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?

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?

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?

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...

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...

A process is in statistical control with ?̿ = 39.7 and ? = 2.5.
The control chart uses a sample size of ? = 2. Specifications for
the process are at 40±5. The quality characteristic is normally
distributed. What is the process capability ratio?

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...

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...

A luxury hotel tracks the number of complaints per month. When
the process is in control, there is an average of 36 complaints per
month. Assume the number of complaints per month is distributed as
Poisson.
Compute upper and lower control limits for a c-chart using 95
percent level of confidence.
Suppose for the past six months the number of complaints per
month were 15, 26, 35, 43, 49, and 56 respectively. Plot the number
of complaints per month on...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 8 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 14 minutes ago

asked 17 minutes ago

asked 17 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 32 minutes ago