Post on 22-Dec-2015
INT 506/706: Total Quality Management
Lec #6, Process Capability
Outline
• Individual values vs. averages• Control limits vs. Specs• 6σ spread versus specs• Calculating Process Capability Indices
2
Process Capability
Individual vs. averages
Individual vs. averages
nX
The ability of X-bar to approximate μ is measured by the following equation:
Individual vs. averages
24
ˆor ˆd
R
c
s
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).
Control limits vs Specifications
A process under control exhibits:
1. 2/3 of points near center
2. Few points close to the center
3. Points around centerline
4. Points balanced on both sides
5. No points beyond control limits
6. No patterns or trends
Control limits vs Specifications
6σ Spread versus Specs
24
ˆor ˆd
R
c
s
3 Possible CASES1) 6σ < USL – LSL2) 6σ = USL – LSL3) 6σ > USL - LSL
CASE #1 6σ < USL – LSL
CASE #2 6σ = USL – LSL
CASE #3 6σ > USL – LSL
Calculating 6σ
Assuming process is STABLE and IN CONTROL
1. 20 subgroups of n=4
2. Calculate sample std dev, si, for each sample
3. Calculate average sample std dev,
4. Calculate pop std dev
5. Multiply pop std dev *6
m
ss
m
ii
1
4
ˆc
s
Example
Example
126.0)021.0(6ˆ6
021.09400.0
02.0ˆ
02.021
414.021
015.0...029.0031.0
4
1
c
s
m
ss
m
ii
Capability Index Cp
6Cp
LSLUSL
Capability Index Cp
794.0126.0
95.1105.12ˆ6
Cp
LSLUSL
EXAMPLE
INTERPRETATION:Process NOT capable (case 3)
Capability Ratio, Cr
LSLUSL
6Cr
Inverse of Cp so larger the ratio, the LESS capable the process is of meeting specifications
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)=
Cpk
Cpk
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?