stastical process control charts

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Statistical Process Control Statistical Process Control

Operations Management - 5th Edition

Operations Management - 5th Edition

Chapter 4Chapter 4

Roberta Russell & Bernard W. Taylor, IIIRoberta Russell & Bernard W. Taylor, III



44--22

Lecture OutlineLecture Outline

Basics of Statistical Process ControlBasics of Statistical Process Control

Control ChartsControl Charts

Control Charts for AttributesControl Charts for Attributes

Control Charts for VariablesControl Charts for Variables

Control Chart PatternsControl Chart Patterns SPC with ExcelSPC with Excel

Process CapabilityProcess Capability



44--33

Basics of StatisticalBasics of Statistical

Process ControlProcess Control

Statistical Process Control (SPC)Statistical Process Control (SPC) monitoring production process tomonitoring production process to

detect and prevent poor qualitydetect and prevent poor quality SampleSample

subset of items produced to use for subset of items produced to use for inspectioninspection

Control ChartsControl Charts process is within statistical controlprocess is within statistical control

limitslimits

UCLUCL

LCLLCL



44--44

VariabilityVariability

RandomRandom

common causescommon causes inherent in a processinherent in a process

can be eliminated onlycan be eliminated only

through improvements inthrough improvements in

the systemthe system

NonNon--RandomRandom

special causesspecial causes due to identifiable factorsdue to identifiable factors

can be modified throughcan be modified through

operator or managementoperator or management

actionaction



44--55

SPC in TQMSPC in TQM

SPCSPC

tool for identifying problems and maketool for identifying problems and makeimprovementsimprovements

contributes to the TQM goal of continuouscontributes to the TQM goal of continuous

improvementsimprovements



44--66

Quality MeasuresQuality Measures

AttributeAttribute

a product characteristic that can be evaluated with aa product characteristic that can be evaluated with adiscrete responsediscrete response

goodgood ± ± bad; yesbad; yes -- nono

VariableVariable

a product characteristic that is continuous and can bea product characteristic that is continuous and can bemeasuredmeasured

weightweight -- lengthlength



44--77

Nature of defect is different in servicesNature of defect is different in services Service defect is a failure to meet customer Service defect is a failure to meet customer

requirementsrequirements

Monitor times, customer satisfactionMonitor times, customer satisfaction

Applying SPC toApplying SPC to

ServiceService



44--88


Service (cont.)Service (cont.)

HospitalsHospitals timeliness and quickness of care, staff responses to requests, accuracy of timeliness and quickness of care, staff responses to requests, accuracy of

lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittancelab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittanceand checkoutsand checkouts

Grocery StoresGrocery Stores waiting time to check out, frequency of outwaiting time to check out, frequency of out--of of--stock items, quality of foodstock items, quality of food

items, cleanliness, customer complaints, checkout register errorsitems, cleanliness, customer complaints, checkout register errors

Airlines Airlines flight delays, lost luggage and luggage handling, waiting time at ticketflight delays, lost luggage and luggage handling, waiting time at ticket

counters and checkcounters and check--in, agent and flight attendant courtesy, accurate flightin, agent and flight attendant courtesy, accurate flightinformation, passenger cabin cleanliness and maintenanceinformation, passenger cabin cleanliness and maintenance



44--99


Service (cont.)Service (cont.)

FastFast--Food RestaurantsFood Restaurants waiting time for service, customer complaints, cleanliness, foodwaiting time for service, customer complaints, cleanliness, food

quality, order accuracy, employee courtesyquality, order accuracy, employee courtesy

CatalogueCatalogue--Order CompaniesOrder Companies order accuracy, operator knowledge and courtesy, packaging,order accuracy, operator knowledge and courtesy, packaging,

delivery time, phone order waiting timedelivery time, phone order waiting time

Insurance CompaniesInsurance Companies billing accuracy, timeliness of claims processing, agentbilling accuracy, timeliness of claims processing, agent

availability and response timeavailability and response time



44--1010

Where to Use Control ChartsWhere to Use Control Charts

Process has a tendency to go out of controlProcess has a tendency to go out of control

Process is particularly harmful and costly if it goes out of Process is particularly harmful and costly if it goes out of

controlcontrol ExamplesExamples

at the beginning of a process because it is a waste of time andat the beginning of a process because it is a waste of time andmoney to begin production process with bad suppliesmoney to begin production process with bad supplies

before a costly or irreversible point, after which product is difficultbefore a costly or irreversible point, after which product is difficultto rework or correctto rework or correct

before and after assembly or painting operations that might cover before and after assembly or painting operations that might cover defectsdefects

before the outgoing final product or service is deliveredbefore the outgoing final product or service is delivered



44--1111

Control ChartsControl Charts

A graph that establishes A graph that establishescontrol limits of a processcontrol limits of a process

Control limitsControl limits upper and lower bands of aupper and lower bands of a

control chartcontrol chart

Types of chartsTypes of charts

Attributes Attributes pp--chartchart

cc--chartchart

VariablesVariables

range (Rrange (R--chart)chart)

mean (x bar mean (x bar ± ± chart)chart)



44--1212

Process ControlProcess Control

ChartChart

11 22 33 44 55 66 77 88 99 1010

Sample number Sample number

Upper Upper controlcontrol

limitlimit

ProcessProcessaverageaverage

Lower Lower

controlcontrollimitlimit

Out of controlOut of control



44--1313

Normal Distribution Normal Distribution

QQ=0=0 11WW 22WW 33WW--11WW--22WW--33WW

95%

99.74%



44--1414

A Process Is inA Process Is in

Control If «Control If «

1. « no sample points outside limits2. « most points near process average

3. « about equal number of points above

and below centerline

4. « points appear randomly distributed



44--1515

Control Charts for Control Charts for

AttributesAttributes

p-charts uses portion defective in a sample

c-charts

uses number of defects in an item



44--1616

p p--ChartChart

UCL = p + z W p

LCL = p - z W p

z = number of standard deviations from

process average

p = sample proportion defective; an estimate

of process averageW p = standard deviation of sample proportion

WW p p == p p(1(1 -- p p))

nn



44--1717

p p--Chart Exam pleChart Exam ple

20 samples of 100 pairs of jeans20 samples of 100 pairs of jeans

NUMBER OFNUMBER OF PROPORTIONPROPORTIONSAMPLESAMPLE DEFECTIVESDEFECTIVES DEFECTIVEDEFECTIVE

11 66 .06.06

22 00 .00.00

33 44 .04.04

:: :: ::

:: :: ::

2020 1818 .18.18

200200



44--1818

p p--Chart Exam ple (cont.)Chart Exam ple (cont.)

UCL = p + z = 0.10 + 3 p(1 - p)

n

0.10(1 - 0.10)

100

UCL = 0.190

LCL = 0.010

LCL = p - z = 0.10 - 3 p(1 - p)

n

0.10(1 - 0.10)

100

= 200 / 20(100) = 0.10total defectives

total sample observations p =



44--1919

0.020.02

0.040.04

0.060.06

0.080.08

0.100.10

0.120.12

0.140.14

0.160.16

0.180.18

0.200.20

P r o p o r t i o n d e

f e c t i v e

P r o p o r t i o n d e

f e c t i v e


22 44 66 88 1010 1212 1414 1616 1818 2020

UCL = 0.190

LCL = 0.010

p = 0.10

p p--ChartChartExam pleExam ple(cont.)(cont.)



44--2020

cc--ChartChart

UCL = UCL = c c + + z z WWc c

LCL = LCL = c c -- z z WWc c

where

c = number of defects per sample

WWc c = = c c



44--2121

cc--Chart (cont.)Chart (cont.)Number of defects in 15 sample roomsNumber of defects in 15 sample rooms

1 121 12

2 82 8

3 163 16

: :: :

: :: :15 1515 15

190190

SAMPLESAMPLE

c c = = 12.67= = 12.67190190

1515

UCLUCL = = c c + + z z WWc c

= 12.67 + 3 12.67= 12.67 + 3 12.67

= 23.35= 23.35

LCLLCL = = c c + + z z WWc c

= 12.67= 12.67 -- 3 12.673 12.67

= 1.99= 1.99

NUMBER

OF

DEFECTS



44--2222

33

66

99

1212

1515

1818

2121

2424

N u m b e

r o f d e f e c t s

N u m b e

r o f d e f e c t s


22 44 66 88 1010 1212 1414 1616

UCL = 23.35

LCL = 1.99

c = 12.67

cc--ChartChart(cont.)(cont.)



44--2323

Control Charts for Control Charts for

VariablesVariables

Mean chart ( x -Chart )

uses average of a sample

Range chart ( R-Chart )

uses amount of dispersion in a

sample



44--2424

xx--bar Chart bar Chart

x x = =

x x 11 + + x x 22 + ...+ ... x x k k

k k

==

UCL = UCL = x x + + A A22R R LCL = LCL = x x -- A A22R R == ==

wherewhere

x x = average of sample means= average of sample means==



44--2626

UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08

LCL =

x

-A

2R

= 5.01 - (0.58)(0.115) = 4.94

=

=

x = = = 5.01 cm= § x

k

50.09

10

xx-- bar Chart bar Chart

Exam ple (cont.)Exam ple (cont.)

Retrieve Factor Value A2



44--2727

xx-- bar bar ChartChartExam pleExam ple

(cont.)(cont.)

UCL = 5.08

LCL = 4.94

M e a n

Sample number

|

1

|

2

|

3

|

4

|

5

|

6

|

7

|

8

|

9

|

10

5.10 ±

5.08 ±

5.06 ±

5.04 ±

5.02 ±

5.00 ±

4.98 ±

4.96 ±

4.94 ±

4.92 ±

x = 5.01=



44--2828

R R-- ChartChart

UCL = UCL = DD44R R LCL = LCL = DD33R R

R R = = §§R R

k k

wherewhere

R R = range of each sample= range of each sample

k k = number of samples= number of samples



44--2929

R R--Chart Exam pleChart Exam ple

OBSERVATIONS (SLIPOBSERVATIONS (SLIP--RING DIAMETER, CM)RING DIAMETER, CM)

SAMPLE SAMPLE k k 11 2 2 33 44 5 5 x x R R

11 5.025.02 5.015.01 4.944.94 4.994.99 4.964.96 4.984.98 0.080.08

22 5.015.01 5.035.03 5.075.07 4.954.95 4.964.96 5.005.00 0.120.12

33 4.994.99 5.005.00 4.934.93 4.924.92 4.994.99 4.974.97 0.080.0844 5.035.03 4.914.91 5.015.01 4.984.98 4.894.89 4.964.96 0.140.14

55 4.954.95 4.924.92 5.035.03 5.055.05 5.015.01 4.994.99 0.130.13

66 4.974.97 5.065.06 5.065.06 4.964.96 5.035.03 5.015.01 0.100.10

77 5.055.05 5.015.01 5.105.10 4.964.96 4.994.99 5.025.02 0.140.14

88 5.095.09 5.105.10 5.005.00 4.994.99 5.085.08 5.055.05 0.110.1199 5.145.14 5.105.10 4.994.99 5.085.08 5.095.09 5.085.08 0.150.15

1010 5.015.01 4.984.98 5.085.08 5.075.07 4.994.99 5.035.03 0.100.10

50.0950.09 1.151.15

Example 15.3Example 15.3



44--3030

R R--Chart Exam ple (cont.)Chart Exam ple (cont.)

Example 15.3Example 15.3

§R k

R = = = 0.1151.1510

UCL = D4R = 2.11(0.115) = 0.243LCL = D3R = 0(0.115) = 0

Retrieve Factor Values DRetrieve Factor Values D33 and Dand D44



44--3131

R R--Chart Exam ple (cont.)Chart Exam ple (cont.)

UCL = 0.243

LCL = 0

R a n g e

Sample number

R = 0.115

|

1

|

2

|

3

|

4

|

5

|

6|

7

|

8

|

9

|

10

0.28 ±

0.24 ±

0.20 ±

0.16 ±

0.12 ±

0.08 ±

0.04 ±

0 ±



44--3232

Using xUsing x-- bar and R bar and R--ChartsCharts

Together Together

Process average and process variability must be in control.

It is possible for samples to have very narrow ranges, but

their averages is beyond control limits.

It is possible for sample averages to be in control, but

ranges might be very large.



44--3333

Control Chart PatternsControl Chart Patterns

UCLUCL

LCLLCL

Sample observationsSample observations

consistently above theconsistently above the

center linecenter line

LCLLCL

UCLUCL


consistently below theconsistently below thecenter linecenter line



44--3434

Control Chart Patterns (cont.)Control Chart Patterns (cont.)

LCLLCL

UCLUCL


consistently increasingconsistently increasing

UCLUCL

LCLLCL


consistently decreasingconsistently decreasing



44--3535

Zones for Pattern TestsZones for Pattern TestsUCL

LCL

Zone A

Zone B

Zone C

Zone C

Zone B

Zone A

Processaverage

3 sigma = x + A2R =

3 sigma = x - A2R =

2 sigma = x + ( A2R )= 2

3

2 sigma = x - ( A2R )= 23

1 sigma = x + ( A2R )= 1

3

1 sigma = x - ( A2R )= 1

3

x =

Sample number

|

1

|

2

|

3

|

4

|

5

|

6

|

7

|

8

|

9

|

10

|

11

|

12

|

13



44--3636

Control Chart PatternsControl Chart Patterns

8 consecutive points on one side of the center line

8 consecutive points up or down across zones

14 points alternating up or down

2 out of 3 consecutive points in zone A but still

inside the control limits

4 out of 5 consecutive points in zone A or B



44--3737

Performing a Pattern TestPerforming a Pattern Test

11 4.984.98 BB ²² BB

22 5.005.00 BB UU CC

33 4.954.95 BB DD AA44 4.964.96 BB DD AA

55 4.994.99 BB UU CC

66 5.015.01 ²² UU CC

77 5.025.02 AA UU CC

88 5.055.05 AA UU BB

99 5.085.08 AA UU AA

1010 5.035.03 AA DD BB

SAMPLESAMPLE x x ABOVE /BELOWABOVE /BELOW UP/DOWNUP/DOWN ZONEZONE



44--3838

Sam ple SizeSam ple Size

Attribute charts require larger sample sizes

50 to 100 parts in a sample

Variable charts require smaller samples

2 to 10 parts in a sample



44--3939

SPC with ExcelSPC with Excel

UCL=0.19

LCL=0.01



44--4040

SPC with Excel:SPC with Excel:

FormulasFormulas



44--4141

Process Ca pabilityProcess Ca pability

TolerancesTolerances

design specifications reflecting product requirementsdesign specifications reflecting product requirements Process capabilityProcess capability

range of natural variability in a process what werange of natural variability in a process what we

measure with control chartsmeasure with control charts



44--4242

Process Ca pabilityProcess Ca pability

(b) Design specifications(b) Design specificationsand natural variation theand natural variation thesame; process is capablesame; process is capableof meeting specificationsof meeting specificationsmost of the time.most of the time.

DesignDesignSpecificationsSpecifications

ProcessProcess

(a) Natural variation(a) Natural variationexceeds designexceeds designspecifications; processspecifications; processis not capable of is not capable of meeting specificationsmeeting specificationsall the time.all the time.


ProcessProcess



44--4343

Process Ca pability (cont.)Process Ca pability (cont.)

(c) Design specifications(c) Design specificationsgreater than naturalgreater than naturalvariation; process isvariation; process iscapable of alwayscapable of alwaysconforming toconforming tospecifications.specifications.


ProcessProcess

(d) Specifications greater (d) Specifications greater than natural variation, than natural variation, but process off center;but process off center;capable but some outputcapable but some outputwill not meet upper will not meet upper specification.specification.


ProcessProcess



44--4444

Process Ca pability MeasuresProcess Ca pability Measures

Process Capability Ratio

Cp =

=

tolerance range

process range

upper specification limit -lower specification limit

6W



44--4545

Com puting CCom puting C p p

Net weight specification = 9.0 oz s 0.5 oz

Process mean = 8.80 oz

Process standard deviation = 0.12 oz

Cp =

= = 1.39

upper specification limit -lower specification limit

6W

9.5 - 8.5

6(0.12)



44--4646

Process Ca pability MeasuresProcess Ca pability Measures

Process Capability Ind ex Process Capability Ind ex

C C pk pk = minimum= minimum

x x -- lower specification limitlower specification limit

33WW

==

upper specification limitupper specification limit -- x x

33WW

==

,,



44--4747

Com puting CCom puting C pk pk

Net weight specification = 9.0 oz s 0.5 oz

Process mean = 8.80 oz

Process standard deviation = 0.12 oz

Cpk = minimum

= minimum , = 0.83

x - lower specification limit

3W

=

upper specification limit - x

3W

=

,

8.80 - 8.50

3(0.12)

9.50 - 8.80

3(0.12)



44 4848

FactFactorsors

n A2 D3 D4

SAMPLE SIZE FACTOR FOR x -CHART FACTORS FOR R -CHART

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 1.928 0.37 0.14 1.86

9 0.44 0.18 1.82

10 0.11 0.22 1.78

11 0.99 0.26 1.74

12 0.77 0.28 1.72

13 0.55 0.31 1.69

14 0.44 0.33 1.6715 0.22 0.35 1.65

16 0.11 0.36 1.64

17 0.00 0.38 1.62

18 0.99 0.39 1.61

19 0.99 0.40 1.61

20 0.88 0.41 1.59

Appendix:

Determining Control Limits for x-bar and R-Charts

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