Question

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?

Answer #1

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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 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?

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 operating at 0.15 fraction nonconforming.
We desire to catch a shift to 0.19 fraction nonconforming on the
fraction nonconforming chart with probability 90% on the first
sample taken after the shift. What should be the sample size
??

A process is operating at 0.15 fraction nonconforming. We desire
to catch a shift to 0.19 fraction nonconforming on the fraction
nonconforming chart with probability 90% on the first sample taken
after the shift. What should be the sample size ?

A process is operating at 0.15 fraction nonconforming. We desire
to catch a shift to 0.19 fraction nonconforming on the fraction
nonconforming chart with probability 90% on the first sample taken
after the shift. What should be the sample size ??

A process is operating at 0.15 fraction nonconforming. We desire
to catch a shift to 0.19 fraction nonconforming on the fraction
nonconforming chart with probability 90% on the first sample taken
after the shift. What should be the sample size ??

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 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.

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