Introduction to Statistical Quality Control

7th Edition

ISBN: 9781118146811

Author: Montgomery, Douglas C.

Publisher: John Wiley & Sons Inc

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Textbook Question

Chapter 3, Problem 61E

Derive the mean and variance of the exponential distribution.

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 3, Problem 60E

Chapter 3, Problem 62E

Chapter 3 Solutions

Introduction to Statistical Quality Control

Ch. 3 - The content of liquid detergent bottles is being...Ch. 3 - The bore diameters of eight randomly selected...Ch. 3 - The service time in minutes from admit to...Ch. 3 - The Really Cool Clothing Company sells its...Ch. 3 - The nine measurements that follow are furnace...Ch. 3 - Consider the furnace temperature data in Exercise...Ch. 3 - Yield strengths of circular tubes with end caps...Ch. 3 - The time to failure in hours of an electronic...Ch. 3 - The data shown in Table 3E.2 are chemical process...Ch. 3 - An article in Quality Engineering (Vol. 4, 1992,...

Ch. 3 - Construct and interpret a normal probability plot...Ch. 3 - Construct and interpret a normal probability plot...Ch. 3 - Construct a normal probability plot of the failure...Ch. 3 - Construct a normal probability plot of the...Ch. 3 - Consider the viscosity data in Exercise 3.10....Ch. 3 - Table 3E.4 contains 20 observations on cycles to...Ch. 3 - An important quality characteristic of water is...Ch. 3 - Consider the outpatient service times in Exercise...Ch. 3 - Consider the call handling limes in Exercise 3.4....Ch. 3 - Consider the viscosity data in Exercise 3.10....Ch. 3 - Reconsider the yield data in Exercise 3.9....Ch. 3 - Consider the concentration of suspended solids...Ch. 3 - Consider the chemical process yield data in...Ch. 3 - Consider the chemical process yield data in...Ch. 3 - Construct a box plot for the data in Exercise 3.1.Ch. 3 - Construct a box plot for the data in Exercise 3.2.Ch. 3 - Suppose that two fair dice are tossed and the...Ch. 3 - Find the mean and variance of the random variable...Ch. 3 - A mechatronic assembly is subjected to a final...Ch. 3 - The probability distribution of x is f(x) = kex, 0...Ch. 3 - The random variable x takes on the values 1, 2, or...Ch. 3 - The probability distribution of the discrete...Ch. 3 - A manufacturer of electronic calculators offers a...Ch. 3 - The net contents in ounces of canned soup is a...Ch. 3 - A production process operates with 1 %...Ch. 3 - Continuation of Exercise 3.35. Consider the...Ch. 3 - A random sample of 50 units is drawn from a...Ch. 3 - A sample of 100 units is selected from a...Ch. 3 - Suppose that 10% of the adult population has blood...Ch. 3 - Patients arriving at an outpatient clinic are...Ch. 3 - A stock brokerage has four computers that are used...Ch. 3 - A computer system uses passwords consisting of the...Ch. 3 - An electronic component for a medical X-ray unit...Ch. 3 - A lot of size N = 30 contains three nonconforming...Ch. 3 - A textbook has 500 pages on which typographical...Ch. 3 - Surface-finish defects in a small electric...Ch. 3 - Glass bottles are formed by pouring molten glass...Ch. 3 - The billing department of a major credit card...Ch. 3 - A production process operates in one of two...Ch. 3 - An inspector is looking for nonconforming welds in...Ch. 3 - The tensile strength of a metal part is normally...Ch. 3 - The output voltage of a power supply is normally...Ch. 3 - Continuation of Exercise 3.52. Reconsider the...Ch. 3 - If x is normally distributed with mean and...Ch. 3 - The life of an automotive battery is normally...Ch. 3 - A lightbulb has a normally distributed light...Ch. 3 - Derive the mean and variance of the binomial...Ch. 3 - Derive the mean and variance of the Poisson...Ch. 3 - Derive the mean and variance of the exponential...Ch. 3 - Derive the mean and variance of the geometric...

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