04 statistical process control

8/8/2019 04 Statistical Process Control

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Statistical Process Control

Douglas M. Stewart, Ph.D.

The Anderson Schools of ManagementThe University of New Mexico


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Quality Control (QC) Control the activity of ensuring

conformance to requirements and taking

corrective action when necessary to

correct problems

Importance

Daily management of processes

Prerequisite to longer-term improvements


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Designing the QC System Quality Policy andQuality Manual

Contract management, design control and

purchasing Process control, inspection and testing

Corrective action and continual improvement

Controlling inspection, measuring and test

equipment (metrology, measurement system analysisand calibration)

Records, documentation and audits


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Example ofQC: HACCP System

1. Hazard analysis

2. Critical control points

3. Preventive measures with critical limits for

each control point4. Procedures to monitor the critical control

points

5. Corrective actions when critical limits are

not met6. Verification procedures

7. Effective record keeping and documentation


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Inspection/Testing Points

Receiving inspection

In-process inspectionFinal inspection


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Receiving Inspection

Spot check procedures

100 percent inspectionAcceptance sampling


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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


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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 andvalue-added

How much to inspect?

All, nothing, or a sample


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Economic Model

C1= cost of inspection and removal of

nonconforming item

C2 = 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


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Human Factors in Inspection

complexity

defect rate

repeated inspections

inspection rate

Inspection should never be a means of assuringquality. The purpose of inspection should be to gather

information to understand and improve the processes

that produce products and services.


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Gauges and

Measuring Instruments

Variable gauges

Fixed gauges Coordinate measuring machine

Vision systems


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Examples of Gauges


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Metrology - Science of Measurement

Accuracy - closeness of agreement

between an observed value and a

standard

Precision - closeness of agreement

between randomly selected individual

measurements


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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


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Repeatability and

Reproducibility Studies Quantify and evaluate the capability of a

measurement system

Select m operators and n parts

Calibrate the measuring instrument

Randomly measure each part by each

operator for r trials Compute key statistics to quantify

repeatability and reproducibility


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Reliability and Reproducibility

Studies(2)

allorangeaverage

operatoreachorrangeaverage

operatoreachorparteachorrange)(min)(maxR

averagesoperatoro(range)di erence)(min)(max

operatoreachoraverage

r)to1rom(kTrials

inn)to1rom(jarts

onm)to1rom(iOperators

bymade( )teasuremen

ij

m

R

R

n

R

R

MM

xxx

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M

x

i

i

j

ij

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ijkk

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R&RConstants

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


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R&REvaluation

Under10% error - OK

10-30% error - may be OK

over 30% error - unacceptable


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R&RExample

R&R Study is to be conducted on a gauge being used tomeasure the thickness of a gasket having specificationof0.50 to 1.00 mm. We have three operators, each

taking measurement on 10 parts in 2 separate trials.

017.0

034.0

037.0

829.0

774.0

830.0

3

2

1

3

2

1

!

!

!

!

!

!

R

R

R

x

x

x


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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


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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 appropriate

SPC relies on control charts


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Common

Causes

Special

Causes


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Histograms do nottake into account

changes over time.

Control charts

can tell us

when a process

changes


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Control Chart Applications

Establish state of statistical

controlMonitor a process and signal

when it goes out of control

Determine process capability


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Commonly Used Control Charts

Variables data

x-bar and R-charts

x-bar and s-charts Charts for individuals (x-charts)

Attribute data

For defectives (p-chart, np-chart)

For defects (c-chart, u-chart)


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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


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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


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Typical ut-of-Control Patterns Point outside control limits

Sudden shift in process average

Cycles

Trends

Hugging the center line

Hugging the control limits

Instability


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Shift in Process Average


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Identifying Potential Shifts


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Cycles


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Trend


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Final Steps5. Use as a problem-solving tool

Continue to collect and plot data Take corrective action when

necessary

6. Compute process capability


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Process Capability Capability Indices

mmmmmm

C

LTLUTLC

p

p

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minimum)often themore(1.5capableasdefinedis1if

6

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W

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y

!pC


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TargettheisT

12

2W

Q T

CC

p

pm

!

10.7171mmatcenteredisprocessassumebutabove,assame:Example

2where1

,min

3

3

Tolerance

TKKCC

CCC

LTLC

UTLC

ppk

puplpk

pl

pu

!!

!

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!

Q

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Capability ersus Control

Control

Capability

Capable

Not Capable

In Control Out ofControl

IDEAL


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Process Capability Calculations


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Excel Template


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Special ariables Control Charts

x-bar and s charts

x-chart for individuals


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Charts for Attributes

Fraction nonconforming (p-chart)Fixed sample size

Variable sample size

np-chart for number nonconforming

Charts for defects

c-chart

u-chart


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Control Chart Selection

Quality Characteristic

variable attribute

n>1?

n>=10 or

computer?

x and MR

no

yes

x and s

x and Rno

yes

defective defect

constant

sample

size?

p-chart with

variable sample

size

no

p or

np

yes constant

sampling

unit?

c u

yes no


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Control Chart Design Issues

Basis for sampling

Sample size

Frequency of sampling

Location of control limits


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Pre-Control

nominal

value

Green Zone

Yellow Zones

Red

Zone

Red

Zone

LTL UTL


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SPC Implementation

Requirements Top management commitment

Project champion

Initial workable project

Employee education and training

Accurate measurement system

04 statistical process control

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