Operations Management. Due Thursday 4pm

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SPCandControlCharts.pdf

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C ontrolling P

rocesses

“C ontrol” = ?

1. M

onitoring –

Looking for _ _ ? •

A bnorm

alities –

S uch as?

» P

oor perform ance, increased accidents, drop

in orders, etc

2. M

aking adjustm ents

– W

hat kind of adjustm ents?

3. D

eploying the new standard w

ay –

Involves _ _ ?

4. R

epeating the “w heel”

“C ontrol” = ?

1. M

onitoring –

Looking for _ _ ? •

A bnorm

alities –

S uch as?

» P

oor perform ance

2. M

aking adjustm ents

– W

hat kind of adjustm ents?

3. D

eploying the new standard w

ay –

Involves _ _ ?

4. R

epeating the “w heel”

The “W hat, W

hy, and W hen” of C

ontrol - -

1) W hat do you w

ant/need to control? 2) W

hy? -

insights into ___ 3) W

hen abnorm al conditions exist, w

hat A

C TIO

N S

are w arranted?

E xam

ple: N ew

P roduct D

evelopm ent

1)W hat to control?

2)W hy? W

hat are you looking for?

“C ontrol” = ?

• “S

ituational A w

areness” –

F rom

m ilitary

– P

art of “S ituational U

N D

E R

S TA

N D

IN G

” •

D ifference?

= O n-going know

ledge of conditions in G em

ba –

“N orm

al”? “A bnorm

al”? –

H ow

do you acquire S ituational A

w areness?

• E

ffective aw areness?

• E

fficient acquisition?

A pproaches

to S ituational A

w areness

1. The “Lean P roduction S

ystem ” approach = ?

– V

isual m anagem

ent –

G em

ba m anagem

ent –

100% participation

• E

x: T otal P

roductive M aintenance

Latent flaw s

2. S tatistics and D

ata

= “S P

C ”

S tatistical P

rocess C ontrol

O utline:

• T

argets of S P

C –

A nalyzing

a process for _ _ _ ?

“C ontrol” = ?

1. M

onitoring –

Looking for _ _ ? •

A bnorm

alities –

S uch as?

» P

oor perform ance

2. M

aking adjustm ents

– W

hat kind of adjustm ents?

3. D

eploying the new standard w

ay –

Involves _ _ ?

4. R

epeating the “w heel”

Targets of S P

C ?

S tatistical P

rocess C ontrol

O utline:

• T

argets of S P

C –

A nalyzing

a process for _ _ _ ?

• S

trategies and T actics of S

P C

– D

escriptive S tatistics, A

cceptance S am

pling, D

O E

, etc

– C

ontrol C harts

T he M

eaning of Q uality in a B

usiness

D efinition: 2. Q

uality of a w ork process:

W hether or not the process is in

a “desirable state”

D im

ensions of “desirable state” of a process = ?

D im

ensions of the

desirable state of a process

• T

he process is:

1.A ccurate

2.C onsistent

C onsistency

• A

“consistent” process _ _ _ –

H as “basically” the sam

e resultfrom one cycle

to the next

= Is precise

= Is stable

= Is predictable

– It’s output m

ay be good, or m

ay be bad

– Lack of consistency

is due to variability in the

process over tim e

Is the process of kicking field goals a consistent process?

Is there variability in it?

C an it be consistent and yet still be off the m

ark?

C ontrol C

harts T

opics: •

G oals/uses

• S

ources of V ariability

– C

om m

on causes, A ssignable causes

• S

tate of a process –

In-control, out-of-control

• T

ools - -

C ontrol C

harts –

T ype of data being tracked

– T

ype of charts (X bar, R

, P )

– Interpretation of results

G oals of C

ontrol C harts (3)

1. M

easure the variation

in the key characteristic •

A ssign a specific m

etric

“V ariation” of w

hat ?

O f one or m

ore key characteristics of the process

V ariation of? M

etric?

G oals of C

ontrol C harts

1. M

easure the variation

2. U

nderstand the causes and sources of

variation

S ources

of V ariation

• C

om m

on causes of variation

– R

andom causes that w

e cannot identify –

U navoidable

– e.g. slight

differences in process variables like diam

eter, w eight, service tim

e, tem perature

• A

ssignable causes of variation

– C

auses can be identified and elim inated

– e.g. w

orn tool, O T

H E

R S

S ources

of V ariation

• C

om m

on causes of variation

– R

andom causes that w

e cannot identify –

U navoidable

– e.g. slight differences in process variables like diam

eter, w eight, service tim

e, tem perature

• A

ssignable causes of variation

– C

auses can be identified and elim inated

– e.g. poor em

ployee training, w orn tool, m

achine needing repair

T he process is “in control”

T he process is “out of control”

A n “O

ut of C ontrol” process -

- •

Im plies that there is a correctable

cause of variability

• M

anagem ent action called for

• T

herefore, a key value or utility of a control chart is1.

S ignaling

that m anagem

ent intervention is now

arranted

2. T

here is statistical evidence that som

ething is “out of the ordinary”

3. “M

anagem ent by E

xception” (of the quality of a w

ork process)

G oals of C

ontrol C harts

1. M

easure the variation

2. U

nderstand the causes and sources of

variation

3. R

educe the variation w

hen called for

K eeping a process in control:

S P

C C

ontrol C harts

T he tool or chart -

T he C

ontrol C hart

• E

lem ents of a control chart:

1. C

enter Line (C

L): central tendency of the sam ple

data (m ean, average)

O ften, the data for the center line com

es from

sam ples over tim

e _ _ _

P rocess: H

am ner-C

ole real estate office -

- volum

e of business brought in by agents (4)

• G

oal: intervene w hen agents

productivity becom es “too low

” –

or “too high”?

• F

irstsnapshot: m onth 1

A gent

1 2

3 4

S ales

($1000) 60

200 120

180

A v

140

P rocess: H

am ner-C

ole real estate office -

- volum

e of business brought in by agents (4)

• G

oal: intervene w hen agents

productivity becom es “too low

” –

O r “too high”?

• N

ext snapshot: m onth 2

A gent

1 2

3 4

A v

S ales

($1000) 130

500 300

280 302

Individual M easurem

ents (m

onthly $ sales)

Sam ple M

eans

T im

e O

rd e

re d

Q u

a lity

C o

n tro

l D a

X bar = $250,000

and S

igm a = $80,000

$40K $60K

$70K $50K

etc

$140K

T he C

ontrol C hart

• E

lem ents of a control chart:

1. C

enter Line (C

L): central tendency of the sam ple

data (m ean, average)

T he C

ontrol C hart

• E

lem ents of a control chart:

1. C enter line

2. U

pper and Low er C

ontrol Lim its

P urpose of C

ontrol Lim its:

– S

erve as a signalw hen the process has changed

U pper C

ontrol Lim it (U

C L):

– “too big to be like the others”

Low er C

ontrol Lim it (LC

L): –

“too sm all to be like the others”

Individual M easurem

ents

T im

e O

rd e

re d

Q u

a lity

C o

n tro

l D a

L C

L U

C L

Individual M easurem

ents

Sam ple M

eans

T im

e O

rd e

re d

Q u

a lity

C o

n tro

l D a

X bar = $250,000

and S

igm a = $80,000

L C

L U

C L

T he C

ontrol C hart

• E

lem ents of a control chart:

2. C ontrol Lim

its

T he C

ontrol C hart

• E

lem ents of a control chart:

2. C ontrol Lim

its

0.0 3.0

6.0 9.0

12.0 M

ean

Low er 95%

C onfidence

Lim it

U pper 95%

C onfidence

Lim it

C onfidence Lim

its “like” C ontrol Lim

its

S am

ple m eans

are inside these lim

its 95% of the tim

O utside

lim its 5%

of the tim e

2.5 % 2.5 %

X bar

Sam ple M

eans

T im

e O

rd e

re d

Q u

a lity

C o

n tro

l D a

2 sigm a

control lim

its

X bar = $250,000

and S

igm a = $80,000

LC L

U C

L = $250K + (2)($80k)

2.5 % 2.5 %

95.0 %

“z” --your callValue to use?

T im

m ean

+ z s

-z s

U C

L C

W hy “2” sigm

a? W hy “3”%

C ontrol C

hart Z -V

alue z

= 3.00 is a standard value

= 99.7% C

onfidence Interval

C ontrol C

hart Z -V

alue z

= 2.00 is a standard value

= 95.4% C

onfidence Interval

C ontrol C

hart Z -V

alue S

m aller

Z-value m

akes the control chart:

M ore sensitive -

- m

ore intervention + m

ore investigation, m ore im

provem ent

- m

ore cost

C ontrol C

hart Z -V

alue S

m aller

Z-value m

akes the control chart:

B U

T -

- M

ore prone to “false alarm s”

C ontrol C

hart Z -V

alue S

m aller

Z-value m

akes the control chart:

B U

T -

- 2. M

ore prone to false alarm s

Im plication as to cause?

You deem the process to be have assignable causes

w hen in fact it turns out that

there are N O

special causes present

D eveloping

a C ontrol C

hart

D esign phase:

1. D

ecide on the level of control you w ant

2. S

et or com pute the param

eters of the chart

U se phase:

3. T

ake periodic sam ples; P

lot sam ple points

on control chart

4. Interpret the results A

S Y

O U

G O

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

Values of the Variable of interest

S alt ( %

)

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

U pper

control lim

P rocess

average

Low er

control lim

Values of the Variable of interest

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

Values of the Variable of interest

B ag

S alt content

1 1.4 %

2 0.8

3 1.2

4 1.0

S alt ( %

)

1 2

3 4

5 6

7 8

9 10

S am

ple num ber --over tim

U pper

control lim

P rocess

average

Low er

control lim

1.25 %

1.80 %

1.10 %

W as this salt %

sam ple _ _ _

T he basis question:

1 2

3 4

5 6

7 8

9 10

S am

ple num ber --over tim

U pper

control lim

P rocess

average

Low er

control lim

1.80 %

1.10 %

G enerated by a the process that

had this distribution?

C onclusion?

Likelihood?

1.25 %

1 2

3 4

5 6

7 8

9 10

S am

ple num ber --over tim

U pper

control lim

P rocess

average

Low er

control lim

1.80 %

1.10 %

A fter 2

nd sam

ple_ _ _ C onclusion?

1.38 %

1.25 %

1 2

3 4

5 6

7 8

9 10

S am

ple num ber --over tim

U pper

control lim

P rocess

average

Low er

control lim

1.80 %

1.10 %

A fter 3

rd sam

ple_ _ _

C onclusion?

1.30 %

1.25 % 1.38

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

W ere these salt %

sam ples _ _ _

C ontinuing -

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

U pper

control lim

P rocess

average

Low er

control lim

M ean + 3σ

= 1.8 %

1.39 %

M ean -

3σ = 1.10 %

G enerated from

a process that had been producing chips that follow

ed this distribution

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

U pper

control lim

P rocess

average

Low er

control lim

M ean + 3σ

= 1.8 %

1.39 %

M ean -

3σ = 1.10 %

G enerated from

a process that had been producing chips that follow

ed this distribution “S

om ething is going on”

Types of C

ontrol C harts

1. C

ontrol chart for variables •

are used to m onitor characteristics that can be

m easured, e.g. length, w

eight, diam eter, tim

– X

-bar C hart

– R

C hart

2. C ontrol charts for attributes

– P

C hart

– C

C hart

T ype of data?

• U

S P

ipe: –

T o m

onitor results of m elting?

– R

esults of casting?

• E

ngineering S ervices ?

C ontrol C

harts for V

ariables •

X -bar C

hart: M ean

– P

lots sam ple averages

– M

easures central tendency (location) of the process

• R

C hart: R

ange –

P lots sam

ple ranges –

M easures dispersion (variation) of the process

• M

U S

T use B

O T

H charts together to

effectively m onitor and control variable quality

characteristics

E xam

ple - -

C oral G

lass; Variable = cutting tool life

X bar C

hart

U C

L X

z or X

A R

L C

L X

z or X

A R

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

U pper

control lim

P rocess

average

Low er

control lim

1. F or x-C

harts w hen w

e know s

U pper control lim

it (U C

L) = x + zs

Low er control lim

it (LC L) = x

-zs x

w here

x =

m ean of the sam

ple m eans (or a target

value set for the process) z

= num

ber of norm al standard deviations

s x

= standard deviation of the sam

ple m eans

= s

/ n s

= population

standard deviation n

= sam

ple size

C hart P

aram eters -

U C

L X

z or X

A R

L C

L X

z or X

A R

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

U pper

control lim

P rocess

average

Low er

control lim

C hart P

aram eters -

X -bar C

hart C alculations

sam ple size

num ber of sam

ples average of the sam

ple m eans

From T

able 6-1, p. 182 param

eter (A

SSU M

PT IO

N : 3

nkXA levelofcontrol

s22

U C

L L

C L

X A R

Factor for x-C hart

A 2

D 3

D 4

2 1.88

0.00 3.27

3 1.02

0.00 2.57

4 0.73

0.00 2.28

5 0.58

0.00 2.11

6 0.48

0.00 2.00

7 0.42

0.08 1.92

8 0.37

0.14 1.86

9 0.34

0.18 1.82

10 0.31

0.22 1.78

11 0.29

0.26 1.74

12 0.27

0.28 1.72

13 0.25

0.31 1.69

14 0.24

0.33 1.67

15 0.22

0.35 1.65

Factors for R -C

hart S

am ple S

ize (n)

194

E xam

ple for V ariable C

ontrol C

harts

O bservation

S am

ple 1 S

am ple 2

S am

ple 3 x

1 15.8

16.1 16.0

x 2

16.0 16.0

15.9 x

3 15.8

15.8 15.9

x 4

15.9 15.9

15.8

• A

quality control inspector at the C ocoa F

izz soft drink com

pany has taken three sam ples w

ith four observations each of the volum

e of bottles filled (ounces). U se the data

below to develop R

and X -bar control charts w

ith three sigm

a control lim its for the 16 oz. bottling operation.

Layout can be inverted

X -bar

C hart E

xam ple

O bservation

S am

ple 1 S

am ple 2

S am

ple 3 x

1 15.8

16.1 16.0

x 2

16.0 16.0

15.9 x

3 15.8

15.8 15.9

x 4

15.9 15.9

15.8 S

am ple M

ean 15.875

15.950 15.900

n =?

k =?

C enter line = ?

U C

L = ? A

2 = ?

LC L = ?

Factor for x-C hart

A 2

D 3

D 4

2 1.88

0.00 3.27

3 1.02

0.00 2.57

4 0.73

0.00 2.28

5 0.58

0.00 2.11

6 0.48

0.00 2.00

7 0.42

0.08 1.9 2

8 0.37

0.14 1.86

9 0.34

0.18 1.82

10 0.31

0.22 1.78

11 0.29

0.26 1.74

12 0.27

0.28 1.72

13 0.25

0.31 1.69

14 0.24

0.33 1.67

15 0.22

0.35 1.65

Factors for R -C

hart S

am ple S

ize (n)

X -bar

C hart E

xam ple

4315.875 15.95

15.90

15.91 3

0.73

nkXA U

C L

15.91 0.73(0.233)

16.08 L

C L

15.91 0.73(0.233)

15.74

O bservation

S am

ple 1 S

am ple 2

S am

ple 3 x

1 15.8

16.1 16.0

x 2

16.0 16.0

15.9 x

3 15.8

15.8 15.9

x 4

15.9 15.9

15.8 S

am ple

M ean

15.875 15.950

15.900

X -bar C

hart E xam

ple, cont.

X -bar C

hart

15.7

15.8

15.9

16.0

16.1

1 2

3 S

am ple N

um ber

C ontrol C

harts for V

ariables •

X -bar C

hart: M ean

– P

lots sam ple averages

– M

easures central tendency (location) of the process

• R

C hart: R

ange –

P lots sam

ple ranges –

M easures dispersion (variation) of the process

R C

hart 4

U C

L D R

1 2

3 4

5 6

7 8

9 10

S am

ple num ber

U pper

control lim

P rocess

average

Low er

control lim

it 3

L C

L D R

R bar

sz R

U C L

E xam

ple for V ariable C

ontrol C

harts

O bservation

S am

ple 1 S

am ple 2

S am

ple 3 x

1 15.8

16.1 16.0

x 2

16.0 16.0

15.9 x

3 15.8

15.8 15.9

x 4

15.9 15.9

15.8

• A

quality control inspector at the C ocoa F

izz soft drink com

pany has taken three sam ples w

ith four observations each of the volum

e of bottles filled (ounces). U se the data

below to develop R

and X -bar control charts w

ith three sigm

a control lim its for the 16 oz. bottling operation.

R -C

hart “Factors”

sam ple size

num ber of sam

ples average sam

ple range

From T

able 6-1, p. 182 L

C L

param eter

U C

L param

eter

nkRDD

U C

L L

C L

D R

Factor for x-C hart

A 2

D 3

D 4

2 1.88

0.00 3.27

3 1.02

0.00 2.57

4 0.73

0.00 2.28

5 0.58

0.00 2.11

6 0.48

0.00 2.00

7 0.42

0.08 1.92

8 0.37

0.14 1.86

9 0.34

0.18 1.82

10 0.31

0.22 1.78

11 0.29

0.26 1.74

12 0.27

0.28 1.72

13 0.25

0.31 1.69

14 0.24

0.33 1.67

15 0.22

0.35 1.65

Factors for R -C

hart S

am ple S

ize (n)

R -C

hart E xam

ple

3 4

430.2 0.3

0.2

0.233 3

0.00, 2.28

nkRD D

U C

L 2.28(0.233)

0.53 L

C L

0.00(0.233) 0.00

O bservation

S am

ple 1

S am

ple 2 S

am ple 3

x 1

15.8 16.1

16.0 x

2 16.0

16.0 15.9

x 3

15.8 15.8

15.9 x

4 15.9

15.9 15.8

R ange

0.2 0.3

0.2

R -C

hart E xam

ple, cont.

R C

hart

0.00 0.10 0.20 0.30 0.40 0.50 0.60

1 2

3 S

am ple N

um ber

N ote: LC

L on R chart N

E V

E R

negative- -

round to 0

Types of C

ontrol C harts

1. C

ontrol chart for variables •

are used to m onitor characteristics that can be

m easured, e.g. length, w

eight, diam eter, tim

– X

-bar C hart

– R

C hart

2. C ontrol charts for attributes

– P

C hart

– C

C hart

C ontrol C

harts for A ttributes

• p-C

harts

– D

iscrete values and can be counted •

E ach item

= Y es/no or good/ bad

• E

xam ples of this type of quality variable?

– C

alculate the proportion of non- conform

ing parts or deliverables in each

sam ple

(% defective)

P C

hart C alculations

sam ple size (num

ber in each sam ple)

average percent defective in a sam ple

(1 )

std. deviation of percent defective in a sam ple

num ber of std. deviations aw

ay from process average

(

p np

p p

n z

usually 3.0 or 2.0)

U C

L C

L m

ax{ ,0}

p z p z

W here does “z” com

e from ?

If you w anted to have lim

its that trap, say, 97.5% of the observations that w

ill occur, then z = ?

F inding z for desired control

97.5% (1)

F inding z for desired control

97.5% 1.00 -

.975 = .025 (2)

F inding z for desired control1.00 -

.975 = .025

A nd since w

e w ant .025 split on both ends, then .025/2 = .0125

.0125 .0125

(3)

(2)

F inding z for desired control

.4875

(3)

S o that from

the O N

E S

ID E

D table, z is based on .5000 -.0125 = .4875

and therefore z = ?

.0125

F or P

rob = 0.4875

z = 2.24

P -C

hart E xam

ple

S am

ple N

um ber

of D

efective Tires

N um

ber of Tires in each

S am

ple

P roportion

D efective

1 3

20 2

2 20

3 1

20 4

2 20

5 1

20 Total

9 100

• A

P roduction m

anager for a tire com

pany has inspected the num

ber of defective tires in five random

sam ples w

ith 20 tires in each sam

ple. T he

table show s the num

ber of defective tires in each sam

ple of 20 tires. C alculate

the proportion defective for each sam

ple, the center line, and control lim

its using z

= 3.00. n = ? k = num

ber of sam ples = ?

p = ? C

L = ?

P -C

hart E xam

ple, cont.

20, 3.00 #D

efectives 9

C L

0.09 T

otal Inspected 100

(0.09 )(0.91)

0.064 20

0.09 3(0.064

) 0.282

0.09 3(0.064

) 0.102

n z

U C L

L C L

P -C

hart E xam

ple, cont.

P -C

hart

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1 2

3 4

5 S

am ple N

um ber

D eveloping

a C ontrol C

hart 1.

C om

pute the C L, U

C L and LC

L •

C L, U

C L and LC

L should be based on sam ple m

easurem ents

w hen the process is in-control

2. T

ake periodic sam ples

• If assignable causes are present then discard the data

3. P

lot sam ple points on control chart

4. Interpret the chart -

- determ

ine if process is “in control”

• A

re there any “A ssignable” causes of the variability

noted?

S ources

of V ariation

• C

om m

on causes of variation

– R

andom causes that w

e cannot identify –

U navoidable

– e.g. slight differences in process variables like diam

eter, w eight, service tim

e, tem perature

• A

ssignable causes of variation

– C

auses can be identified and elim inated

– e.g. poor em

ployee training, w orn tool, m

achine needing repair

T he process is “in control”

T he process is “out of control”

A P

rocess is “In C ontrol” if -

1. N

o sam ple points are outside lim

its

Im plication: this 9

th sam

ple is “not like” the others

I’m 99.7%

sure (ie, 3 sigm

a confident)

1.N o sam

ple points are outside lim its

2. T

here are no P

A TTE

R N

s in the observations

¾ T

he observations are N O

T random

¾ S

ystem atic

fluctuations ¾

T here exist som

e B IA

S in the process now

A P

rocess is “In C ontrol” if -

Individual M easurem

ents

X bar chart Sam

ple M eans

LC L

U C

Individual M easurem

ents

X bar chart Sam

ple M eans

LC L

U C

W hat do you E

xpect to see if this process is IN C

ontrol?

“A bout an equal num

ber of sam ple points

are above and below the average”

Individual M easurem

ents

In c

o n

tro l ?

N ext 9 days

LC L

U C

R ules to detect P

atterns

• S

et up A , B

, and C “zones”

“A ”

“B ”

“C ”

R ules to detect P

atterns

• S

et up A , B

, and C “zones”

“A ”

“B ”

“C ”

A ny observations in the A

zone?

A ny observations in the B

zone? C

zone?

O thers -

Im plications?

1.A pattern

exist, and therefore -

2. T here is an abnorm

al B ias in the process

so that _ _

3. It is O ut of control -

- an A

ssignable cause of variation likely exist (w

ith probability ___% )

P atterns

• U

se “zones” to identify “bias”

W estern E

lectric rules (N ote: these apply to sym

m etric charts like X

bar, but not to asym

m etric charts like R

charts) - -

C ontrolling P

rocesses

N ext: C

apability of P rocesses