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# Introduction to SQC - D Montgomery - Ch04 rev

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Introduction to SQC - D Montgomery - Ch04 rev

Introduction to SQC - D Montgomery - Ch04 rev

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• 1. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 1
• 2. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 2
• 3. Learning Objectives Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 3
• 4. 4.1 Statistics and Sampling Distributions4.1 Statistics and Sampling Distributions • Statistical inference is concerned with drawingg conclusions about populations (or processes) based on sample data from that system • Random sample – a sample that is selected so that the• Random sample a sample that is selected so that the observations are independent – a random sample has the property that it has the same probability of selection as any other sampleselection as any other sample. • Statistic – any function of the observations in a sample that doesn't contain unknown parameters • The sample mean, the sample variance, and the sample standard deviation are all statistics Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 4
• 5. Observations in a sample are used to drawp conclusions about the population Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 5
• 6. Sampling DistributionsSampling Distributions • A statistic is a random variable because aA statistic is a random variable, because a different sample with produce a different observed value of the statisticobserved value of the statistic • Every statistic has a probability distribution Th b bili di ib i f i i i• The probability distribution of a statistic is called a sampling distribution Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 6
• 7. Sampling from a Normal Distribution Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 7
• 8. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 8
• 9. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 9
• 10. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 10
• 11. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 11
• 12. Sampling from a Bernoulli Distribution Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 12
• 13. Sampling from a Poisson Distribution Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 13
• 14. 4.2 Point Estimation of Process Parameters4.2 Point Estimation of Process Parameters • Distributions are described by their parametersDistributions are described by their parameters • Parameters are generally unknown and must be estimatedestimated • Point estimator – a statistic that a single i l l h i h i f hnumerical value that is the estimate of the parameter • Examples, page 110 & 111 Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 14
• 15. Properties of Point Estimators Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 15
• 16. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 16
• 17. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 17
• 18. 4.3 Statistical Inference for a Single Sample4.3 Statistical Inference for a Single Sample • Statistical inference = decision makingStatistical inference decision making • Hypothesis testing N ll h th i H– Null hypothesis, H0 – Alternative hypothesis, H1 • Confidence intervals • These two techniques are closely relatedq y Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 18
• 19. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 19
• 20. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 20
• 21. 4.3.1 Inference on the Mean of a Population, Variance Known Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 21
• 22. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 22
• 23. Minitab output Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 23
• 24. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 24
• 25. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 25
• 26. Upper and lower confidence bounds Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 26
• 27. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 27
• 28. 4 3 2 P-Values4.3.2 P Values Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 28
• 29. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 29
• 30. 4.3.3 Inference on the Mean of a Normal Distribution, Variance UnknownDistribution, Variance Unknown Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 30
• 31. Checking the normality assumption – we will see how to do this in Example 4.3 Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 31
• 32. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 32
• 33. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 33
• 34. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 34
• 35. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 35
• 36. 4.3.4 Inference on the Variance of a Normal Distribution Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 36
• 37. Upper and lower fidconfidence bounds Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 37
• 38. 4.3.5 Inference on a Population Proportion Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 38
• 39. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 39
• 40. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 40
• 41. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 41
• 42. 4.3.6 Type II Error and Sample Size4.3.6 Type II Error and Sample Size Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 42
• 43. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 43
• 44. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 44
• 45. Minitab can perform sample size and power calculations. From Example 4.7: From Example 4.3: Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 45
• 46. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 46
• 47. 4.4 Statistical Inference for Two Samples4.4 Statistical Inference for Two Samples Comparing means, comparing variances, comparing proportions Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 47
• 48. 4.4.1 Inference on the Difference in Means, Variances Known Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 48
• 49. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 49
• 50. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 50
• 51. This is a two-sided CI. The one-sided confidence bounds would be found by using only one of thebounds would be found by using only one of the limits in Equation (4.49) with α/2 replaced by α. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 51
• 52. 4.4.2 Inference on the Difference in Means of T N l Di ib i V i U kTwo Normal Distributions, Variances Unknown Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 52
• 53. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 53
• 54. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 54
• 55. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 55
• 56. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 56
• 57. Confidence Intervals – Case 1: Case 2: Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 57
• 58. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 58
• 59. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 59
• 60. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 60
• 61. Paired Data: Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 61
• 62. 4.4.3 Inference on the Variances of Two Normal Distributions Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 62
• 63. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 63
• 64. The two-sided CI is: Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 64
• 65. 4.4.4 Inference on Two Proportions Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 65
• 66. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 66
• 67. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 67
• 68. 4.5 What if There Are More Than Two Populations? Th A l i f V iThe Analysis of Variance Example: Does changing the hardwood concentration in the pulp affectExample: Does changing the hardwood concentration in the pulp affect the mean tensile strength of paper? Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 68
• 69. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 69
• 70. The Analysis of Variance (ANOVA) Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 70
• 71. The ANOVA is based on the following partitioning of the total sum of squares (which measures the total variability in the sample data):q ( y p ) Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 71
• 72. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 72
• 73. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 73
• 74. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 74
• 75. The ANOVA test statistic is: If F is greater than the critical value F then the nullIf F0 is greater than the critical value Fα,a-1, a(n-1) then the null hypothesis of equal treatment means is rejected. A P-value approach can also be used. The P-value would be the probability above F0 in the F 1 ( 1) distribution Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 75 above F0 in the Fa-1, a(n-1) distribution.
• 76. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 76
• 77. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 77
• 78. Graphical comparison of individual means 20% hardwood produces higher mean strength than thep g g others; 5% hardwood produces lower strength; 10% and 15% hardwood don’t differ but give lower strength than 20%. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 78
• 79. 4.5.3 Checking Assumptions: Residual Analysis4.5.3 Checking Assumptions: Residual Analysis . ˆij ij ij ij ie y y y y   j j j j Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 79
• 80. Resid al PlotsResidual Plots: Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 80
• 81. 4.6 Linear Regression Models Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 81
• 82. Models that are not linear in the regressors can still be fit using linearModels that are not linear in the regressors can still be fit using linear regression techniques, so long as they are linear in the parameters. Important cases include models with interaction terms and l i lpolynomials. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 82
• 83. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 83
• 84. The method of least squares: Least squares lnormal equations Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 84
• 85. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 85
• 86. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 86
• 87. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 87
• 88. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 88
• 89. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 89
• 90. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 90
• 91. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 91
• 92. The test procedure is to calculate the test statistic Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 92
• 93. The regression sum of squares is Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 93
• 94. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 94
• 95. See Table 4.12 ( lid 91) f th t(slide 91) for the t- tests on the individual regressors in the ficonsumer finance model – both variables are significant Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 95
• 96. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 96
• 97. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 97
• 98. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 98
• 99. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 99
• 100. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 100
• 101. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 101
• 102. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 102
• 103. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 103
• 104. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 104
• 105. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 105
• 106. Other Diagnostic ToolsOther Diagnostic Tools • Standardized and Studentized residualsStandardized and Studentized residuals • R-student – an outlier diagnostic h SS i i• The PRESS statistic • R2 for prediction based on PRESS – a measure of how well the model will predict new data • Measure of leverage – hat diagonalsg g • Cook’s distance – a measure of influence Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 106
• 107. Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 107
• 108. Learning Objectivesg j Chapter 4 Introduction to Statistical Quality Control, 6th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 108