
Introduction . Variable - a single quality characteristic that can be measured on a numerical scale . When working with variables, we should monitor both the mean value of the characteristic and the variability associated with the characteristic . Control Charts for and R (1).
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Control Charts for Variables
Notation for variables control charts
Control Charts for Variables
Notation and values
Ri = xmax - xmin
Control Charts for Variables
Statistical Basis of the Charts
Control Charts for Variables
Statistical Basis of the Charts
Control Charts for Variables
Control Limits for the chart
Control Charts for Variables
Control Limits for the R chart
Control Charts for Variables
Estimating the ProcessStandard Deviation
Relative range: W=R/σ
E(W)=E(R/σ)=d2
Control Charts for Variables
Trial Control Limits
Control Charts for Variables
Trial control limits and the out-of-control process
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
規格公差
T
=
Cp=
6σ
6個估計標準差
單邊規格:
=
規格上限-製程平均值
SU-X
=
Cp=
3σ
3個估計標準差
或
=
製程平均值-規格下限
X-SL
=
Cp=
3σ
3個估計標準差
製程精密度Cp(process capability ratio,PCR)Control Charts for Variables
Control Charts for Variables
If Cp > 1, then a low number of nonconforming items will be produced.
Control Charts for Variables
**The Cp statistic assumes that the process mean is centered at the midpoint of the specification band – it measures potential capability.
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Allocating Sampling Effort
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Limits
A2、D3、D4 are selected for the new sample size
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
L= multiple of standard error in the control limits
k = shift in process mean (#of standard deviations).
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
ATS=ARLh
I=nARL
Control Charts for Variables
where c4 is a constant
Control Charts for Variables
Control Charts for Variables
No Standard σGiven
sample standard deviation,
Control Charts for Variables
Chart when Using S
The upper and lower control limits for the chart are given as
where A3 is found in the Appendix
Control Charts for Variables
Estimating Process Standard Deviation
Control Charts for Variables
Control Charts for Variables
m = the number of samples selected.
ni = size of the ith sample
Control Charts for Variables
Control Charts for Variables
Control Charts for Variables
where and are points found from the chi-square distribution.
Control Charts for Variables
n = 1.
Control Charts for Variables
Control Charts for Variables
Moving Range Chart
MRi = |xi - xi-1|
which will indicate possible shifts or changes in the process from one observation to the next.
Control Charts for Variables
X and Moving Range Charts
where
Control Charts for Variables
X and Moving Range Charts
Control Charts for Variables
Control Charts for Variables
Example
Ten successive heats of a steel alloy are tested for hardness. The resulting data are
Heat Hardness Heat Hardness
1 52 6 52
2 51 7 50
3 54 8 51
4 55 9 58
5 50 10 51
Control Charts for Variables
Interpretation of the Charts
Control Charts for Variables
Average Run Lengths
Control Charts for Variables
Control Charts for Variables