六西格玛黑带培训教材

Process Performance
Cpk
Reject Rate
1.0
0.13 – 0.27 %
1.1
0.05 – 0.10 %
1.2
0.02 – 0.03 %
1.3
48.1 – 96.2 ppm
1.4
13.4 – 26.7 ppm
1.5
3.4 – 6.8 ppm
1.6
794 – 1589 ppb
Specification Limits (LSL and USL)
• created by design engineering in response to customer requirements to specify the tolerance for a product’s characteristic
Cp
Reject Rate
1.00
0.270 %
1.33
0.007 %
1.50
6.8 ppm
2.00
2.0 ppb
Process Potential
a)
b)
c) a) Process is highly capable (Cp>2) b) Process is capable (Cp=1 to 2) c) Process is not capable (Cp<1)
• A process operating in the presence of assignable causes of variation is said to be “out-of-control”
Process Capability
Process Capability is the inherent reproducibility of a process’s output. It measures how well the process is currently behaving with respect to the output specifications. It refers to the uniformity of the process.
Process Potential
The Cp index compares the allowable spread (USL-LSL) against the process spread (6). It fails to take into account if the process is not centered between the specification limits.
a) percentage (%) b) parts per million (ppm) c) parts per billion (ppb)
Process Capability
Process Capability studies can • indicate the consistency of the process output • indicate the degree to which the output meets specifications • be used for comparison with another process or competitor
Process is centered
Process is not centered
Process Performance
The Cpk index relates the scaled distance between the process mean and the nearest specification limit.
Inherent or Natural Variation
• Due to the cumulative effect of many small unavoidable causes • A process operating with only chance causes of variation present is
Process Potential Index (Cp)
Cpk
1.0
1.2
1.4
1.6
1.8
2.0
1.0 2,699.9 1,363.3 1,350.0 1,350.0 1,350.0 1,350.0
• Process Performance – Cpu – Cpl – Cpk
Process Potential
The Cp index assesses whether the natural tolerance (6 ) of a process is within the specification limits.
Example 1A
Example 1B
Example 1C
Example 1D
Process Capability
For a normally distributed characteristic, the defective rate F(x) may be
estimated via the following:
• Short-Term vs Long-Term Process Capability • Process Capability for Non-Normal Data
– Cycle-Time (Exponential Distribution) – Reject Rate (Binomial Distribution) – Defect Rate (Poisson Distribution)
Process Variation
Process Variation is the inevitable differences among individual measurements or units produced by a process.
Sources of Variation
• within unit • between units • between lots • between lines • across time • measurement error
Three Types of Limits
Distribution of Individual Values Distribution of Sample Averages
Process Capability Indices
Two measures of process capability
• Process Potential – Cp
六西格玛黑带培训教材
2020年5月22日星期五
Scope of Module
• Process Variation • Process Capability
– Specification, Process and Control Limits – Process Potential vs Process Performance
Process Capability vs Specification Limits
a)
b)
c)
a) Process is highly capable b) Process is marginally capable c) Process is not capable
Three Types of Limits
LSL
USL
For characteristics with only one specification limit: a) LSL only b) USL only
Example 2
Specification Limits :
4 to 16 g
Machine (a) (b) (c) (d)
Mean 10 10 7 13
1,350
1,350
2,700
7
2
-1.5 4.5
66,807
3 66,811
13
1
-9.0 3.0
0
1,350
1,350
Lower Spec Limit = 4 g Upper Spec Limit = 16 g
Process Potential vs Process Performance
(a) Poor Process Potential (b) Poor Process Performance
Process Potential
A Cp of 1.0 indicates that a process is judged to be “capable”, i.e. if the process is centered within its engineering tolerance, 0.27% of parts produced will be beyond specification limits.
Example 1
Specification Limits :
4 to 16 g
Machine (a) (b) (c) (d)
Mean 10 10 7 13
Std Dev 4 2 2 1
Determine the corresponding Cp and Cpk for each machine.
said to be “in statistical control”
Types of Variation
Special or Assignable Variation
• May be due to a) improperly adjusted machine b) operator error c) defective raw material
1.7
170 – 340 ppb
1.8
33 – 67 ppb
1.9
6 – 12 ppb
2.0
1 – 2 ppb
Process Performance
a)
Cp = 2
Cpk = 2
b)
Cp = 2 Cpk = 1
c)
Cp = 2
Cpk < 1
a) Process is highly capable (Cpk>1.5) b) Process is capable (Cpk=1 to 1.5) c) Process is not capable (Cpk<1)
Std Dev 4 2 2 1
Determine the defective rate for each machine.
Example 2
Mean Std Dev ZLSL ZUSL
10
4
-1.5 1.5
F(x<LSL) F(x>USL) F(x)
66,807
66,807 133,614
ቤተ መጻሕፍቲ ባይዱ10
2
-3.0 3.0
(positional variation) (unit-unit variation) (lot-lot variation) (line-line variation) (time-time variation) (repeatability & reproducibility)
Types of Variation
LSL
USL
LSL
USL
Experimental Design • to reduce variation
Experimental Design • to center mean • to reduce variation
Process Potential vs Process Performance
Capability is often thought of in terms of the proportion of output that will be within product specification tolerances. The frequency of defectives produced may be measured in
Process Limits (LPL and UPL)
• measures the variation of a process • the natural 6 limits of the measured characteristic
Control Limits (LCL and UCL)
• measures the variation of a sample statistic (mean, variance, proportion, etc)