Statistical Quality Control, 7th Edition by Douglas C. Montgomery.

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Presentation transcript:

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Learning Objectives Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.1 Statistics and Sampling Distributions Statistical inference is concerned with drawing conclusions about populations (or processes) based on sample data from that system 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 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 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Observations in a sample are used to draw conclusions about the population Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Sampling Distributions A statistic is a random variable, because a different sample with produce a different observed value of the statistic Every statistic has a probability distribution The probability distribution of a statistic is called a sampling distribution Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Sampling from a Normal Distribution Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Sampling from a Bernoulli Distribution Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Sampling from a Poisson Distribution Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.2 Point Estimation of Process Parameters Distributions are described by their parameters Parameters are generally unknown and must be estimated Point estimator – a statistic that a single numerical value that is the estimate of the parameter Examples, page 110 & 111 Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Properties of Point Estimators Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Relative efficiency of the range: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3 Statistical Inference for a Single Sample Statistical inference = decision making Hypothesis testing Null hypothesis, H0 Alternative hypothesis, H1 Confidence intervals These two techniques are closely related Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3.1 Inference on the Mean of a Population, Variance Known Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Minitab output Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Upper and lower confidence bounds Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3.2 P-Values Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3.3 Inference on the Mean of a Normal Distribution, Variance Unknown Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Checking the normality assumption – we will see how to do this in Example 4.3 Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

P-values for t-Tests The tables of the standard normal distribution can give exact P-values for the Z test for values of Z to two decimals The t-table only has a selection of probabilities (see the column headings in the table) Unless the value of the test statistic exactly matches a value in the table, only an approximate P-value can be obtained See text, page 124, for an example P-values can also be obtained from Minitab by using the “Probability Distribution” function “Calc” menu Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3.4 Inference on the Variance of a Normal Distribution Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Upper and lower confidence bounds Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3.5 Inference on a Population Proportion Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.3.6 Type II Error and Sample Size Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Minitab can perform sample size and power calculations. From Example 4 Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.4 Statistical Inference for Two Samples Comparing means, comparing variances, comparing proportions Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.4.1 Inference on the Difference in Means, Variances Known Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Test Procedures: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Confidence Interval on the Difference in Means This is a two-sided CI. The one-sided confidence bounds would be found by using only one of the limits in Equation (4.49) with α/2 replaced by α. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.4.2 Inference on the Difference in Means of Two Normal Distributions, Variances Unknown Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc. .

Confidence Intervals – Case 1: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Paired Data: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.4.3 Inference on the Variances of Two Normal Distributions Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The two-sided CI is: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.4.4 Inference on Two Proportions Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4. 5 What if There Are More Than Two Populations 4.5 What if There Are More Than Two Populations? The Analysis of Variance Example: Does changing the hardwood concentration in the pulp affect the mean tensile strength of paper? Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The Analysis of Variance (ANOVA) Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The ANOVA is based on the following partitioning of the total sum of squares (which measures the total variability in the sample data): Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Computing Formulas: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The ANOVA test statistic is: If 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 Fa-1, a(n-1) distribution. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Graphical comparison of individual means 20% hardwood produces higher mean strength than the others; 5% hardwood produces lower strength; 10% and 15% hardwood don’t differ but give lower strength than 20%. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.5.3 Checking Assumptions: Residual Analysis Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Residual Plots: Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

4.6 Linear Regression Models Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Important cases include models with interaction terms and polynomials. Models 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 polynomials. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The method of least squares: Least squares normal equations Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The test procedure is to calculate the test statistic Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

The regression sum of squares is Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

See Table 4.12 (slide 91) for the t-tests on the individual regressors in the consumer finance model – both variables are significant Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Other Diagnostic Tools Standardized and Studentized residuals R-student – an outlier diagnostic The PRESS statistic R2 for prediction based on PRESS – a measure of how well the model will predict new data Measure of leverage – hat diagonals Cook’s distance – a measure of influence Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.

Learning Objectives Chapter 4 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.