Two decision rules are given here. Assume they apply to a normally distributed quality characteristic and the sample size is n = 5. Q2. Two decision rules are given here. Assume they apply to a normally distributed qualitycharacteristic and the sample size is n = 5.(a) Rule 1: The control chart uses the three-sigma control limits. If one or more of the next sevensamples yield values of the sample average that fall outside the control limits, conclude that theprocess is out of control.i) What is the probability that a sample average is outside the 3-sigma control limits?ii) What is the a-error probability for the control chart under Rule 1?(b) Rule 2: If all of the next seven sample averages fall on the same side of the center line, concludethat the process is out of control.i) What is the probability of a sample average fall on the upper side of the center line?ii) What is the a-error probability for the control chart under Rule 2?

Answered: Q2. Two decision rules are given here.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Two decision rules are given here. Assume they apply to a normally distributed quality characteristic and the sample size is n = 5.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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The sample size is $n = 5$ .