Question

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?

Answer #1

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...

Broody Plastics produces plastic bottles for the customer
orders. Statistical process control charts is being used to monitor
all the process. assume that the sample size is 4 and the
specification for the bottle neck diameter is 6.00+-0.35.
(Note that the central line of chart for the sample means is set
at 6.00 and the range at 0.4 in.)
(a) Calculate control limits for the mean and range charts.
(b) If the firm is looking for the three-sigma performance, is...

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 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 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 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?

A process is known to be in a state of statistical control with
a mean of 10 microns and a standard deviation of 2 microns. What is
the probability that a single sample taken from this process will
yield a value of 14 microns or larger?

The following are quality control data for a manufacturing
process at Kensport Chemical Company. The data show the temperature
in degrees centigrade at five points in time during a manufacturing
cycle.
Sample
x
R
1
95.72
1.0
2
95.24
0.9
3
95.18
0.7
4
95.42
0.4
5
95.46
0.5
6
95.32
1.1
7
95.40
0.9
8
95.44
0.3
9
95.08
0.2
10
95.50
0.6
11
95.80
0.6
12
95.22
0.2
13
95.58
1.3
14
95.22
0.6
15
95.04
0.8
16...

A process in control has an estimated standard deviation of 2
mm. The product produced by this process has specification limits
of 120 ± 8 mm and a target value of 120 mm.
Calculate the process capability indices Cp and
Cpk for the process if the process mean shifts from 118 mm
first to 122 mm and then to 124 mm, but the process variability
remains the same.
What will be the yield of the process for each of three...

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