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Statistical Process ControlStatistical Process Control
Operations Management - 5th EditionOperations Management - 5th Edition
Chapter 4Chapter 4
Roberta Russell & Bernard W. Taylor, IIIRoberta Russell & Bernard W. Taylor, III
4-4-22
Basics of Statistical Basics of Statistical Process ControlProcess Control
Statistical Process Control Statistical Process Control (SPC)(SPC) Monitoring production process Monitoring production process
to detect and prevent poor to detect and prevent poor qualityquality
SampleSample Subset of items produced to Subset of items produced to
use for inspectionuse for inspection Control ChartsControl Charts
Process is within statistical Process is within statistical control limitscontrol limits
UCLUCL
LCLLCL
4-4-33
VariabilityVariability
RandomRandom Inherent in a processInherent in a process Can be eliminated Can be eliminated
only through only through improvements in the improvements in the systemsystem
Non-RandomNon-Random Special causesSpecial causes Due to identifiable Due to identifiable
factorsfactors Can be modified Can be modified
through operator or through operator or management actionmanagement action
4-4-44
SPC in TQMSPC in TQM
SPCSPC Tool for identifying problems and Tool for identifying problems and
making improvementsmaking improvements Contributes to the TQM goal of Contributes to the TQM goal of
continuous improvementscontinuous improvements
4-4-55
Quality MeasuresQuality Measures
AttributeAttribute a product characteristic that can be a product characteristic that can be
evaluated with a discrete responseevaluated with a discrete response good – bad; yes - nogood – bad; yes - no
VariableVariable a product characteristic that is continuous a product characteristic that is continuous
and can be measuredand can be measured weight - lengthweight - length
4-4-66
Nature of defect is different in servicesNature of defect is different in services Service defect is a failure to meet Service defect is a failure to meet
customer requirementscustomer requirements Monitor times, customer satisfactionMonitor times, customer satisfaction
Applying SPC to ServiceApplying SPC to Service
4-4-77
Applying SPC to Applying SPC to Service (cont.)Service (cont.)
HospitalsHospitals Timeliness and quickness of care, staff responses to Timeliness and quickness of care, staff responses to
requests, accuracy of lab tests, cleanliness, courtesy, requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkoutsaccuracy of paperwork, speed of admittance and checkouts
Grocery StoresGrocery Stores Waiting time to check out, frequency of out-of-stock items, Waiting time to check out, frequency of out-of-stock items,
quality of food items, cleanliness, customer complaints, quality of food items, cleanliness, customer complaints, checkout register errorscheckout register errors
AirlinesAirlines Flight delays, lost luggage and luggage handling, waiting time Flight delays, lost luggage and luggage handling, waiting time
at ticket counters and check-in, agent and flight attendant at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin courtesy, accurate flight information, passenger cabin cleanliness and maintenancecleanliness and maintenance
4-4-88
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 Process is particularly harmful and costly if it goes
out of controlout of control ExamplesExamples
At the beginning of a process because it is a waste of At the beginning of a process because it is a waste of time and money to begin production process with bad time and money to begin production process with bad suppliessupplies
Before a costly or irreversible point, after which product Before a costly or irreversible point, after which product is difficult to rework or correctis difficult to rework or correct
Before and after assembly or painting operations that Before and after assembly or painting operations that might cover defectsmight cover defects
Before the outgoing final product or service is deliveredBefore the outgoing final product or service is delivered
4-4-99
Control ChartsControl Charts
A graph that establishes A graph that establishes control limits of a control limits of a processprocess
Control limitsControl limits Upper and lower bands of Upper and lower bands of
a control charta control chart
Types of chartsTypes of charts AttributesAttributes
p-chartp-chart c-chartc-chart
VariablesVariables range (R-chart)range (R-chart) mean (x bar – chart)mean (x bar – chart)
4-4-1010
Process Control Process Control ChartChart
11 22 33 44 55 66 77 88 99 1010Sample numberSample number
UpperUppercontrolcontrol
limitlimit
ProcessProcessaverageaverage
LowerLowercontrolcontrol
limitlimit
Out of controlOut of control
4-4-1111
Normal DistributionNormal Distribution
=0=0 11 22 33-1-1-2-2-3-3
95%
99.74%
4-4-1212
A Process Is in A Process Is in Control If …Control If …
1. … no sample points outside limits
2. … most points near process average
3. … about equal number of points above and below centerline
4. … points appear randomly distributed
4-4-1313
Control Charts for Control Charts for AttributesAttributes
p-charts uses proportion defective in a
sample
c-charts uses number of defects in an item
4-4-1414
p-Chartp-Chart
UCL = p + zp
LCL = p - zp
z = number of standard deviations from process averagep = sample proportion defective; an estimate of process averagep= standard deviation of sample proportion
pp = = pp(1 - (1 - pp))
nn
4-4-1515
p-Chart Example p-Chart Example (p.138)(p.138)
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
4-4-1616
p-Chart Example (cont.)p-Chart Example (cont.)
UCL = p + z = 0.10 + 3p(1 - p)
n
0.10(1 - 0.10)
100
UCL = 0.190
LCL = 0.010
LCL = p - z = 0.10 - 3p(1 - p)
n
0.10(1 - 0.10)
100
= 200 / 20(100) = 0.10total defectives
total sample observationsp =
4-4-1717
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
Pro
po
rtio
n d
efec
tive
Pro
po
rtio
n d
efec
tive
Sample numberSample number22 44 66 88 1010 1212 1414 1616 1818 2020
UCL = 0.190
LCL = 0.010
p = 0.10
p-Chart p-Chart Example Example (cont.)(cont.)
4-4-1818
c-Chartc-Chart
UCL = UCL = cc + + zzcc
LCL = LCL = cc - - zzcc
where
c = number of defects per sample
cc = = cc
4-4-1919
c-Chart (cont. – c-Chart (cont. – p.141p.141))Number of defects in 15 sample roomsNumber of defects in 15 sample rooms
1 121 122 82 83 163 16
: :: :: :: :15 1515 15 190190
SAMPLESAMPLE
cc = = 12.67 = = 12.67190190
1515
UCLUCL = = cc + + zzcc
= 12.67 + 3 12.67= 12.67 + 3 12.67= 23.35= 23.35
LCLLCL = = cc + + zzcc
= 12.67 - 3 12.67= 12.67 - 3 12.67= 1.99= 1.99
NUMBER OF
DEFECTS
4-4-2020
33
66
99
1212
1515
1818
2121
2424
Nu
mb
er o
f d
efec
tsN
um
ber
of
def
ects
Sample numberSample number
22 44 66 88 1010 1212 1414 1616
UCL = 23.35
LCL = 1.99
c = 12.67
c-Chart c-Chart (cont.)(cont.)
4-4-2121
Control Chart PatternsControl Chart Patterns
UCLUCL
LCLLCL
Sample observationsSample observationsconsistently above theconsistently above thecenter linecenter line
LCLLCL
UCLUCL
Sample observationsSample observationsconsistently below theconsistently below thecenter linecenter line
4-4-2222
Control Chart Patterns (cont.)Control Chart Patterns (cont.)
LCLLCL
UCLUCL
Sample observationsSample observationsconsistently increasingconsistently increasing
UCLUCL
LCLLCL
Sample observationsSample observationsconsistently decreasingconsistently decreasing
4-4-2323
Zones for Pattern TestsZones for Pattern TestsUCL
LCL
Zone A
Zone B
Zone C
Zone C
Zone B
Zone A
Process average
3 sigma = x + A2R=
3 sigma = x - A2R=
2 sigma = x + (A2R)= 23
2 sigma = x - (A2R)= 23
1 sigma = x + (A2R)= 13
1 sigma = x - (A2R)= 13
x=
Sample number
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
|11
|12
|13
4-4-2424
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
4-4-2525
Performing a Pattern TestPerforming a Pattern Test
11 4.984.98 BB —— BB
22 5.005.00 BB UU CC
33 4.954.95 BB DD AA
44 4.964.96 BB DD AA
55 4.994.99 BB UU CC
66 5.015.01 —— 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 xx ABOVE/BELOWABOVE/BELOW UP/DOWNUP/DOWN ZONEZONE
4-4-2626
Sample SizeSample 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