ARL refers to the average number of samples (or points) plotted to see an out-of-control signal
For a process that is in-control,
ARL0=1/a
For a process that is out-of-control,
ARL1=1/(1-b)
ARLs are used to help evaluate decisions on sample size and sampling frequency
Sampling Frequency: In-Control ARL (ARL0)
For the X-chart with 3s limits, a = 0.0027
Therefore, in-control ARL = 1/0.0027 = 370.
This means that if the process
remains unchanged, one
out-of-control signal will be
generated every 370 samples.
If the sampling interval is 1 hr,
one false alarm will be seen
every 370 hrs typically.
Sampling Frequency: Out-of-Control ARL
Now suppose the process has drifted by 3s.
Probability of X still within the 3s limits = 0.5
Thus, out-of-control ARL = 1/(1 - 0.5) = 2.
This means from the time the
process shifted, the chart needs
2 samples to detect the shift.
If the sampling interval is 1 hr,
Average Time to Signal (ATS)
or exposure is 2 hrs typically.
shiny888 (2007-8-15 20:14:25)
Master can u tell me where are this terms from?TS 5 tools or others?
junezhang (2007-8-15 21:00:17)
Thank the 2nd floor for clear description. Now I know the actual meaning.Before I have uncertain understanding.
最新回复
大风雪 (2007-8-15 13:32:52)
For a process that is in-control,
ARL0=1/a
For a process that is out-of-control,
ARL1=1/(1-b)
ARLs are used to help evaluate decisions on sample size and sampling frequency
Sampling Frequency: In-Control ARL (ARL0)
For the X-chart with 3s limits, a = 0.0027
Therefore, in-control ARL = 1/0.0027 = 370.
This means that if the process
remains unchanged, one
out-of-control signal will be
generated every 370 samples.
If the sampling interval is 1 hr,
one false alarm will be seen
every 370 hrs typically.
Sampling Frequency: Out-of-Control ARL
Now suppose the process has drifted by 3s.
Probability of X still within the 3s limits = 0.5
Thus, out-of-control ARL = 1/(1 - 0.5) = 2.
This means from the time the
process shifted, the chart needs
2 samples to detect the shift.
If the sampling interval is 1 hr,
Average Time to Signal (ATS)
or exposure is 2 hrs typically.
shiny888 (2007-8-15 20:14:25)
junezhang (2007-8-15 21:00:17)
chao19837181 (2007-8-15 21:35:05)
yongyouyang (2007-8-18 10:54:19)