Probability and Statistics for Engineering and the Sciences

9th Edition

ISBN: 9781305251809

Author: Jay L. Devore

Publisher: Cengage Learning

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Textbook Question

Chapter 16.5, Problem 31E

The standard deviation of a certain dimension on an aircraft part is .005 cm. What CUSUM procedure will give an in-control ARL of 600 and an out-of-control ARL of 4 when the mean value of the dimension shifts by .004 cm?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 16.5, Problem 30E

Chapter 16.5, Problem 32E

Chapter 16 Solutions

Probability and Statistics for Engineering and the Sciences

Ch. 16.1 - A control chart for thickness of rolled-steel...Ch. 16.1 - Refer to Exercise 1 and suppose the ten most...Ch. 16.1 - Suppose a control chart is constructed so that the...Ch. 16.1 - A cork intended for use in a wine bottle is...Ch. 16.1 - If a process variable is normally distributed, in...Ch. 16.2 - In the case of known and , what control limits...Ch. 16.2 - Consider a 3-sigma control chart with a center...Ch. 16.2 - The table below gives data on moisture content for...Ch. 16.2 - Refer to the data given in Exercise 8, and...Ch. 16.2 - When installing a bath faucet, it is important to...

Ch. 16.2 - The accompanying table gives sample means and...Ch. 16.2 - The accompanying table gives sample means and...Ch. 16.2 - Prob. 13E Ch. 16.2 - Prob. 14E Ch. 16.2 - Prob. 15E Ch. 16.3 - A manufacturer of dustless chalk instituted a...Ch. 16.3 - Subgroups of power supply units are selected once...Ch. 16.3 - Prob. 18E Ch. 16.3 - The accompanying table gives sample means and...Ch. 16.3 - Prob. 20E Ch. 16.4 - On each of the previous 25 days, 100 electronic...Ch. 16.4 - A sample of 200 ROM computer chips was selected on...Ch. 16.4 - Prob. 23E Ch. 16.4 - Prob. 24E Ch. 16.4 - Prob. 25E Ch. 16.4 - Prob. 26E Ch. 16.4 - Prob. 27E Ch. 16.4 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - The standard deviation of a certain dimension on...Ch. 16.5 - Prob. 32E Ch. 16.6 - Consider the single-sample plan with c = 2 and n =...Ch. 16.6 - A sample of 50 items is to be selected from a...Ch. 16.6 - Prob. 35E Ch. 16.6 - Develop a single-sample plan for which AQL = .02...Ch. 16.6 - Consider the double-sampling plan for which both...Ch. 16.6 - Prob. 38E Ch. 16.6 - Refer to Example 16.11, in which a single-sample...Ch. 16.6 - Consider the single-sample plan that utilizes n =...Ch. 16 - Observations on shear strength for 26 subgroups of...Ch. 16 - The number of scratches on the surface of each of...Ch. 16 - The following numbers are observations on tensile...Ch. 16 - Prob. 44SE Ch. 16 - Prob. 46SE

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The standard deviation of a certain dimension on an aircraft part is .005 cm. What CUSUM procedure will give an in-control ARL of 600 and an out-of-control ARL of 4 when the mean value of the dimension shifts by .004 cm?

Solution Summary: The author calculates the CUSUM procedure for an in-control AR of 600 and an out-of- control ARL of 4 when the mean value of the dimension shifts by 0.004.

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Chapter 16 Solutions