statistical process control operations management
DESCRIPTION
TRANSCRIPT
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Statistical Process Control
Operations Management
Dr. Ron Tibben-Lembke
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Designed Size
10 11 12 13 14 15 16 17 18 19 20
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Natural Variation
14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5
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Theoretical Basis of Control Charts
95.5% of allX fall within ± 2
Properties of normal distribution
X
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Theoretical Basis of Control ChartsProperties of normal distribution
99.7% of allX fall within ± 3
X
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Design Tolerances
Design tolerance: Determined by users’ needs UTL -- Upper Tolerance Limit LTL -- Lower Tolerance Limit Eg: specified size +/- 0.005 inches
No connection between tolerance and completely unrelated to natural variation.
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Process Capability and 6
A “capable” process has UTL and LTL 3 or more standard deviations away from the mean, or 3σ.
99.7% (or more) of product is acceptable to customers
LTL UTL
3 6
LTL UTL
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Process Capability
LTL UTL LTL UTL
Capable Not Capable
LTL UTL LTL UTL
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Process Capability Specs: 1.5 +/- 0.01 Mean: 1.505 Std. Dev. = 0.002 Are we in trouble?
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Process Capability Specs: 1.5 +/- 0.01
LTL = 1.5 – 0.01 = 1.49 UTL = 1.5 + 0.01 = 1.51
Mean: 1.505 Std. Dev. = 0.002 LCL = 1.505 - 3*0.002 = 1.499 UCL = 1.505 + 0.006 = 1.511
1.499 1.511.49 1.511
ProcessSpecs
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Capability Index Capability Index (Cpk) will tell the position of
the control limits relative to the design specifications.
Cpk>= 1.0, process is capable
Cpk< 1.0, process is not capable
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Process Capability, Cpk
Tells how well parts produced fit into specs
33min
XUTLor
LTLXC pk
ProcessSpecs
3 3LTL UTLX
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Process Capability Tells how well parts produced fit into specs
For our example:
Cpk= min[ 0.015/.006, 0.005/0.006] Cpk= min[2.5,0.833] = 0.833 < 1 Process not capable
33min
XUTLor
LTLXC pk
006.0
505.151.1
006.0
49.1505.1min orC pk
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Process Capability: Re-centered If process were properly centered Specs: 1.5 +/- 0.01
LTL = 1.5 – 0.01 = 1.49 UTL = 1.5 + 0.01 = 1.51
Mean: 1.5 Std. Dev. = 0.002 LCL = 1.5 - 3*0.002 = 1.494 UCL = 1.5 + 0.006 = 1.506
1.494 1.511.49 1.506
ProcessSpecs
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If re-centered, it would be Capable
1.494 1.511.49 1.506
ProcessSpecs
67.1006.0
01.0,
006.0
01.0min
006.0
5.151.1,
006.0
49.15.1min
pk
pk
C
C
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Packaged Goods What are the Tolerance Levels? What we have to do to measure capability? What are the sources of variability?
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Production Process
Make Candy
Package Put in big bagsMake Candy
Make Candy
Make Candy
Make Candy
Make Candy
Mix
Mix %
Candy irregularity
Wrong wt. Wrong wt.
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Processes Involved Candy Manufacturing:
Are M&Ms uniform size & weight? Should be easier with plain than peanut Percentage of broken items (probably from printing)
Mixing: Is proper color mix in each bag?
Individual packages: Are same # put in each package? Is same weight put in each package?
Large bags: Are same number of packages put in each bag? Is same weight put in each bag?
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Your Job Write down package #
Weigh package and candies, all together, in grams and ounces
Write down weights on form Optional:
Open package, count total # candies Count # of each color Write down Eat candies
Turn in form and empty complete wrappers for weighing
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The effects of rounding
17.00
18.00
19.00
20.00
21.00
22.00
23.00
24.00
25.00
14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5
Original Weight in grams
Ro
un
de
d W
eig
ht
- g
ram
s
0.50
0.60
0.70
0.80
Ro
un
de
d W
eig
ht
- O
un
ce
s
g - rounded
oz - rounded 0.7 Ounces
20 grams
0.6 Ounces
19 grams
18 grams
21 grams
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Peanut Color Mix website
Brown 17.7% 20% Yellow 8.2% 20% Red 9.5% 20% Blue 15.4% 20% Orange 26.4% 10% Green 22.7% 10%
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Class website Brown 12.1% 30% Yellow 14.7% 20% Red 11.4% 20% Blue 19.5% 10% Orange 21.2% 10% Green 21.2% 10%
Plain Color Mix
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So who cares? Dept. of Commerce National Institutes of Standards & Technology NIST Handbook 133 Fair Packaging and Labeling Act
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Acceptable?
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Package Weight “Not Labeled for Individual Retail Sale” If individual is 18g MAV is 10% = 1.8g Nothing can be below 18g – 1.8g = 16.2g
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Goal of Control Charts collect and present data visually allow us to see when trend appears see when “out of control” point occurs
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0102030405060
1 2 3 4 5 6 7 8 9 10 11 12
Process Control Charts Graph of sample data plotted over time
UCL
LCL
Process Average ± 3
Time
X
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0102030405060
1 2 3 4 5 6 7 8 9 10 11 12
Process Control Charts Graph of sample data plotted over time
Assignable Cause Variation
Natural Variation
UCL
LCL
Time
X
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Attributes vs. VariablesAttributes: Good / bad, works / doesn’t count % bad (P chart) count # defects / item (C chart)
Variables: measure length, weight, temperature (x-bar
chart) measure variability in length (R chart)
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p Chart ExampleYou’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control (use z = 3)?
© 1995 Corel Corp.
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p Chart Hotel DataNo. No. Not
Day Rooms Ready Proportion
1 200 16 16/200 = .0802 200 7 .0353 200 21 .1054 200 17 .0855 200 25 .1256 200 19 .0957 200 16 .080
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p Chart Control Limits
n
n
k
ii
k
1 14007
200
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p Chart Control Limits16 + 7 +...+ 16
p
X
n
ii
k
ii
k
1
1
1211400
0864.n
n
k
ii
k
1 14007
200
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p Chart Control Limits
# Defective Items in Sample i
Sample iSize
UCL p zp
n
p
X
n
p
ii
k
ii
k
(1 - p)
1
1
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p Chart Control Limits
# Defective Items in Sample i
Sample iSize
UCL p zp p)
n
p
X
n
p
ii
k
ii
k
(1
1
1
z = 2 for 95.5% limits; z = 3 for 99.7% limits
# Samples
n
n
k
ii
k
1
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p Chart Control Limits
# Defective Items in Sample i
# Samples
Sample iSize
z = 2 for 95.5% limits; z = 3 for 99.7% limits
LCL p z
n
n
kp
X
n
p
ii
k
ii
k
ii
k
1 1
1
and
p p)
n
(1
UCL p zp p)
np (1
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p Chart
pp 3 0864 3.n
p p) (1
200
.0864 * (1-.0864)
p
X
n
ii
k
ii
k
1
1
1211400
0864.n
n
k
ii
k
1 14007
200
16 + 7 +...+ 16
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p Chart
0864 0596 1460. . . or & .0268
pp 3 0864 3.n
p p) (1
200
.0864 * (1-.0864)
p
X
n
ii
k
ii
k
1
1
1211400
0864.n
n
k
ii
k
1 14007
200
16 + 7 +...+ 16
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0.00
0.05
0.10
0.15
1 2 3 4 5 6 7
P
Day
p Chart
UCL
LCL
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R Chart Type of variables control chart
Interval or ratio scaled numerical data
Shows sample ranges over time Difference between smallest & largest values in
inspection sample
Monitors variability in process Example: Weigh samples of coffee & compute
ranges of samples; Plot
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You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?
Hotel Example
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Hotel Data
Day Delivery Time
1 7.30 4.20 6.10 3.45 5.552 4.60 8.70 7.60 4.43 7.623 5.98 2.92 6.20 4.20 5.104 7.20 5.10 5.19 6.80 4.215 4.00 4.50 5.50 1.89 4.466 10.10 8.10 6.50 5.06 6.947 6.77 5.08 5.90 6.90 9.30
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R &X Chart Hotel Data Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32
7.30 + 4.20 + 6.10 + 3.45 + 5.55 5
Sample Mean =
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R &X Chart Hotel Data Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32 3.85
7.30 - 3.45Sample Range =
Largest Smallest
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R &X Chart Hotel Data Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32 3.852 4.60 8.70 7.60 4.43 7.62 6.59 4.273 5.98 2.92 6.20 4.20 5.10 4.88 3.284 7.20 5.10 5.19 6.80 4.21 5.70 2.995 4.00 4.50 5.50 1.89 4.46 4.07 3.616 10.10 8.10 6.50 5.06 6.94 7.34 5.047 6.77 5.08 5.90 6.90 9.30 6.79 4.22
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R Chart Control Limits
UCL D R
LCL D R
R
R
k
R
R
ii
k
4
3
1
Sample Range at Time i
# Samples
From Exhibit 6.13
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Control Chart Limits
n A2 D3 D4
2 1.88 0 3.278
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
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R
R Chart Control Limits
R
k
ii
k
1 3 85 4 27 4 227
3 894. . .
.
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R Chart Solution
From 6.13 (n = 5)
R
R
k
UCL D R
LCL D R
ii
k
R
R
1
4
3
3 85 4 27 4 227
3 894
(2.11) (3.894) 8 232
(0)(3.894) 0
. . ..
.
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02468
1 2 3 4 5 6 7
R, Minutes
Day
R Chart Solution
UCL
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X Chart Control Limits
UCL X A R
X
X
k
X
ii
k
2
1
Sample Range at Time i
# SamplesR
R
k
iii
k
1
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X Chart Control Limits
UCL X A R
LCL X A R
X
X
kR
R
k
X
X
ii
k
ii
k
2
2
1 1
Sample Range at Time i
# Samples
Sample Mean at Time i
From 6.13
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Exhibit 6.13 Limits
n A2 D3 D4
2 1.88 0 3.278
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
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R &X Chart Hotel Data Sample
Day Delivery Time Mean Range
1 7.30 4.20 6.10 3.45 5.55 5.32 3.852 4.60 8.70 7.60 4.43 7.62 6.59 4.273 5.98 2.92 6.20 4.20 5.10 4.88 3.284 7.20 5.10 5.19 6.80 4.21 5.70 2.995 4.00 4.50 5.50 1.89 4.46 4.07 3.616 10.10 8.10 6.50 5.06 6.94 7.34 5.047 6.77 5.08 5.90 6.90 9.30 6.79 4.22
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X Chart Control Limits
X
X
k
R
R
k
ii
k
ii
k
1
1
5 32 6 59 6 797
5 813
3 85 4 27 4 227
3 894
. . ..
. . ..
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X Chart Control Limits
From 6.13 (n = 5)
X
X
k
R
R
k
UCL X A R
ii
k
ii
k
X
1
1
2
5 32 6 59 6 797
5 813
3 85 4 27 4 227
3 894
5 813 0 58 * 3 894 8 060
. . ..
. . ..
. . . .
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X Chart Solution
From 6.13 (n = 5)
X
X
k
R
R
k
UCL X A R
LCL X A R
ii
k
ii
k
X
X
1
1
2
2
5 32 6 59 6 797
5 813
3 85 4 27 4 227
3 894
5 813 (0 58)
5 813 (0 58)(3.894) = 3.566
. . ..
. . ..
. .
. .
(3.894) = 8.060
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X Chart Solution*
02468
1 2 3 4 5 6 7
X, Minutes
Day
UCL
LCL
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Thinking ChallengeYou’re manager of a 500-room hotel. The hotel owner tells you that it takes too long to deliver luggage to the room (even if the process may be in control). What do you do?
© 1995 Corel Corp.
N
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Redesign the luggage delivery process Use TQM tools
Cause & effect diagrams Process flow charts Pareto charts
Solution
Method People
Material Equipment
Too Long
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Dilbert’s View
11/27/06
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Fortune Story 58 large companies have announced Six
Sigma efforts 91% trailed S&P 500 since then, according to
Qualpro, (which has its own competing system)
July 11, 2006
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Qualpro’s “Six Problems with Six Sigma” Six sigma novices get “low hanging fruit” “Without years of
experience under the guidance of an expert, they will not develop the needed competence”
Green belts get advice from people who don’t have experience implementing it
Loosely organized methodology doesn’t guarantee results (and they do?)
Six Sigma uses simple math – not “Multivariable Testing” (MVT)
Six Sigma training for all is expensive, time-consuming Pressure to “do something” – low value projects
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Six Sigma Narrow focus on improving existing
processes Best and Brightest not focused on developing
new products Fortune July 11, 2006
Can be overly bureaucratic
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Final Thought Early 1980’s, IBM Canada,
(Markham Ont.) Ordered from new supplier in Japan. Acceptable quality level 1.5%
defects, a fairly high standard at the time.
The Japanese firm sent the order with a few parts packed separately, & the following letter ...
© 1995 Corel Corp.
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Final Thought
Dear IBM:
We don’t know why you want 1.5% defective parts, but for your convenience we have packed them separately.
Sincerely,
© 1995 Corel Corp.