Two decision rules are given here. Assume they apply to a normally distributed quality characteristic and the sample size is n = 5. Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that 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 α-error probability for the control chart under Rule 2?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question

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

Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that 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 α-error probability for the control chart under Rule 2?

(b) Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude
that 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?
Transcribed Image Text:(b) Rule 2: If all of the next seven sample averages fall on the same side of the center line, conclude that 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?
Q2. Two decision rules are given here. Assume they apply to a normally distributed quality
characteristic and the sample size is n = 5.
Transcribed Image Text:Q2. Two decision rules are given here. Assume they apply to a normally distributed quality characteristic and the sample size is n = 5.
Expert Solution
Step 1

Sol:-

i) Assuming that the quality characteristic is normally distributed, the probability of a sample average falling on the upper side of the center line can be calculated using the standard normal distribution.

The center line represents the mean of the process, so if the process is in control, the probability of a sample average falling on the upper side of the center line is 0.5.

 

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON