrument, operators, parts, and intended use. For attribute inspection, agreement studies are needed; high agreement among inspectors does not prove that their common judgement is correct.

Measurement-system improvement may involve calibration, fixture redesign, clearer operational definitions, automated data capture, operator training, or improved resolution. A poor measurement system should not be “corrected” by widening control limits. That merely reduces sensitivity to real process changes.

5. Sampling strategies

5.1 The sampling question

Sampling design answers four questions:

1. What units or events are eligible?
2. How are they selected?
3. When are they observed?
4. How many are included in each subgroup?

The objective is not always statistical representativeness in the survey-research sense. In SPC, the objective is to obtain information about process behaviour in a way that makes meaningful changes detectable while preserving the relationship between observations and their generating conditions.

5.2 Common sampling approaches

• Consecutive sampling: select successive units. This is often suitable for studying short-term within-run variation.
• Systematic sampling: select every kth unit or event. It is practical, but the interval should not coincide with a hidden periodic pattern.
• Stratified sampling: sample separately by machine, shift, product family, supplier, location, or other known source. This avoids masking differences.
• Random sampling: select units using a random mechanism when each eligible unit should have a known or comparable chance of selection.
• Cluster sampling: select groups such as batches or shifts. It is efficient but may estimate between-cluster variation rather than ordinary unit-to-unit variation.
• Risk-based sampling: allocate greater sampling effort to high-severity, high-uncertainty, or poorly observable conditions.
• Acceptance sampling: inspect a sample to decide whether to accept a lot. This is a distinct decision framework and should not be confused with ongoing SPC.

Sampling plans should state how exceptions, rework, missing records, and stopped processes are handled. If only successful transactions are recorded, the resulting chart may be biased by survivorship or selection effects.

5.3 Sampling frequency

Sampling frequency should be linked to process dynamics and risk. Relevant factors include:

• expected rate at which assignable causes can arise;
• time required for a shift to create harmful output;
• production or transaction volume;
• cost and destructiveness of measurement;
• time needed to investigate and contain a signal;
• customer or regulatory exposure;
• historical instability; and
• the detection capability of the selected chart.

A useful design principle is to sample often enough that a meaningful deterioration is detected before unacceptable exposure becomes large, while avoiding excessive measurement that creates cost and false alarms. Frequency may be event-based rather than clock-based: for example, one observation per batch, per setup, or per changeover. High-risk operations may require 100% automated monitoring, while low-risk stable processes may justify reduced sampling with periodic verification.

Sampling frequency should be reviewed after process changes, new equipment, supplier changes, repeated signals, or evidence that the chart detects changes too slowly. “One sample per shift” is not a universal standard; it is a decision that requires justification.

6. Rational subgroups

6.1 Definition and purpose

A rational subgroup is a set of observations collected so that variation within the subgroup represents the short-term or routine variation of interest, while differences between subgroups have a reasonable chance of revealing changes over time or across conditions.

The correct subgroup depends on the question. If the objective is to detect gradual drift during a production run, consecutive units may be grouped together. If the objective is to compare shifts, each subgroup may contain observations from one shift. If the objective is to detect machine-to-machine differences, observations should not be mixed across machines unless the combined process is explicitly the subject of study.

6.2 Within- and between-subgroup variation

For subgroup i of size n, observations are commonly represented as x_ij, where j indexes units within subgroup i. The subgroup mean is:

The subgroup range is:

These statistics are meaningful only when the subgrouping reflects the intended process conditions. Mixing different machines or products can inflate within-subgroup variation and conceal between-source differences. Conversely, creating subgroups from widely separated observations may make a changing process appear artificially stable within each group.

For an X̄–R chart with constant subgroup size n, commonly used limits are:

Here, X̄̄ is the average of subgroup means, R̄ is the average subgroup range, and A₂, D₃, and D₄ are constants determined by subgroup size and the chosen range-based estimation method. The constants are not universal across all chart types. For varying subgroup sizes, use limits and estimates appropriate to each size rather than applying a constant-size formula indiscriminately.

6.3 Subgroup size is a design decision

Larger subgroups estimate the subgroup mean more precisely but may delay detection, increase measurement cost, and combine observations across changing conditions. Smaller subgroups increase sampling opportunities but provide less information about within-subgroup dispersion. The design should be based on the change that matters operationally, not on a desire to maximise sample size.

When observations are naturally individual and autocorrelation is important, an individuals–moving-range chart may be considered. A moving range of order two is commonly defined as:

This approach assumes that the ordering and dependence structure are understood. Strong autocorrelation, seasonality, or nonstationary behaviour may require time-series methods or a redesigned sampling scheme rather than a routine individuals chart.

7. Choosing the chart after designing the data

Chart selection follows the characteristic and sampling structure. Examples include:

Control limits should be estimated using data representing the process conditions to which the chart will be applied. Normality is not required for every chart, and normality tests alone should not determine chart selection. For counts, binomial or Poisson assumptions may be relevant, but overdispersion, dependence, changing opportunity, and zero inflation may require alternative models.

8. Phase I and Phase II SPC

8.1 Phase I: retrospective analysis and stabilisation

Phase I uses historical or initial data to understand how the process behaved over a defined period. The objectives are to:

• identify obvious special causes;
• assess whether the process definition and stratification are sensible;
• estimate baseline centre and variation after appropriate investigation;
• determine whether the process is stable enough for routine monitoring; and
• establish a documented set of operating conditions.

Phase I is investigative. Analysts may revise subgrouping, separate product families, correct data errors, investigate signals, and recalculate limits after justified action. However, limits should not be repeatedly recalculated simply to hide signals. Every exclusion must have a documented process explanation, such as equipment failure or a known measurement error, rather than the fact that the point was inconvenient.

8.2 Phase II: prospective monitoring

Phase II begins when a rational baseline and monitoring plan have been established. New observations are compared with limits or decision rules derived from the baseline. The central question is: has the process changed from its established state?

Phase II requires:

• fixed operational definitions;
• a defined sampling schedule;
• control limits that are not casually altered;
• explicit rules for signals and out-of-control conditions;
• a reaction plan; and
• periodic review for process changes or model inadequacy.

Phase II limits are not specification limits. Nor should every out-of-control signal automatically trigger adjustment of the process. The appropriate response is to verify the signal, protect potentially affected output, investigate the process, remove or control the special cause where justified, and document the decision.

8.3 Signal interpretation

A point outside a control limit is one signal of special-cause variation. Other evidence can include a sustained run on one side of the centre line, a trend, cyclic behaviour, or unusually long-term changes in dispersion. The exact supplementary rules should be selected deliberately because adding many rules increases false-alarm probability.

Signal rules must be linked to action. A chart without a reaction plan is a passive display, not a functioning SPC system. The plan should identify who responds, what is checked first, how material or service cases are contained, when production may continue, and who has authority to stop or release the process.

9. Worked design example: an illustrative medical-device assembly process

Background

The following is a fictional illustrative case. A manufacturer assembles a disposable medical connector. A critical functional requirement is the force required to separate the connector after assembly. Too little force may create leakage or disconnection; too much force may make clinical use difficult.

Problem definition

The process includes component receipt, automated assembly, curing, visual inspection, and functional testing. Historical records combine three assembly machines and two connector models. Operators currently test one unit at the end of each shift. Complaints indicate occasional loose connections, but the existing data cannot identify when or where the problem arises.

Analysis and process design

The team maps the process and identifies machine, model, curing temperature, material lot, and operator as potential sources. FMEA ranks separation force as a high-severity CTQ. The team verifies the test fixture and conducts a measurement-system study. The fixture is found to have poor repeatability near the lower requirement; it is repaired and the test method is standardised.

The team then defines the CTQ operationally: separation force in newtons, measured after a specified curing time and at a specified test speed. The measurement is taken before visual inspection can remove marginal units. Data are stratified by machine and connector model because the assembly conditions differ.

Sampling and rational subgroups

During Phase I, the team collects five consecutive units from each machine-model combination at the start, middle, and end of selected production runs. This design allows assessment of short-term variation within a run and possible changes across time. The subgroup consists of consecutive units produced under the same machine, model, material lot, and setup. A single end-of-shift sample would not reveal within-shift drift.

After stabilisation, the Phase II plan uses one subgroup of three consecutive units per machine-model combination every two hours, with additional sampling after setup, material-lot change, curing interruption, or maintenance. Automated temperature data are monitored continuously because temperature can change rapidly and is inexpensive to record.

Phase I findings

The initial chart shows two distinct centres when machine data are combined. Separate charts reveal that Machine 2 has higher mean separation force and greater within-run dispersion. Investigation finds a worn assembly tool and inconsistent curing-temperature control. After repair and temperature-control adjustment, the team collects a new baseline. The revised data show stable behaviour within each machine-model stratum.

Phase II response plan

If a subgroup mean exceeds a control limit, the operator pauses release of affected output, verifies the measurement system, checks the most recent setup and temperature records, and notifies the process engineer. If the range chart signals, the team checks tooling, fixture alignment, and component seating. Product produced since the last confirmed in-control check is identified and evaluated according to the quality procedure. Control limits are not recalculated until a formal review confirms a sustained process change.

Outcome and learning points

The new system detects tool wear earlier, reduces dependence on end-of-shift inspection, and provides traceability to machine and model. The principal improvement did not come from selecting a more sophisticated chart. It came from defining the CTQ, correcting the measurement system, separating unlike processes, forming rational subgroups, and connecting chart signals to operational action.

10. Governance, ethics, and contemporary technology

SPC data can influence product release, worker evaluation, supplier status, and customer safety. Governance is therefore essential. Data definitions, timestamps, revisions, exclusions, and limit changes should be traceable. Analysts should not remove unfavourable data without a documented technical reason. If a process is regulated, electronic records and approvals must meet applicable quality-system and data-integrity requirements.

Automation and AI can support SPC through sensor integration, anomaly detection, image inspection, adaptive sampling, and predictive maintenance. However, an algorithmic alert is not automatically a special cause. Models may learn from biased historical data, confuse product mix with process change, or generate excessive alarms. AI-supported monitoring should therefore include validated data pipelines, human review, model-performance checks, version control, cybersecurity, and clear accountability.

Contemporary SPC increasingly combines traditional control charts with multivariate monitoring, change-point detection, time-series analysis, and streaming data. These methods are valuable when characteristics are correlated or measurements are frequent. They also increase modelling assumptions and governance requirements. A complex method is justified only when it improves decisions over a transparent, simpler alternative.

11. Implementation framework and common failure modes

A practical implementation sequence is:

1. Define the business, customer, safety, or compliance problem.
2. Map the process and identify controllable sources of variation.
3. Select and operationally define CTQs.
4. Confirm measurement-system adequacy.
5. Select the sampling frame, subgroup structure, and frequency.
6. Choose a chart or analytical model consistent with the data.
7. Conduct Phase I analysis and investigate special causes.
8. Freeze and document the Phase II baseline.
9. Establish signal rules, reaction plans, responsibilities, and escalation.
10. Review performance and redesign the system when the process or risk changes.

Common failure modes include:

• charting data before defining the process;
• mixing products, machines, or shifts that should be separated;
• using specification limits as control limits;
• treating every point beyond a limit as proof of a particular cause;
• recalculating limits after every signal;
• sampling too infrequently to protect customers;
• measuring a characteristic with an inadequate gauge;
• using a control chart when the data are strongly autocorrelated without investigation;
• collecting data that no one is authorised or prepared to act upon; and
• evaluating employees by isolated chart signals, which can encourage concealment or tampering.

Chapter Summary

Designing an SPC system is a process-engineering and management task, not a charting exercise. The design begins with a clear process boundary, customer and regulatory requirements, and a map of inputs, activities, outputs, interfaces, and sources of variation. CTQs must be operationally defined and prioritised according to their consequences and controllability. Measurement-system adequacy is a prerequisite for interpreting process variation.

Sampling strategy determines what the data can reveal. Rational subgroups should represent the variation of interest within comparable operating conditions while allowing meaningful changes between subgroups to be detected. Sampling frequency should reflect process dynamics, risk, exposure, cost, and response time. Chart selection follows the characteristic and sampling structure rather than preceding them.

Phase I is a retrospective period of learning, stratification, investigation, and baseline establishment. Phase II is prospective monitoring against an established process state. Both phases require disciplined data governance and explicit reaction plans. Effective SPC connects statistical evidence to timely, ethical, and technically appropriate action.

Key Terms

Acceptance sampling: Sampling used to decide whether to accept or reject a lot.

Assignable cause: Another term for a special cause that can be identified and investigated.

Common cause: Variation arising from the ordinary process system.

Control limit: A statistically calculated boundary used to detect evidence of process change.

Critical-to-quality characteristic: A measurable characteristic with important customer, safety, regulatory, or business consequences.

Defect: An individual nonconformity or failure to meet a requirement.

Defective unit: A unit that fails at least one specified requirement.

Measurement-system analysis: Evaluation of the adequacy, accuracy, precision, and stability of a measurement process.

Phase I SPC: Retrospective analysis used to understand, stabilise, and establish a process baseline.

Phase II SPC: Prospective monitoring of new observations against an established baseline.

Process capability: The ability of a stable process to meet specification requirements.

Process map: A structured representation of process steps, inputs, outputs, decisions, and interfaces.

Rational subgroup: A group of observations selected to represent a defined source of routine variation.

Reaction plan: Documented actions and responsibilities for responding to SPC signals.

Sampling frequency: The rate or event rule at which observations are collected.

Special cause: An unusual or identifiable influence that is not part of routine process variation.

Specification limit: A requirement boundary established by design, customer, regulation, or policy.

Stratification: Separating data by meaningful sources such as machine, shift, product, or supplier.

Review Questions

Short Answer Questions

1. Why must process mapping precede control-chart selection?
2. Distinguish a CTQ characteristic from a specification limit.
3. What is the purpose of a rational subgroup?
4. State two differences between Phase I and Phase II SPC.
5. Why should measurement-system adequacy be assessed before interpreting control-chart signals?

Long Answer Questions

1. Explain how customer requirements can be translated into CTQs, operational definitions, measurement methods, and reaction plans.
2. Compare consecutive, systematic, stratified, random, cluster, and risk-based sampling in SPC applications.
3. Explain how subgroup size and subgroup composition affect estimates of within-process variation.
4. Describe a complete Phase I-to-Phase II SPC implementation, including data governance and signal response.
5. Critically evaluate the statement: “A stable process is necessarily a capable process.”

Analytical / Application Questions

1. A service centre combines response-time data from three channels with different staffing patterns. Design a process map, stratification scheme, rational subgroup structure, and sampling frequency, and justify each decision.
2. A production process has stable control-chart behaviour but regularly exceeds its upper specification limit. Diagnose the likely implications and propose an improvement plan without changing control limits merely to remove the problem.
3. A chart produces frequent signals after a new automated sensor is installed. Develop an investigation sequence that distinguishes process change, measurement-system change, autocorrelation, sampling error, and a genuinely unstable process.

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 detects evidence of process change, while a specification limit defines an acceptance requirement.

C. Both are calculated from the same historical data and have identical purposes.

D. A specification limit is used only during Phase I, while a control limit is used only during inspection.

Correct Answer: B. A control limit detects evidence of process change, while a specification limit defines an acceptance requirement.

Question 2

What is the primary purpose of a rational subgroup?

A. To maximise the number of observations collected regardless of process conditions.

B. To ensure that every product family is combined in one chart.

C. To represent a defined source of routine variation while allowing meaningful changes to be detected between subgroups.

D. To replace the need for a measurement-system study.

Correct Answer: C. To represent a defined source of routine variation while allowing meaningful changes to be detected between subgroups.

Question 3

Which characteristic is most clearly a CTQ for a medical connector?

A. The colour of the operator’s workstation

B. The separation force affecting connection safety and usability

C. The number of charts displayed in the quality office

D. The age of the production schedule template

Correct Answer: B. The separation force affecting connection safety and usability

Question 4

In Phase I SPC, which activity is appropriate?

A. Ignoring all historical signals to avoid recalculating limits

B. Investigating special causes and establishing a justified baseline

C. Using specification limits as control limits

D. Changing limits after every inconvenient observation without investigation

Correct Answer: B. Investigating special causes and establishing a justified baseline

Question 5

If a process produces one defect opportunity per unit but the number of opportunities varies substantially among units, which chart family is generally more appropriate than a c chart?

A. u chart

B. Individuals chart

C. R chart

D. np chart

Correct Answer: A. u chart

Question 6

For a subgroup of observations x₁, x₂, and x₃, which expression gives the subgroup mean?

A. x₁ + x₂ + x₃

B. (x₁ − x₂ − x₃) ÷ 3

C. (x₁ + x₂ + x₃) ÷ 3

D. max(x₁,x₂,x₃) − min(x₁,x₂,x₃)

Correct Answer: C. (x₁ + x₂ + x₃) ÷ 3

Question 7

Which sampling design is most directly intended to prevent machine or shift differences from being hidden in one combined distribution?

A. Stratified sampling

B. Convenience sampling only

C. Unrecorded sampling

D. Post hoc deletion of unusual values

Correct Answer: A. Stratified sampling

Question 8

A process is statistically stable but has a capability index below the organisation’s requirement. What is the most appropriate interpretation?

A. The process is stable but its natural variation or centring is inadequate for the specifications.

B. The control limits should be replaced with specification limits.

C. The process is necessarily out of control.

D. The measurement system must automatically be invalid.

Correct Answer: A. The process is stable but its natural variation or centring is inadequate for the specifications.

Question 9

Which factor is least appropriate as the sole basis for setting sampling frequency?

A. Time required for harmful deterioration to occur

B. Risk and customer exposure

C. Cost and destructiveness of measurement

D. A universal rule that every process must be sampled once per shift

Correct Answer: D. A universal rule that every process must be sampled once per shift

Question 10

What is a suitable first response to a Phase II control-chart signal?

A. Automatically recalculate the limits using the signalled point

B. Verify the signal, contain potentially affected output, and investigate the process

C. Assume the operator is responsible and issue discipline immediately

D. Delete the observation so that the chart remains stable

Correct Answer: B. Verify the signal, contain potentially affected output, and investigate the process