int 506/706: total quality management
DESCRIPTION
INT 506/706: Total Quality Management. Lec #6, Process Capability. Outline. Individual values vs. averages Control limits vs. Specs 6 σ spread versus specs Calculating Process Capability Indices. Process Capability. Individual vs. averages. Individual vs. averages. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/1.jpg)
INT 506/706: Total Quality ManagementLec #6, Process Capability
![Page 2: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/2.jpg)
Outline
• Individual values vs. averages• Control limits vs. Specs• 6σ spread versus specs• Calculating Process Capability Indices
2
![Page 3: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/3.jpg)
Process Capability
![Page 4: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/4.jpg)
Individual vs. averages
![Page 5: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/5.jpg)
Individual vs. averages
nX
The ability of X-bar to approximate μ is measured by the following equation:
![Page 6: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/6.jpg)
Individual vs. averages
24
ˆor ˆdR
cs
IF the process can be assumed to be normal, the population standard deviation can be estimated from either
the sample standard deviation (s) or the range (R).
![Page 7: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/7.jpg)
Control limits vs Specifications
A process under control exhibits:1. 2/3 of points near center 2. Few points close to the center3. Points around centerline4. Points balanced on both sides5. No points beyond control limits6. No patterns or trends
![Page 8: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/8.jpg)
Control limits vs Specifications
![Page 9: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/9.jpg)
6σ Spread versus Specs
24
ˆor ˆdR
cs
3 Possible CASES1) 6σ < USL – LSL2) 6σ = USL – LSL3) 6σ > USL - LSL
![Page 10: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/10.jpg)
CASE #1 6σ < USL – LSL
![Page 11: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/11.jpg)
CASE #2 6σ = USL – LSL
![Page 12: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/12.jpg)
CASE #3 6σ > USL – LSL
![Page 13: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/13.jpg)
Calculating 6σ
Assuming process is STABLE and IN CONTROL
1. 20 subgroups of n=42. Calculate sample std dev, si, for each sample3. Calculate average sample std dev,
4. Calculate pop std dev5. Multiply pop std dev *6
m
ss
m
ii
1
4
ˆcs
![Page 14: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/14.jpg)
Example
![Page 15: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/15.jpg)
Example
126.0)021.0(6ˆ6
021.09400.002.0ˆ
02.021414.0
21015.0...029.0031.0
4
1
cs
m
ss
m
ii
![Page 16: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/16.jpg)
Capability Index Cp
6Cp
LSLUSL
![Page 17: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/17.jpg)
Capability Index Cp
794.0126.0
95.1105.12ˆ6
Cp
LSLUSL
EXAMPLE
INTERPRETATION:Process NOT capable (case 3)
![Page 18: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/18.jpg)
Capability Ratio, Cr
LSLUSL
6Cr
Inverse of Cp so larger the ratio, the LESS capable the process is of meeting specifications
![Page 19: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/19.jpg)
Cpk
3(min)Cpk
Z
Cp and Cr do not take into account the centering of the process
ˆ)(
ˆ)(Z
LSLXLSLZ
or
XUSLUSL
Where Z(min)=
![Page 20: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/20.jpg)
Cpk
![Page 21: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/21.jpg)
Cpk
![Page 22: INT 506/706: Total Quality Management](https://reader035.vdocuments.net/reader035/viewer/2022062410/568161e8550346895dd21574/html5/thumbnails/22.jpg)
Review
• Review pdf file in blackboard – “CapabilityCaseStudy”– Put into Minitab and run capability modules to see
what you come up with• Is it the same as the case study?• Do you understand the interpretation of the case study?