IE 361 Exam Keys F2011

# IE 361 Exam Keys F2011 - IE 316 Exam 1 Fall 2011 I have...

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1 IE 316 Exam 1 Fall 2011 I have neither given nor received unauthorized assistance on this exam. ________________________________________________________ Name Signed Date _________________________________________________________ Name Printed

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2 1. Suppose the actual diameters x in a batch of steel cylinders are normally distributed with mean 2.5025 x inch and standard deviation .004 x inch. Suppose further, that associated with the measurement of any cylinder is a measurement error independent of (a randomly selected) x and normal with mean 0 and standard deviation device .003 inch. ( is perhaps produced by small inconsistencies in how the measuring device is used and unavoidable/unpredictable small mechanical and electrical effects in the device.) a) Modeling a measurement y (of a randomly selected cylinder) as yx exactly what probability distribution is appropriate for y ? (Name the distribution and give numerical values for its parameters.) b) The modeling in a) (and, actually, all we've done in IE 361) ignores the fact that real measurement is digital (measurements are made only "to the nearest something"). Sometimes (not always) this is OK. But more careful modeling treats a digital measurement * y derived from y by "rounding to the nearest something" as discrete. In the present context, measurements to the nearest .01 inch might be described using the pmf below. Show how the probability for * 2.50 y was derived. Then compare the mean and standard deviation of * y to those of y (from a) ) and x . * y * fy 2.52 .0062 2.51 .3023 2.50 .6247 2.49 .0666 2.48 .0002 7 pts 7 pts
3 2. See ±²³ Reports #1 attached at the end of this exam. They concerns some measurements made on the machined inside diameter of a single steel forklift wheel (units are inches) using a single gauge. Use the information on those reports in answering the following questions. (The 18 measurements together have sample mean 2.04748 inch and sample standard deviation .00343 inch.) a) Consider first only the measurements made by Operators #1 and #2. Give 95% confidence limits for the difference in measurement biases for the two operators. b) What would your interval from a) estimate if every measurement had been made on a different wheel produced by a stable production process (assuming that the two "gauge-operator" combinations constitute linear measurement devices)? Now consider the measurements from all 6 operators (on the single wheel). c) Give 95% confidence limits for a repeatability standard deviation. d) Give 95% confidence limits for the standard deviation of operator biases. 7 pts 5 pts 6 pts 6 pts

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4 e) Under the one-way random effects model, the Operator-sample-means are from a normal distribution with standard deviation 22 reproducibility repeatability 1 3 . If one computes the sample standard deviation of the operator-sample-means here, one gets the value .003633 inch. Use this to make 95% confidence limits for reproducibility repeatability 1 3 . Say why your limits are (or are not) consistent with your answer to d) .
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IE 361 Exam Keys F2011 - IE 316 Exam 1 Fall 2011 I have...

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