Question

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?

Answer #1

A fraction nonconforming control chart with center line 0.10,
UCL = 0.19, and LCL = 0.01 is used to control a process.
Find the average run length if the process fraction noncon-
forming shifts to 0.20.

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 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 control chart indicates that the current process
fraction nonconforming is 0.02. If 50 items are
inspected each day, what is the probability of detect-
ing a shift in the fraction nonconforming to 0.04 on
the first day after the shift? By the end of the third
day following the shift?

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...

Determine the fraction of nonconforming product control chart
upper limit when the standard given is 0.01 proportion of
nonconfroming
Determine the Average Run Length (ARL) of a x-bar chart with
limits where the process has shifted 0.25 times the standard
deviation in one direction

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?

Random samples of size n= 400 are taken from a
population with p= 0.15.
a.Calculate the centerline, the upper control
limit (UCL), and the lower control limit (LCL) for the p
chart.
b.Suppose six samples of size 400 produced the
following sample proportions: 0.06, 0.11, 0.09, 0.08, 0.14, and
0.16. Is the production process under control?

A rum producer monitors the position of its label on the bottle
by sampling two bottles from each batch. One quantity measured is
the distance from the bottom of the bottle neck to the top of the
label. The process mean should be μ = 1.6 inches. Past experience
indicates that the distance varies with σ = 0.15 inch. (a) The mean
distance x for each batch sample is plotted on an x control chart.
Calculate the center line and...

A rum producer monitors the position of its label on the bottle
by sampling three bottles from each batch. One quantity measured is
the distance from the bottom of the bottle neck to the top of the
label. The process mean should be μ = 1.6 inches. Past
experience indicates that the distance varies with σ =
0.15 inch.
(a) The mean distance x for each batch sample is
plotted on an x control chart. Calculate the center line and...

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