Transcript GAGE AND MEASUREMENT SYSTEM CAPABILITY STUDIES

IE405 QUALITY MANAGEMENT
Recitation 7
-Process Capability Cp and Cpk
values
-Gage and Measurement System
Capability Studies
NOVEMBER 26TH 2002
Process Capability Ratios
POTENTIAL
CAPABILITY
USL  LSL
Cp 
6ˆ
ACTUAL
CAPABILITY
(USL  ˆ )
Cpu 
3ˆ
( ˆ  LSL )
Cpl 
3ˆ
Cpk  min(Cpu, Cpl)
Rec7 Q1
S b a r  7 5 0/ 2 5  3 0
S b a r/ c 4  0,9 2 1 3
780  620
Cp 
 160 / 195 .372  0.818
6ˆ
PROCESS IS NOT CAPABLE
POSSIBLE ALTERNATIVES
-Change specification limits
-Reduce variability
Rec7 Q1
Cpk for 700:
– Cpu:0,818 ; Cpl:0,818
Process is producing product that does not
conform to specifications.
Cpk for 740
-Cpu: 0,4094 ; Cpl:1,22 Choose Cpu
Producing products that do not conform to
specifications
Rec7 Q1
Cpk for 780:
– Cpu:0 ; Cpl:1,637
Choose Cpu
Average is equal to one of the specification
limits
Cpk for 740
-Cpu:- 0.409 ; Cpl:2,0473 Choose Cpu
Average is outside specifications.
Rec7 Q2
R CHART for diameters on N.C. Lathe
Machine
0,05
UCL=0,04564
0,04
R
0,03
0,02
0,02
0,02
0,02
0,02
Centerline=0,02
0,01
0,01
LCL=0
0,00
1
2
3
Batch
Number
4
5
Rec 7 Q2
X CHART for diameters of N.C. Lathe Machine
2,045
UCL
2,04
2,04
2,035
2,03
X
Centerline
2,025
2,02
2,02
LCL
2,015
1
2
3
C3
4
5
Rec7 Q2
•
•
•
•
Cp=2.05-1,99/6*0,0971 =0,1029
Process is not capable
Cpk (Cpu:0,0186 ; Cpl:-0,187) choose Cpl
Average is outside specification limits
• P(x<1.99) +P(x>2.05) =0.017
1.7% defective
GAGE AND MEASUREMENT
SYSTEM CAPABILITY STUDIES
 TOTAL   PRODUCT   GAGE
2
2
2
Characteristics of the X and R charts in gage and
measurement system capability studies
• X chart shows the DISCRIMINATING
POWER of the instrument, ability of the
gage to distinguish between units of
product.
• R chart shows the MAGNITUDE of
measurement error, or gage capability.
• R values represent the difference between
measurements made on the same unit
using the same instrument.
Components of Measurement Error
• Reproducibility : due to different
operators using the gage (different time
periods,different environments, or in general
different conditions)
• Repeatibility: as reflecting the basic
inherent precision of the gage itself
 measuremen terror   gage
2
2
  gage   repeatibility  
2
2
2
reproducibility
OPE
R
A
T
O
R
2
OPE
R
A
T
O
R
1
Part Number
Xbar
R
1
2
3
1
5
4
5
4,666667
2
4
4
4
3
5
5
4
4
5
5
Xbar
R
1
2
3
1
5
5
4
4,666667
1
4
0
4
4
5
4,333333
1
4
4,666667
1
4
4
4
4
0
4
5
4,333333
1
3
4
4
3,666667
1
5
5
5
0
5
5
6
5,333333
1
4,533333
0,6
4,4
0,8
Rec7 Q3
 2 gage r 2epeatibility   2reproducibility
REPRODUCIBILITY
REPEATABILITY
1
* ( R1  R2 )  0,4134
2
d 2  1,693......
Rx  X max X min
R
sin ce....n  3
R
   0,7 / 1,693  0,4134
d2
Rx  4.533 4.4  0.133
R
   0,133/ 1,128  0,1179
d2
Rec7 Q3
P (6 *ˆ gage ) 6 * (0,1847)


 0,3694
T USL  LSL
4,5  1,5
P/T OF 0.1 or LESS often implies
adequate gage capability