Download Quality - SUNY New Paltz

Quality:
Statistical
Process
Control
Common Causes
n
∑x
x=
∑(x − x)
2
i
σ=
i =1
n
425
Assignable Causes
Grams
Average
Grams
Assignable Causes
Average
(c) Shape
n−1
Assignable Causes
Average
(a) Location
i
Grams
(b) Spread
Grams
Effects of Assignable Causes on
Process Control
Out of control
(assignable causes present)
Sample Means and the
Process Distribution
Effects of Assignable Causes on
Process Control
Mean
Process
distribution
In Control
(no assignable causes)
425
Sample Means and the
Process Distribution
Mean
Grams
The Normal
Distribution
Distribution of
sample means
σ = Standard deviation
Process
distribution
425
Mean
–3σ –2σ –1σ
+1σ +2σ +3σ
68.26%
95.44%
99.74%
Grams
Control Charts
UCL
1
Assignable
causes likely
2
Samples
Using Control Charts for
Process Improvement
Nominal
•
•
LCL
•
•
3
Measure the process
When changes are indicated, find
the assignable cause
Eliminate problems, incorporate
improvements
Repeat the cycle
Control Chart Examples
Variations
UCL
Nominal
LCL
Sample number
LCL
Control Chart Examples
Nominal
LCL
Sample number
UCL
Variations
UCL
Variations
Nominal
Sample number
Control Chart Examples
Nominal
LCL
Sample number
Control Chart Examples
Control Limits and Errors
UCL
Variations
UCL
Variations
Control Chart Examples
Type I error:
Probability of searching for
a cause when none exists
Type II error:
Probability of concluding
that nothing has changed
Nominal
UCL
LCL
Shift in process
average
Sample number
Process
average
LCL
Two-sigma limits
Control Charts
for Variables
Special Metal Screw
Sample
Number
1
2
3
4
5
1
0.5014
0.5021
0.5018
0.5008
0.5041
Sample
2
3
0.5022 0.5009
0.5041 0.5024
0.5026 0.5035
0.5034 0.5024
0.5056 0.5034
Control Charts
for Variables
Control Charts – Special Metal Screw
R-Charts
4
0.5027
0.5020
0.5023
0.5015
0.5047
R = 0.0021
UCLR = D4R
LCLR = D3R
Control Charts
for
Variables
Control Chart
Factors
Size of
Sample
(n)
Factor for UCL
and LCL for
x-Charts
(A2)
Factor for
LCL for
R-Charts
(D3)
Factor
UCL for
R-Charts
(D4)
2
3
4
5
6
7
1.880
1.023
0.729
0.577
0.483
0.419
0
0
0
0
0
0.076
3.267
2.575
2.282
2.115
2.004
1.924
Control Charts
for Variables
Control Charts—Special Metal Screw
R-Charts
R = 0.0021
UCLR = D4R
LCLR = D3R
D4 = 2.282
D3 = 0
UCLR = 2.282 (0.0021) = 0.00479 in.
LCLR = 0 (0.0021) = 0 in.
Control Charts
for Variables
Range Chart Special Metal Screw
Control Charts—Special Metal Screw
x-Charts
R = 0.0021
x= = 0.5027
A2 = 0.729
UCLx = x= + A2R
LCLx = x= - A2R
UCLx = 0.5027 + 0.729 (0.0021) = 0.5042 in.
LCLx = 0.5027 – 0.729 (0.0021) = 0.5012 in.
x-Chart—
Special Metal Screw
x-Chart—
Special Metal Screw
•
•
•
•
Control Charts
for Variables Using σ
UCLx = x= + zσx
LCL = x= – zσ
x
σx = σ / n
x
Sunny Dale Bank
=
x = 5.0 minutes
σ = 1.5 minutes
n = 6 customers
z = 1.96
Measure the process
Find the assignable cause
Eliminate the problem
Repeat the cycle
Control Charts
for Variables Using σ
UCLx = x= + zσx
LCL = x= – zσ
x
x
σx = σ / n
Sunny Dale Bank
=
x = 5.0 minutes
σ = 1.5 minutes
n = 6 customers
z = 1.96
UCLx = 5.0 + 1.96(1.5)/
6 = 6.20 min
UCLx = 5.0 – 1.96(1.5)/
6 = 3.80 min
Control Charts
for Attributes
Control Charts
for Attributes
Hometown Bank
Hometown Bank
UCLp = p + zσp
LCLp = p – zσp
σp =
p(1 – p)/n
Sample
Number
Wrong
Account Number
1
2
3
4
5
6
7
8
9
10
11
σ12
p =
Total
15
12
19
2
19
4
24
7
10
17
15
3
UCLp = p + zσp
LCLp = p - zσp
Control Charts
for Attributes
Control Charts
for Attributes
Hometown Bank
Hometown Bank
n = 2500 p = 0.0049
n = 2500
Total defectives
p = Total observations
UCLp = p + zσp
LCLp = p – zσp
σp =
p(1 - p)/n
147
Control Charts
for Attributes
p(1 – p)/n
p-Chart
Wrong Account Numbers
Hometown Bank
n = 2500 p = 0.0049
UCLp = 0.0049 + 3(0.0014)
LCLp = 0.0049 – 3(0.0014)
σp = 0.0014
p-Chart
Wrong Account Numbers
•
•
•
•
Measure the process
Find the assignable cause
Eliminate the problem
Repeat the cycle
Control Charts
for Attributes
Woodland
Paper
Company
Control Charts
for Attributes
Woodland
Paper
Company
c = 20
Control Charts
for Attributes
Woodland
Paper
Company
z=2
UCLc = c + z
c
LCLc = c – z c
•
•
•
•
Woodland
Paper
Company
Control Charts
for Attributes
Measure the process
Find the assignable cause
Incorporate the problem
Repeat the cycle
Process Capability
Nominal
value
Process distribution
Lower
specification
800
Upper
specification
1000
1200
Hours
(a) Process is capable
Process Capability
Process Capability
Nominal value
Six sigma
Nominal
value
Four sigma
Process distribution
Lower
specification
800
Upper
specification
1000
(b) Process is not capable
1200
Two sigma
Lower
specification
Upper
specification
Hours
Mean
Process Capability
Process Capability
Lightbulb Production
Lightbulb Production
Upper specification = 1200 hours
Lower specification = 800 hours
Average life = 900 hours σ = 48 hours
Upper specification = 1200 hours
Lower specification = 800 hours
Average life = 900 hours σ = 48 hours
Cp =
Upper specification Lower specification
6σ
Process Capability Ratio
Process Capability
Process Capability
Lightbulb Production
Lightbulb Production
Cp = 1.39
Upper specification = 1200 hours
Lower specification = 800 hours
Average life = 900 hours σ = 48 hours
Cp = 1.39
Upper specification = 1200 hours
Lower specification = 800 hours
Average life = 900 hours σ = 48 hours
Cpk =
Minimum of
x= – Lower specification
3σ
Process
Capability
Index
Process Capability
Lightbulb Production
Upper specification = 1200 hours
Lower specification = 800 hours
Average life = 900 hours σ = 48 hours
Cpk = 0.69
Cp = 1.39
Process
Capability
Index
Process
Capability
Ratio
Upper specification – =
x
3σ
,