Statistical Process Control

Douglas M. Stewart, Ph.D.

The Anderson Schools of Management

The University of New Mexico

Quality Control (QC)

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

ImportanceDaily management of processesPrerequisite to longer-term improvements

Designing 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

Example 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

5

Inspection/Testing Points

Receiving inspectionIn-process inspectionFinal inspection

6

Receiving Inspection

Spot check procedures100 percent inspectionAcceptance sampling

7

Acceptance Sampling

Lot received for inspection

Sample selected and analyzed

Results compared with acceptance criteria

Accept the lot

Send to production or to customer

Reject the lot

Decide on disposition

Pros and Cons of Acceptance Sampling

Arguments for: Provides an assessment

of risk Inexpensive and suited

for destructive testing Requires less time than

other approaches Requires less handling Reduces inspector

fatigue

Arguments against: Does not make sense for

stable processes Only detects poor quality;

does not help to prevent it Is non-value-added Does 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 itemC2 = cost of repair p = 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 Instruments

Variable gaugesFixed gaugesCoordinate measuring machineVision systems

Examples 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 (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

Quantify and evaluate the capability of a measurement systemSelect 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)

all of range average

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R&R Constants

Number of Trials

2 3 4 5

K1 4.56 3.05 2.50 2.21

Number of Operators

2 3 4 5

K2 3.65 2.70 2.30 2.08

R&R Evaluation

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

R&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.

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Calibration

Calibration - comparing a measurement device or system to one having a known relationship to national standards

Traceability to national standards maintained by NIST, National Institute of Standards and Technology

24

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 appropriate

SPC 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 control

Monitor a process and signal when it goes out of control

Determine process capability

28

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 Charts

1. Prepare Choose measurement Determine how to collect data, sample size,

and frequency of sampling Set up an initial control chart

2. Collect Data Record data Calculate appropriate statistics Plot statistics on chart

Next Steps

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

4. Analyze and interpret results Determine if in control Eliminate out-of-control points Recompute control limits as

necessary

36

Typical Out-of-Control PatternsPoint outside control limitsSudden shift in process averageCyclesTrendsHugging the center lineHugging the control limitsInstability

Shift in Process Average

Identifying Potential Shifts

Cycles

Trend

Final Steps

5. Use as a problem-solving tool Continue to collect and plot data Take corrective action when

necessary

6. Compute process capability

Process Capability

Capability Indices

mmmmmm

C

LTLUTLC

p

p

0868.0 25.75.10 ision specificatPart :Example

minimum) often the more (1.5 capable as defined is 1 if6

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Tolerance

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44

Capability Versus Control

Control

Capability

Capable

Not Capable

In Control Out of Control

IDEAL

Process Capability Calculations

Excel Template

Special Variables Control Charts

x-bar and s chartsx-chart for individuals

Charts for AttributesFraction nonconforming (p-chart)

Fixed sample sizeVariable sample size

np-chart for number nonconforming

Charts for defectsc-chartu-chart

64

Control Chart Selection

Quality Characteristicvariable attribute

n>1?

n>=10 or computer?

x and MRno

yes

x and s

x and Rno

yes

defective defect

constant sample size?

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

nominal value

Green Zone

Yellow Zones

RedZone

RedZone

LTL UTL

68

SPC Implementation Requirements

Top management commitmentProject championInitial workable projectEmployee education and trainingAccurate measurement system