Questions and Answers > Concordia Institute for Information Systems Engineering INSE 6220 – Advanced Statistical Approaches to Quality Midterm Exam 1 -- Fall 2007

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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). 2 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. 3 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. [Show More]

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