Cp Cpk & GRR
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TV = tolerance value
• • • • • Different appraiser Different offset Different position Different condition Long time
GRR ( Repeatability, Reproducibility )
Data list
Run Device 1 2 3 4 5 6 7 8 9 10 1 0.58 0.67 0.49 0.84 0.49 0.77 0.72 0.58 0.58 0.54 2 0.67 0.84 0.56 0.72 0.49 0.67 0.74 0.44 0.81 0.63 3 0.58 0.70 0.60 0.86 0.47 0.77 0.74 0.42 0.77 0.51 4 0.65 0.84 0.44 0.70 0.54 0.72 0.65 0.56 0.79 0.65 5 0.63 0.70 0.49 0.84 0.44 0.74 0.70 0.37 0.74 0.54 6 0.65 0.65 0.56 0.79 0.51 0.70 0.77 0.47 0.79 0.58 7 0.74 0.70 0.60 0.72 0.44 0.81 0.63 0.49 0.84 0.60 8 0.70 0.72 0.54 0.79 0.47 0.54 0.77 0.63 0.74 0.58 9 0.56 0.86 0.51 0.77 0.47 0.79 0.58 0.42 0.77 0.54
K : | ( USL + LSL ) / 2 - μ | / ( ( USL – LSL ) / 2 ) LCL : Lower Standard Limit UCL : Higher Standard Limit
GRR ( Repeatability, Reproducibility )
Repeatibility – Equipment variation
RC DC
Repeatability
It based on range data
RX = Average ( RA , RB , RC ) R = RX * K1
K1 = 3.55
Reproducibility
It based on reading data
Groups Average range ( RY ) RY = Max ( DA , DB , DC ) - Min ( DA , DB , DC )
RA DA
Data List - group B
Device 1 2 3 4 5 6 7 8 9 10 Ave 4 0.65 0.84 0.44 0.70 0.54 0.72 0.65 0.56 0.79 0.65 0.654 5 0.63 0.70 0.49 0.84 0.44 0.74 0.70 0.37 0.74 0.54 0.619 0.640 6 Range 0.65 0.02 0.65 0.19 0.56 0.12 0.79 0.14 0.51 0.10 0.70 0.04 0.77 0.12 0.47 0.19 0.79 0.05 0.58 0.11 0.647 0.108
RB DB
Data List - group C
Device 1 2 3 4 5 6 7 8 9 10 Ave 7 0.74 0.70 0.60 0.72 0.44 0.81 0.63 0.49 0.84 0.60 0.657 8 0.70 0.72 0.54 0.79 0.47 0.54 0.77 0.63 0.74 0.58 0.648 0.644 9 Range 0.56 0.18 0.86 0.16 0.51 0.09 0.77 0.07 0.47 0.03 0.79 0.27 0.58 0.19 0.42 0.21 0.77 0.10 0.54 0.06 0.627 0.136
Cpl
• Cpl = ( μ - LSL ) / 3 σ
• Cpu = ( USL - μ ) / 3 σ
Cpu
LSL USL
: Lower Standard Limit : Higher Standard Limit
CP
CP = ( USL - LSL ) / 6σ CP < 1.0 1.0 - 1.3 Rating non-capable barely capable
R2 = | ( RY*K2 )2 - R2 / D * G |
K2 D G
= = =
3.14 10 3
( no of devices ) ( no of group )
GRR
GRR2 = R2 + R2
GRR % =Hale Waihona Puke BaiduGRR / TV * 100%
GRR % < 10% 10 - 20% 20 - 30% > 30% Rating Excellent good performance acceptable non-acceptable
• • • • • • Same appraiser Same offset Same device Same position Same condition Short time
GRR ( Repeatability, Reproducibility )
Reproducibility – Appraiser variation
Data List - group A
Device 1 2 3 4 5 6 7 8 9 10 Ave 1 0.58 0.67 0.49 0.84 0.49 0.77 0.72 0.58 0.58 0.54 0.626 2 0.67 0.84 0.56 0.72 0.49 0.67 0.74 0.44 0.81 0.63 0.657 0.642 3 Range 0.58 0.09 0.70 0.17 0.60 0.11 0.86 0.14 0.47 0.02 0.77 0.10 0.74 0.02 0.42 0.16 0.77 0.23 0.51 0.12 0.642 0.116
1.3 – 1.6
> 2.0
good capability
excellent capability
Cpk
• Cpl = ( μ - LSL ) / 3 σ
• Cpu = ( USL - μ ) / 3 σ • Cp = ( USL - LSL ) / 6 σ • Cpk = Min ( Cpl , Cpu ) or ( 1 – K ) x Cp
Cp Cpk & GRR
Written by Ivan Liu 2002/02/01
Data distribution - I
Data Analysis
• μ ( average ) μ = x1+ x2+….+ xN / N
•
σ ( Standard deviation ) σ2 = (x1 -μ)2+ (x2 -μ)2+…..+ (xN -μ)2 / ( N – 1 )