Question

A process is in control and normally distributed with ? control chart limits of 45 and 15. The subgroup size is 4. Suppose the process variance suddenly triples while process mean remains unchanged. What is the probability that the first subsequent subgroup average will fall outside the control limits? What are the ? probability and ARL?

Answer #1

note that ...P(Z<z) has been calculated from the standard Normal table

A process is in control and normally distributed with ? control
chart limits of 45 and 15. The subgroup size is 4. Suppose the
process variance suddenly triples while process mean remains
unchanged. What is the probability that the first subsequent
subgroup average will fall outside the control limits? What are the
? probability and ARL? Suppose the process variance suddenly
triples while process mean shifts downward to 10. What are the β
probability and ARL now?

A control chart for fraction nonconforming indicates that the
current process average is 0.03. The sample size is constant at 200
units. a) Find the three-sigma control limits for the control
chart. b) What is the probability that a shift in the process
average to 0.08 will be detected on the first subsequent sample?
(Hint: use normal approximation) c) What is the probability that
this shift will be detected on the second sample taken after the
shift?

A process is controlled with a fraction nonconforming control
chart with three-sigma limits, ? = 100. Suppose that the center
line = 0.10.
(a) Suppose that the percentage of conforming units in sample ?
is ?? . What distribution should ?? follow? Use a Normal
distribution to approximate the distribution of ?? . Specify the
mean and the variance of this Normal distribution.
(b) Find the upper and lower control limit for this fraction
nonconforming chart.
(c) Find the equivalent...

1
An x̅ chart with a sample size of 4 is used to control the mean
of a normally distributed quality characteristic. It is known that
process standard deviation is 8. The upper and lower control limits
of the chart are 147 and 123 respectively. Assume the process mean
shifts to 121.
What is the probability that this shift is detected on the first
subsequent sample?
What is expected number of samples taken before the shift is
detected?
2
The...

A fraction nonconforming control chart with n = 400 has the
following parameters: UCL = 0.0962, Center line = 0.0500, LCL =
0.0038
a. Find the width of the control limits in standard deviation
units.
b. Suppose the process fraction nonconforming shifts to 0.15.
What is the probability of detecting the shift on the first
subsequent sample?

Process in statistical control has a mean of 100.0 and standard
deviation of 3.0. ?_bar and ? charts with subgroups of size 7 are
used to monitor the process. If the process center shifts downward
to 96.0, what is the probability of first point falling outside
?_bar chart control limits is on the third sample taken after the
shift?

Aspen Plastics produces plastic bottles to customer order. To
monitor the
process, statistical process control charts are used. The central
line of the chart for
the sample means is set at 8.50 and the range at 0.31in. Assume
that the sample
size is 6 and the specification for the bottle neck diameter is
8.50 ± 0.25.
a. Calculate the control limits for the mean and range charts. (3
points)
b. Suppose that the standard deviation of the process distribution
is...

The inspection unit of the manufacturing process is one unit of
product. Suppose 20 nonconformities were identified in inspecting
41 units and a control chart is to be set up for this manufacturing
process. What are the three-sigma control limits and ?-risk for
this control chart? What is the ?-risk and ARL if the average
number of nonconformities per unit is two?

The inspection unit of a manufacturing process is one unit of
product. Suppose 20 nonconformities were identified in inspecting
41 units and a control chart is to be set up for this manufacturing
process. What are the three-sigma control limits and ?-risk for
this control chart? What is the ?-risk and ARL if the average
number of nonconformities per unit is two?

Control charts for x bar and R with subgroup size=4
are used to monitor a normally distributed quality characteristic.
The control charts parameter were: X bar chart UCL=813, x bar chart
CL=800, x bar chart LCL=787. R chart UCL=46.98, R chart CL=20.59, R
chart LCL=0, both charts exhibit control. If the process mean shift
from 800 to 780. What is the probability of detecting this shift on
or before the second sample?
A.
0.9934
B.
0.9834
C.
0.9993
D.
0.9894...

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