Concept explainers
Consider a 3-sigma control chart with a center line at µ0 and based on n = 5. Assuming normality, calculate the probability that a single point will fall outside the control limits when the actual process
a. µ0 + .5σ
b. µ0 − σ
c. µ0 + 2σ
a.
Find the probability that a single point will fall outside the control limits when the actual process mean is
Answer to Problem 7E
The probability that a single point will fall outside the control limits when the actual process mean is
Explanation of Solution
Given info:
Consider, a 3-sigma control chart based on center line
Calculation:
It is known that for a 3-sigma chart the probability that a single point will fall outside the control limits when the actual process mean is
It is known that, for a random variable X that follows normal distribution with mean
Thus,
Now, for
According to table A.3, “Standard Normal Curve Areas” of Appendix the standard normal variable value for
Thus,
Thus, the probability that a single point will fall outside the control limits when the actual process mean is
b.
Find the probability that a single point will fall outside the control limits when the actual process mean is
Answer to Problem 7E
The probability that a single point will fall outside the control limits when the actual process mean is
Explanation of Solution
Calculation:
It is known that for a 3-sigma chart the probability that a single point will fall outside the control limits when the actual process mean is
It is known that, for a random variable X that follows normal distribution with mean
Thus,
Now, for
According to table A.3, “Standard Normal Curve Areas” of Appendix the standard normal variable value for
Thus,
Thus, the probability that a single point will fall outside the control limits when the actual process mean is
c.
Find the probability that a single point will fall outside the control limits when the actual process mean is
Answer to Problem 7E
The probability that a single point will fall outside the control limits when the actual process mean is
Explanation of Solution
Calculation:
It is known that for a 3-sigma chart the probability that a single point will fall outside the control limits when the actual process mean is
It is known that, for a random variable X that follows normal distribution with mean
Thus,
Now, for
According to table A.3, “Standard Normal Curve Areas” of Appendix the standard normal variable value for
Thus,
Thus, the probability that a single point will fall outside the control limits when the actual process mean is
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Chapter 16 Solutions
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