Concept explainers
Consider a 3-sigma control chart with a center line at µ0 and based on n = 5. Assuming normality, calculate the
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
Want to see more full solutions like this?
Chapter 16 Solutions
Probability and Statistics for Engineering and the Sciences
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill