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2013 | OriginalPaper | Chapter

10. Estimation and Statistical Quality Control

Authors : Cheng-Few Lee, John C. Lee, Alice C. Lee

Published in: Statistics for Business and Financial Economics

Publisher: Springer New York

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Abstract

In the previous two chapters, we discussed the basic principles of sampling and sampling distributions – techniques that enable us to make inferences about a population by looking at a subset of that population. In this chapter, we continue our discussion of inferential statistics by examining point estimation, confidence intervals, and statistical quality control. Note that this chapter draws heavily on your understanding of the standard normal distribution discussed in Chap.​ 7, the fundamental concepts of sampling discussed in Chap.​ 8, and the t distribution and chi-square distribution discussed in Chap.​ 9.

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previous chapter Other Continuous Distributions and Moments for Distributions
next chapter Hypothesis Testing
Appendix
Available only for authorised users
Footnotes
1
From the combination formula discussed in Appendix 1 of Chap.​ 5, we obtain
$$ \left( {\begin{array}{lll} {50} \\{10} \\\end{array}} \right)=\frac{50! }{10!(50-10)! }=\frac{{(50)(49)\cdots (41)}}{{(10)(9)\cdots (1)}}=10,272,278,000 $$
 
2
If we divide the sum of squared discrepancies from \( \bar{X} \) by (n−1) rather than n, Eq. 9.11 in Chap.​ 9 can be used to demonstrate this point.
 
3
R. A. Fisher (1922), “On the Mathematical Foundations of Theoretical Statistics,” Phil. Trans. Roy. Soc. London. Series A, Vol. 222.
 
4
$$ \begin{array}{lll} E{{(\hat{\uptheta} -\uptheta )}^2} & = E{{[\hat{\uptheta} -E(\hat{\uptheta} )+E(\hat{\uptheta} )-\uptheta ]}^2} \\ & = E{{[\hat{\uptheta} -E(\hat{\uptheta} )]}^2}+{{[E(\hat{\uptheta} )-\uptheta ]}^2}+2E[\hat{\uptheta} -E(\hat{\uptheta} )][E(\hat{\uptheta} )-\uptheta ] \\ & = E{{[\hat{\uptheta} -E(\hat{\uptheta} )]}^2}+{{[E(\hat{\uptheta} )-\uptheta ]}^2}\quad \mathrm{ because}\;E[\hat{\uptheta} -E(\hat{\uptheta} )]=0\end{array} $$
 
5
This and the next section are essentially drawn from J. R. Evans and W. M. Lindsay (1989), The Management and Control of Quality (St. Paul, MN: West), Chaps. 12, 13, and 15. Reprinted by permission by West Publishing Company. All rights reserved. The main reason for including quality control in this chapter is that the construction and use of control charts in process control are similar to the construction and use of interval estimates discussed in the last five sections. Note, however, that the interval estimate focused on the static estimate of confidence intervals based on fixed populations, whereas quality control charts involve the dynamic estimate of confidence intervals to detect potential changes in populations.
 
6
W. J. Stevenson (1990), Production/Operations Management, 3rd ed. (Homewood, IL: Irwin); E. L. Grant and R. S. Leavenworth (1988), Statistical Quality Control, 6th ed. (New York: McGraw-Hill); G. K. Griffith (1989), Statistical Process Control Methods for Long and Short Runs (Milwaukee, WI: ASQC Quality Press); and J. R. Evans and W. M. Lindsay (1989), The Management and Control of Quality, (St. Paul, MN: West).
 
7
The formula for determining optimal sample size can be found in Sect. 20.​4.
 
8
In quality control, given standard deviation means the quality standards of a product are given.
 
9
In quality control work, control limits are three standard errors on either side of the mean of the sampling distribution. These limits are called 3−σ limits.
 
10
If the underlying sampling is the Poisson distribution as discussed in Sect. 6.​7, then the \( \bar{x} \) and \( \bar{s} \) can be defined as \( \bar{c} \) and \( \sqrt{\bar{c}} \), respectively (\( \bar{c} \) is defined as the mean number of defects per unit). In this situation the \( \bar{X} \) -chart defined in Eqs. 10.17a and 10.17b is called the C-chart (see Evans and Lindsay, 1989, pp. 366–368).
 
11
See T. T. Ryan (1989), Statistical Methods for Quality Improvement (New York: Wiley), for a detailed discussion of this relationship.
 
12
This example is drawn from J. R. Evans and W. M. Lindsay (1989). The Management and Control of Quality (St. Paul, MN: West), pp. 317–323 and pp. 359–360.
 
13
This example is drawn from Evans and Lindsay (1989), pp. 332–333.
 
14
M. Britto and R. M. Oliver (1986), “Forecasting Donors and Donations,” Journal of Forecasting 5, 39–55.
 
15
H. L. Guffey, J. R. Harris, and J. F. Laumer (1979), “Shopper Attitudes Toward Shoplifting and Shoplifting Prevention Devices,” Journal of Retailing 55, 75–99.
 
16
This section on Miller and Orr’s model for cash management is taken from Cheng F. Lee and Joseph E. Finnerty (1990), Corporate Finance: Theory, Method, and Applications (New York: Harcourt) pp. 595–598.
 
Metadata
Title
Estimation and Statistical Quality Control
Authors
Cheng-Few Lee
John C. Lee
Alice C. Lee
Copyright Year
2013
Publisher
Springer New York
Book
Statistics for Business and Financial Economics

Print ISBN: 978-1-4614-5896-8

Electronic ISBN: 978-1-4614-5897-5

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4614-5897-5_10