Question

The fraction of nonconforming units from a manufacturing process is 0.01. A random sample of 100 units is drawn from the process. What is the probability that at most 1% of the units in the sample are nonconforming?

Answer #1

since, fraction of nonconforming units from a manufacturing process = 0.01 = p

Total sample drawn (n) = 100

Consider, X - number of nonconforming units from a manufacturing process

Since, property(conforming or nonconforming) of each units is independent.

then,

Since 1% 100 = 1

Then Probability that at most 1% of the units in the sample are nonconforming

To obtain this probability we can use excel---

command in excel is ---

The output is ---

This is respective probability.

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 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 ??

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 production process operates with 1% nonconforming output.
Every hour a sample of 30 units of product is taken, and the number
of nonconforming units counted. If one or more nonconforming units
are found, the process is stopped and the quality control
technician must search for the cause of nonconforming
production.
What is the probability that one or more nonconforming units are
found? (hint: binomial distribution)

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 production process operates with 1% nonconforming output.
Every hour a sample of 25 units of product is taken, and the number
of nonconforming units counted. If one or more nonconforming units
are found, the process is stopped and the quality control
technician must search for the cause of nonconforming production.
Evaluate the performance of this decision rule.

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?

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