Statistical Process Control(SPC)

Quality Control (QC)Quality Control (QC)

Control – the activity of ensuring conformance to requirements and taking corrective action when necessary to correct problemsImportance

Daily management of processesPrerequisite to longer-term improvements

Control – the activity of ensuring conformance to requirements and taking corrective action when necessary to correct problemsImportance

Daily management of processesPrerequisite to longer-term improvements

Designing the QC SystemDesigning the QC System

Quality Policy and Quality ManualContract management, design control and purchasingProcess control, inspection and testingCorrective action and continual improvementControlling inspection, measuring and test equipment (metrology, measurement system analysis and calibration)Records, documentation and audits

Quality Policy and Quality ManualContract management, design control and purchasingProcess control, inspection and testingCorrective action and continual improvementControlling inspection, measuring and test equipment (metrology, measurement system analysis and calibration)Records, documentation and audits

Example of QC: HACCP SystemExample of QC: HACCP System1. Hazard analysis2. Critical control points3. Preventive measures with critical

limits for each control point4. Procedures to monitor the critical

control points5. Corrective actions when critical

limits are not met6. Verification procedures7. Effective record keeping and

documentation

1. Hazard analysis2. Critical control points3. Preventive measures with critical

limits for each control point4. Procedures to monitor the critical

control points5. Corrective actions when critical

limits are not met6. Verification procedures7. Effective record keeping and

documentation

5

Inspection/Testing Points

Receiving inspectionIn-process inspectionFinal inspection

6

Receiving Inspection

Spot check procedures100 percent inspectionAcceptance sampling

7

Acceptance SamplingLot received for inspection

Sample selected and analyzed

Results compared with acceptance criteria

Accept the lot

Send to productionor to customer

Reject the lot

Decide on disposition

Pros and Cons of Acceptance Sampling

Pros and Cons of Acceptance SamplingArguments for:

Provides an assessment of riskInexpensive and suited for destructive testingRequires less time than other approachesRequires less handlingReduces inspector fatigue

Arguments for:Provides an assessment of riskInexpensive and suited for destructive testingRequires less time than other approachesRequires less handlingReduces inspector fatigue

Arguments against:Does not make sense for stable processesOnly detects poor quality; does not help to prevent itIs non-value-addedDoes not help suppliers improve

Arguments against:Does not make sense for stable processesOnly detects poor quality; does not help to prevent itIs non-value-addedDoes not help suppliers improve

9

In-Process Inspection

What to inspect?Key quality characteristics that are related to cost or quality (customer requirements)

Where to inspect?Key processes, especially high-cost and value-added

How much to inspect?All, nothing, or a sample

10

Economic Model

C1 = cost of inspection and removal of nonconforming item

C2 = cost of repairp = true fraction nonconforming

Breakeven Analysis: p*C2 = C1

If p > C1 / C2 , use 100% inspection

If p < C1 / C2 , do nothing

Human Factors in Inspection

complexitydefect raterepeated inspectionsinspection rate

Inspection should never be a means of assuring quality. The purpose of inspection should be to gather information to understand and improve the processes that produce products and services.

12

Gauges and Measuring InstrumentsVariable gaugesFixed gaugesCoordinate measuring machineVision systems

Examples of GaugesExamples of Gauges

Metrology - Science of Measurement

Accuracy - closeness of agreement between an observed value and a standardPrecision - closeness of agreement between randomly selected individual measurements

Repeatability and Reproducibility

Repeatability and Reproducibility

Repeatability (equipment variation) – variation in multiple measurements by an individual using the same instrument. Reproducibility (operator variation) -variation in the same measuring instrument used by different individuals

Repeatability (equipment variation) – variation in multiple measurements by an individual using the same instrument. Reproducibility (operator variation) -variation in the same measuring instrument used by different individuals

Repeatability and Reproducibility Studies

Repeatability and Reproducibility Studies

Quantify and evaluate the capability of a measurement system

Select m operators and n partsCalibrate the measuring instrumentRandomly measure each part by each operator for r trialsCompute key statistics to quantify repeatability and reproducibility

Quantify and evaluate the capability of a measurement system

Select m operators and n partsCalibrate the measuring instrumentRandomly measure each part by each operator for r trialsCompute key statistics to quantify repeatability and reproducibility

Reliability and Reproducibility Studies(2)

Reliability and Reproducibility Studies(2)

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Reliability and Reproducibility Studies(3)

Reliability and Reproducibility Studies(3)

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R&R EvaluationR&R Evaluation

Under 10% error - OK10-30% error - may be OKover 30% error - unacceptable

Under 10% error - OK10-30% error - may be OKover 30% error - unacceptable

R&R ExampleR&R Example

R&R Study is to be conducted on a gauge being used to measure the thickness of a gasket having specification of 0.50 to 1.00 mm. We have three operators, each taking measurement on 10 parts in 2 separate trials.

R&R Study is to be conducted on a gauge being used to measure the thickness of a gasket having specification of 0.50 to 1.00 mm. We have three operators, each taking measurement on 10 parts in 2 separate trials.

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CalibrationCalibration

Calibration - comparing a measurement device or system to one having a known relationship to national standardsTraceability to national standards maintained by NIST, National Institute of Standards and Technology

Calibration - comparing a measurement device or system to one having a known relationship to national standardsTraceability to national standards maintained by NIST, National Institute of Standards and Technology

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Statistical Process Control (SPC)

A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriateSPC relies on control charts

Common Causes

Special Causes

Histograms do not take into account changes over time.

Control charts can tell us when a process changes

27

Control Chart Applications

Establish state of statistical controlMonitor a process and signal when it goes out of controlDetermine process capability

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Commonly Used Control Charts

Variables datax-bar and R-chartsx-bar and s-chartsCharts for individuals (x-charts)

Attribute dataFor “defectives” (p-chart, np-chart)For “defects” (c-chart, u-chart)

Developing Control ChartsDeveloping Control Charts

1. PrepareChoose measurementDetermine how to collect data, sample size, and frequency of samplingSet up an initial control chart

2. Collect DataRecord dataCalculate appropriate statisticsPlot statistics on chart

1. PrepareChoose measurementDetermine how to collect data, sample size, and frequency of samplingSet up an initial control chart

2. Collect DataRecord dataCalculate appropriate statisticsPlot statistics on chart

Next StepsNext Steps

3. Determine trial control limitsCenter line (process average)Compute UCL, LCL

4. Analyze and interpret resultsDetermine if in controlEliminate out-of-control pointsRecompute control limits as necessary

3. Determine trial control limitsCenter line (process average)Compute UCL, LCL

4. Analyze and interpret resultsDetermine if in controlEliminate out-of-control pointsRecompute control limits as necessary

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Typical Out-of-Control Patterns

Point outside control limitsSudden shift in process averageCyclesTrendsHugging the center lineHugging the control limitsInstability

Shift in Process AverageShift in Process Average

Identifying Potential ShiftsIdentifying Potential Shifts

CyclesCycles

TrendTrend

Final StepsFinal Steps

5. Use as a problem-solving tool

Continue to collect and plot dataTake corrective action when necessary

6. Compute process capability

5. Use as a problem-solving tool

Continue to collect and plot dataTake corrective action when necessary

6. Compute process capability

Process CapabilityProcess Capability

Capability IndicesCapability Indices

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Process Capability (2)Process Capability (2)

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Capability Versus Control

Control

Capability

Capable

Not Capable

In Control Out of Control

IDEAL

Process Capability Calculations

Process Capability Calculations

Excel Template Excel Template

Special Variables Control ChartsSpecial Variables Control Charts

x-bar and s chartsx-chart for individualsx-bar and s chartsx-chart for individuals

Charts for AttributesCharts for AttributesFraction nonconforming (p-chart)

Fixed sample sizeVariable sample size

np-chart for number nonconforming

Charts for defectsc-chartu-chart

Fraction nonconforming (p-chart)Fixed sample sizeVariable sample size

np-chart for number nonconforming

Charts for defectsc-chartu-chart

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Control Chart SelectionQuality Characteristic

variable attribute

n>1?

n>=10 or computer?

x and MRno

yes

x and s

x and Rno

yes

defective defect

constantsamplesize?

p-chart withvariable samplesize

no

p ornp

yes constantsampling

unit?

c u

yes no

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Control Chart Design Issues

Basis for samplingSample sizeFrequency of samplingLocation of control limits

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Pre-Control

nominalvalue

Green Zone

Yellow Zones

RedZone

RedZone

LTL UTL

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SPC Implementation Requirements

Top management commitmentProject championInitial workable projectEmployee education and trainingAccurate measurement system

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