Section XI, Control Concepts

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Section XI, Control

Concepts

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What is SPC?

Description: Involves the use of statistical signals to identify sources of variation, to maintain or improve performance to a higher quality level, typically through the use of control charts.

Process ControlStatistical

“Quality control by statistical methods is now so extensively applied in all lines of industry, and in all sections of the United States, that everyone who is interested in manufacturing should also have a definite interest in the methods.”

-Control Charts, E.S. Smith - 1947

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Statistical control - shows if the inherent variability of a process is being caused by common causes of variation, as opposed to assignable causes.

Why only common cause variation?

Assignable Cause?

Assignable Cause?

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1. Minimize cost by making economical decisions

2. Attain a consistent process or improve a process

3. Identify when a process has changed

4. Allow everyone to contribute to process improvement

Goals of SPC

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A control chart is simply a distribution of values, turned 90 degrees on its side...

How distributions relate to control charts

Distribution of values

This gives the advantage of seeing when an event occurs. It is highly recommended to use a histogram and control chart together.

…and stretched out over time.

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Warning indicators a.k.a Natural Process Limits (NPL) Usually drawn on the chart at +3

(UCL) and -3 (LCL) from the process average.

Defines the process boundaries of your measured subgroups

Signals you if your process is operating in a state of statistical control, or if it is out of control

Control limits

UNPL - Upper Natural Process LimitUCL - Upper Control Limit

LNPL - Lower Natural Process LimitLCL - Lower Control Limit

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Control chart example

Is there special cause variation present? Does it look normal?

Is there a pattern?Is the process in control?

When do I make a change to the process?

Remember Walter Shewhart? He is credited with the control chart. We will refer to

these as the Shewhart Methods.

I n d i v i d u a l s C h a r t

U C L = 0 . 3 8 6 4

L C L = - 0 . 0 8 1 4

C E N = 0 . 1 5 2 5

- 0 . 2- 0 . 1

00 . 10 . 20 . 30 . 40 . 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0

M o v i n g R C h a r t

U C L = 0 . 2 8 7 2 7

L C L = 0 . 0

C E N = 0 . 0 8 7 9 3

- 0 .1

- 0 . 0 5

00 . 0 5

0 . 1

0 . 1 5

0 . 20 . 2 5

0 . 3

0 . 3 5

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 3 0

Is measurement variation having a big effect?

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Control Charts vs. Histograms

0

1

2

3

4

5

6

7

8

18.0 to <= 18.8 18.8 to <= 19.6 19.6 to <= 20.4 20.4 to <= 21.2 21.2 to <= 22.0

# O

bser

vatio

ns

Weekly Mileage

Histogram

15

16

17

18

19

20

21

22

23

24

25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Weeks

Gas

Mile

age

Histogram of gas mileage data

Control chart based on gas mileage

data

Same data shown using different tools

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1. Analyze where SPC should be done.

2. Decrease any obvious variability3. Verify Gage R&R is acceptable4. Create sampling plan with rational

subgroups5. Create control chart – allow only

common cause variability6. Run the process and verify control7. Calculate process capability8. Monitor process or improve if

necessary9. Pre-control10. Continue to monitor or improve

How to apply SPC to a process

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You always need to take random samples.

1. At random times2. At regular intervals

◦ Time based◦ Quantity based

3. Use “Rational Subgroups”◦ Small variation within groups◦ Large variation between groups

(sources of variation that occur over time)

When do I get the data?

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Let’s remember the assumptions: normal, homogeneous, need rational subgroups1. Typical Shewhart methods will

state rational subgroups of 4, 5, or 6 if you have a lot of data recorded periodically, or 100% for small sample sets

2. Based on process capability

How much data do I need?

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Control chart decision tree

Mea

sure

men

ts

Counts

Median, RangeAverage, Range

Average, sigma

Run chart

IX control chart

np control chart

p control chart

c chart

u chart

n = 2 to 9

n = 10 or more

n = 1non-normal data

normal data

n fixed

n varies

n fixed

n varies

Count pieces

or units

Count occurences

Varia

bles

Attributes

Mea

sure

men

ts

Counts

Median, RangeAverage, Range

Average, sigma

Run chart

IX control chart

np control chart

p control chart

c chart

u chart

n = 2 to 9

n = 10 or more


normal data

n fixed

n varies

n fixed

n varies

Count pieces

or units

Count occurences

Varia

bles

Attribu

Mea

sure

men

ts

Counts

Average, Range

Average, sigma

Run chart

IX control chart

np control chart

p control chart

c chart

u chart

n = 2 to 9

n = 10 or more


normal data

n fixed

n varies

n fixed

n varies

Count pieces

or units

Count occurences

Varia

bles

Attributes

Variable: data provides the most information

Attribute: Needs a lot of data

Control chart – The basic tool of SPC

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1. Select a process measurement2. Stabilize process and decrease

obvious variability3. Check the gages (10:1, GRR)4. Make a sample plan5. Setup the charts and process log6. Setup the histogram7. Take the samples and chart the

points8. Calculate the control limits and

analyze for control9. Calculate the capability and

analyze for capability10. Monitor the process11. Continuous Improvement

11 step procedure for Average and Range control charts

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Average and Range Chart exercise

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Pronounced “individual x and moving range”

The most common chart used with limited data

Each point on the chart represents an individual value

Used when subgroup samples need to be 1

Works well with processes that have trends that develop and disappear quickly

What is an IX and MR chart?

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points – at least 10 measurements before calculations

8. Calculate the control limits and analyze for control - histogram

9. Calculate the capability and analyze for capability

10. Monitor the process ( )11. Continuous Improvement

11 step procedure for IX-MR control charts

andRx

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How to calculate control limits

For the moving range control chart:

For the individual control chart:

RMDLCLRMDUCL

LimitsControl

nMR

RrangeAverage

MR

MR

3

4

M

RMExLCLRMExUCL

LimitsControl

nx

xx

Average

x

x

2

2

estimate s by UCL-LCL 6

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The data below was collected as part of a development process

The tolerance is .655 to .645

IX & MR exercise data

0.6480.6460.6490.6500.6480.6510.6500.6490.6460.652

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1020

1525

3530

0

RUCLXUCL LCL

PART

#

DATE

FEAT

URE

INDI

VIDU

ALS

X &

MOV

ING

RANG

E CH

ART

OPE

RATO

R

OP.

#

ORD

ER #

MAC

H.

SPEE

D

MAT

.

FEED

TOO

L / W

HEEL

TYPE

RUN

CHAR

T

CONT

ROL

CHAR

T

CPK

CR

Comments Section

S/N

or P

air #

Individuals X Chart Moving Range Chart

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points*8. Calculate the control limits and

analyze for control*9. Calculate the capability and

analyze for capability*10. Monitor the process11. Continuous Improvement

11 step procedure for p control charts

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7. Chart the points◦ Sets scales for control chart◦ Calculate each subgroup’s

proportion nonconforming◦ Plot the proportion

nonconforming on the chart8. Calculate control limits and

analyze for control◦ Plot your control limits

p chart control limits

npppUCLp

)1(3

npppLCLp

)1(3

You can use these equations – but it’s better to let the computer do it.

nnp

p

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9. Calculate the capability and analyze for capability

◦ Capability is based on average defective

◦ Is UCL or LCL within your goal value? If UCL > USL or LCL < LSL then

Cpk<1 If UCL < USL or LCL > LSL then

Cpk>1

p chart control limits

nnp

p

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This data represents the number of errors found in purchase orders over a 30 week period.

p chart example

1. Complete a p chart.

2. What can you tell from the data?

3. Complete a np chart.

4. What can you tell from the data?

5. How are these charts different?

# of P.O's ErrorsWeek 1 54 7Week 2 34 5Week 3 54 6Week 4 47 9Week 5 67 7Week 6 54 6Week 7 39 13Week 8 36 2Week 9 46 15Week 10 56 11Week 11 55 12Week 12 47 9Week 13 39 6Week 14 60 8Week 15 48 4Week 16 43 14Week 17 47 5Week 18 52 9Week 19 57 5Week 20 43 4Week 21 49 6Week 22 67 3Week 23 55 2Week 24 45 1Week 25 49 2Week 26 67 3Week 27 56 4Week 28 45 0Week 29 55 1Week 30 67 0

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PART

#FE

ATUR

E

ATTR

IBUT

E CO

NTRO

L CH

ART

Order # & DateOP

ERAT

ION

CHAR

T TY

PE:

P (

Perc

ent D

efec

tive)

Sub

Grou

p #

Sam

ple

Size

No. o

fDe

fect

ives

Prop

ortio

nDe

fect

ive

UCL

LCL

Proportion Defective Units

.0.10

.20

.30

.40

.50

.60

110

98

76

54

32

1116

1514

1312

2322

2120

1918

1730

2928

2726

2524

3635

3433

3231

37

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Normal Distribution50%50%

-1-2-3 +1 +2 +30

± .68261

± .9973 3

± .95462

z value = distance from the center measured in standard deviations

ZonesA B C C B A

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The process creating the data on the control chart is operating under statistical control.

Produces a graphic that will have a high center, and sloping sides.

The points tend to cluster around the center of the chart, show random variation, with only a few points spreading out toward the control limits.

Points look random – good but not too good ◦ Here is an example of a process running

in statistical control:

Normal Patterns

Normal Pattern.4005

.3985

.3990

.3995

.4000

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Data that fluctuates excessively and fails to center itself around the centerline is characteristic of assignable or non-normal variation.

Several of these patterns have been classified. ◦ aka “The Western Electric Rules”

The next few pages describe the most common patterns seen in processes.

Not necessarily a bad thing.◦ Heading in right direction◦ Result of improvement

Non-normal Patterns

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A random part located outside of the control limits (1 point outside of zone A)

Occurs for a number of reasons Any reason requires investigation before

continuing to run the job.

Reasons to occur: ◦ An incorrect machine adjustment that is

immediately noticed and fixed◦ Errors in measurement or plotting◦ A cutting tool that “caught a chip”◦ May be normal variation

Random Parts Out of Control – Freaks (Rule 1)

Random Patterns.1254

.1246

.1248

.1250

.1252

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Occurs when the points occur in clusters

Can be done visually Can be done statistically (2 of

3 points in zone A or beyond – 4 of 5 points in zone B or beyond)

Grouping can be caused by: ◦ Differences in setups◦ Tools moving◦ Method problems

Grouping (Rule 2 and 3)

Grouping.7510

.7490

.7495

.

.7505

.7500

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Set of seven or more consecutive points that are all on one side of the center line indicating the center has changed (8 or more points in zone C or beyond, all on one side of the center line)

Usually temporary / sudden A sudden shift in the level of parts shown

on a chart can be good or bad◦ Good: if the shift is bringing the parts back to

split limit◦ Bad; if the shift is taking the parts away from

split limit Sudden shifts can be caused by:

◦ A change of material, new operator or inspector, an offset change, two or more machines/suppliers on one chart

Sudden Shift in Level – Shifts(Rule 4)

Sudden Shift in Level.0950

.0930

.0935

.0940

.0945

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Defined as consecutive points on a control chart that are steadily increasing or decreasing in value (6 or more consecutive points that either increase or decrease in value – also, 10 out of 11 consecutive points that either increase or decrease in value )

Usually gradual Trends can be caused by:

◦ Air, coolant, or part temperatures that are steadily increasing or decreasing.

◦ Tool wear that allows a part to steadily increase or decrease in size

◦ A fixture that is constantly wearing, causing the parts to steadily increase or decrease in size.

◦ Operator fatigue

Trends – Runs (Rule 5)

Trends.3140

.3120

.3125

.313

.3135

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There are no number rules to identify cycles

Cycles are defined as repeated patterns in a process

Cycles can be caused by: ◦ Machines that are continually heating up

and cooling down◦ Air temperatures in the shop that rise to

a certain point, then are reduced quickly as cooling systems are activated

◦ Tool wear that allows a part to increase or decrease in size until an offset is made

◦ Seasonal

Cycles

Cycles.5005

.4985

.4990

.4995

.5000

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Can be identified by looking for a majority of parts hugging the center line. (15 or more consecutive points inside zone C)

Will have a "sawtooth" look to it.

Stratification can be caused by: ◦ Gaging concerns (rule of 10s)◦ Honest reporting?

Stratification (Rule 6)

Mixtures.4785

.4765

.4770

.4775

.4780

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Can be identified by looking for a majority of parts falling very close to the control limits, with very few in the center of the chart. (5 or more consecutive points outside zone C)

Will have a "sawtooth" look to it. Typically, this type of situation is

actually a combination of two separate distributions within a process, one at high limit, and one at low limit.

Mixtures can be caused by: ◦ Two different gages being used◦ Output from two or more machines mixed

together on the same chart.◦ Gaging concerns (rule of 10s)◦ Honest reporting?

Mixtures (Rule 7)

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Use the right level of control that brings long term stability to the process that you are improving.

There will most likely be a tradeoff between the effectiveness, effort and cost of the control technique.

Poka-Yoke (Mistake Proofing)

Statistical Process Control (SPC)

Verbal Instructions (Training, Sounds, etc….)

Written Procedures (SOPs, FMEAs, etc….)

Finding The Right Level Of Control

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SOP as the control Exercise:Draw a rectangle.

Draw a semi- circle along the left edge.

Draw another rectangle along the right edge of the rectangle.

Draw a trapezoid along the right edge of that rectangle.

Draw a rectangle along the right edge of the trapezoid.

What is your result?

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Class Exercise

2 1 3 4 5

Draw the described figure

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A Control Plan is simply a plan that documents your process◦ Intended to make the process

robust◦ Assures that we meet our customer

expectations ◦ It contains Key Input and Output

Variables◦ Data comes from process map,

fishbone (C-N-X), standard operating procedures, FMEA and error proofing

The Control Plan

Initial: Modified:Date (Orig):Date (Rev):

Size Freq.Oper Process Output

Verification Methods

Tol.Process Name / Operation

Description

Final:Plan StatusControl Plan No:Part Number:

Process Champion:Process Owners:

Process Owners / Responsibilities

Ow

ner B

Ow

ner C

Ow

ner D

Ow

ner E

Part Name: Black Belt

Ow

ner A

Evaluation Method / Verifier

SampleControl Method / Specification

Reaction Plan for when Control Methods Failed

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Example Control Plan

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Documents

Section XI, Control Concepts