Concordia Institute for Information Systems EngineeringINSE 6220 – Advanced Statistical Approaches to QualityMidterm Exam 1 -- Fall 2007Instructor: A. Ben HamzaDate: Friday, October 19, 2007Duration: 90 minutesINSTRUCTIONS:- Answer all questions on these sheets in the space provided, and if you run out of space please usethe back of the page (indicate clearly)- The use of any non-communicating c
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Concordia Institute for Information Systems Engineering
INSE 6220 – Advanced Statistical Approaches to Quality
Midterm Exam 1 -- Fall 2007
Instructor: A. Ben Hamza
Date: Friday, October 19, 2007
Duration: 90 minutes
INSTRUCTIONS:
- Answer all questions on these sheets in the space provided, and if you run out of space please use
the back of the page (indicate clearly)
- The use of any non-communicating calculator is permitted. Only one double-sided sheet of notes is
permitted.
- This exam is 7 pages long, including the cover page and appendices. Check that your copy is
complete.
- This exam is out of 100 points.
GRADING (For Professor’s use only)
1. (40 points) | 2. (30 points) | 3. (30 points)
Total (100 points)
INSE 6220 – Fall 2007 - 1 - Midterm Exam 1
INSE 6220 Fall 2007 Midterm Exam 1
Question 1:
1) Suppose that a random sample of size n is taken from a normal population with mean µ and
variance σ2. Fill in the blank space with TRUE or FALSE.
• ( ) The mean and variance of the Poisson distribution are equal.
• ( ) The variance of the sample mean is var(X) = n σ2
• ( ) The expected value of the sample variance is E(S) = σ
• ( ) The expected value of the average range is E(R) = σ
• ( ) If σ is unknown and you wish to test H0 : µ = µ0, H1 : µ = µ0 using a probability of
type I error α. Then, H0 should not be rejected if -tα/2,n-1 S ≤ √n(X -µ0) ≤ tα/2,n-1 S
2) Samples of n = 4 items are taken from a manufacturing process at regular intervals. A normally
distributed quality characteristic is measured and X and S values are calculated at each sample. After
50 subgroups have been analyzed, we have 50 i=1 Xi = 1000 and 50 i=1 Si = 72. Further, assume that
the upper and lower specification limits are USL = 23 and LSL = 15 respectively.
a) Calculate the control limits for the X chart and S chart.
b) Calculate the process capability potential Cp, and comment on your result.
c) Calculate the probabilities ˆ prework = P(X > USL) and ˆ pscrap = P(X ≤ LSL).
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INSE 6220 Fall 2007 Midterm Exam 1
Question 2:
The output voltage of a power supply is assumed to be normally distributed. The mean voltage is
equal to 12, and the standard deviation is unknown. Sixteen observations taken at random on voltage
are as follows:
10.35 | 9.30 | 10 | 9.96 | 11.65 | 12 | 11.25 | 9.58 | 11.54 | 9.95 | 10.28 | 8.37 | 10.44 | 9.25 | 9.38 | 10.85a) Set up a two-sided hypothesis test.
b) Calculate the test statistic, and comment on your result when α = 0.05.
c) Construct a 90% two-sided confidence interval on µ.
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INSE 6220 Fall 2007 Midterm Exam 1
Question 3: The following data of 20 samples were collected from a process manufacturing power
supplies. The variable of interest is output voltage, and the sample size is n = 5.
Sample number X R | Sample number X R
20 103 2a) Calculate the control limits for the X chart and R chart.
b) Calculate the estimate ˆ σX of the process standard deviation.
c) Calculate the apparent 3-sigma natural tolerance limits X - 3ˆ σX and X + 3ˆ σX
d) What would be your estimate of the process fraction nonconforming if the specifications on the
characteristic were 103 ± 4? Hint: use the probabilities defined in part c) of Question 1.
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