Question

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 lower and upper specification limits of a process are given as 779 and 791 respectively. The process standard deviation is estimated to be 1.8. The process mean has shifted to 782.

What is the potential capability ratio of the process?

Answer 1

What is the actual capability ratio of the process?

3

A process has a target mean of 91. If the process mean shifts to 93, we want to detect this shift using a cusum chart of which control limits are ±8. Suppose we collect individual measurements from the process and the first observed value is 91.8.

What is the first C+ value to be plotted on the cusum chart if
we use a 50% headstart?

What is the first C+ value to be plotted on the cusum chart without
using a headstart?

4

Sample 1 2 3

Defectives 7 8 12

Sample_size 50 90 160

The above table shows the number of nonconforming (defective) units in the three samples. Based on the given sample data, we want to setup a control chart to monitor the fraction nonconforming (defective) of the process.

What is the center line of the chart?

Answer 1

What is the first point, corresponding to the first sample, to be
plotted on the chart?

Answer #1

1)

The null and alternate hypothesis are:

H0: The process is in control.

Ha: The process is out of control.

Required probability = P(shift is detected on the first subsequent sample)

Now,

Now, we know

So, Required probability =

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 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?

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...

A quality manager asked his team to implement p control chart
for a process that was recently introduced. The team collected
samples of size n = 100 parts hourly over a period of 30 hours and
determined the proportion of nonconforming parts for each sample.
The mean proportion of nonconforming parts for 30 samples turned
out to be 0.025.
Determine the upper and lower control limits for the p chart.
(2 Points)
Discuss how you will use the p Chart...

HCH Manufacturing has decided to use a p-Chart with 2-sigma
control limits to monitor the proportion of defective steel bars
produced by their production process. The quality control manager
randomly samples 250 steel bars at 12 successively selected time
periods and counts the number of defective steel bars in the
sample.
Sample Defects
1 7
2 10
3 14
4 8
5 9
6 11
7 9
8 9
9 14
10 11
11 7
12 8
Step 1 of...

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?

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?

Chapter 8, Problem 38
Incorrect.
Samples of size n=6 are collected from a process every hour.
After 20 samples have been collected, we construct the control
chart with σ=1.40, UCL = 21 and LCL=18. Suppose that the
mean shifts to 18.5. (a) What is the probability
that this shift will be detected on the next sample? Round your
answer to four decimal places (e.g. 98.7654). (b)
What is the ARL after the shift? Round your answer to three decimal
places...

Suppose that the sample means and ranges are calculated for 36
samples of size n = 5 for a process that is considered under
statistical control. Then the mean of the 36 sample means and
ranges are calculated, yielding 20.50 and 5.60,
respectively:
Determine the value of the process capability index if the
process specification limits are 20 +- 6 .
Is the process capable?

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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