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Industrial Statistics Industrial Statistics Ronald Christensen and Aparna V. Huzurbazar Department of Mathematics and Statistics University of New Mexico Copyright c 2002, 2021 v To Walt and Ed Contents Preface xiii 0.1 Standards xiii 0.2 Six-Sigma xiii 0.3 Lean xiv 0.4 This Book xiv 0.4.1 Computing xv 1 Introduction1 1.1 Four Principles for Quality1 1.1.1 Institute and Maintain Leadership for Quality Improvement2 1.1.2 Create Cooperation3 1.1.3 Train, Retrain, and Educate5 1.1.4 Insist on Action5 1.2 Some Technical Matters5 1.3 The Shewhart Cycle: PDSA6 1.4 Benchmarking7 1.5 Exercises7 2 Basic Tools 9 2.1 Data Collection9 2.2 Pareto and Other Charts 11 2.3 Histograms 13 2.3.1 Stem and Leaf Displays 16 2.3.2 Dot Plots 18 2.4 Box Plots 19 2.5 Cause and Effect Diagrams 19 2.6 Flow Charts 20 3 Probability 23 3.1 Introduction 23 3.2 Something about counting 25 3.3 Working with Random Variables 26 3.3.1 Probability Distributions, Expected Values 27 3.3.2 Independence, Covariance, Correlation 28 3.3.3 Expected values and variances for sample means 30 3.4 Binomial Distribution 32 3.5 Poisson distribution 34 3.6 Normal Distribution 34 vii viii CONTENTS 4 Control Charts 37 4.1 Individuals Chart 38 4.2 Means Charts and Dispersion Charts 40 4.2.1 Process Capability 46 4.2.1.1 Six-Sigma 47 4.3 Attribute Charts 48 4.4 Control Chart Summary 53 4.5 Average Run Lengths 54 4.6 Discussion 55 4.7 Testing Mean Shifts from a Target 56 4.7.1 Exponentially Weighted Moving Average Charts 56 4.7.1.1 Derivations of results 58 4.7.2 CUSUM charts 60 4.8 Computing 61 4.8.1 Minitab 61 4.8.2 R Commands 63 4.9 Exercises 64 5 Prediction from Other Variables 71 5.1 Scatter Plots and Correlation 72 5.2 Simple Linear Regression 74 5.2.1 Basic Analysis 75 5.2.2 Residual Analysis 76 5.2.3 Prediction 77 5.3 Statistical Tests and Confidence Intervals 79 5.4 Scatterplot Matrix 80 5.5 Multiple Regression 82 5.6 Polynomial Regression 84 5.7 Matrices 84 5.8 Logistic Regression 90 5.9 Missing Data 90 5.10 Exercises 90 6 Time Series 93 6.1 Autocorrelation and Autoregression 94 6.2 Autoregression and Partial Autocorrelation 97 6.3 Fitting Autoregression Models 98 6.4 ARMA and ARIMA Models 100 6.5 Computing 102 6.6 Exercises 103 7 Reliability 107 7.1 Introduction 107 7.2 Reliability/Survival, Hazards and Censoring 107 7.2.1 Reliability and Hazards 107 7.2.2 Censoring 109 7.3 Some Common Distributions 110 7.3.1 Exponential Distributions 110 7.3.2 Weibull Distributions 110 7.3.3 Gamma Distributions 111 7.3.4 Lognormal Distributions 111 7.3.5 Pareto 111 CONTENTS ix 7.4 An Example 112 8 Random Sampling 115 8.1 Acceptance Sampling 115 8.2 Simple Random Sampling 116 8.3 Stratified Random Sampling 117 8.3.1 Allocation 119 8.4 Cluster Sampling 119 8.5 Final Comment. 123 9 Experimental Design 125 9.1 One-way Anova 127 9.1.1 ANOVA and Means Charts 130 9.1.2 Advanced Topic: ANOVA, Means Charts, and Independence 135 9.2 Two-Way ANOVA 137 9.3 Basic Designs 139 9.3.1 Completely randomized designs 139 9.3.2 Randomized complete block designs 140 9.3.3 Latin Squares and Greco-Latin Squares 140 9.3.3.1 Additional Example of a Graeco-Latin Square 143 9.4 Factorial treatment structures 143 9.5 Exercises 150 10 2n factorials 151 10.1 Introduction 151 10.2 Fractional replication 153 10.3 Aliasing 155 10.4 Analysis Methods 158 10.5 Alternative forms of identifying treatments 163 10.6 Placket-Burman Designs 163 10.7 Exercises 164 11 Taguchi Methods 169 11.1 Experiment on Variability 170 11.2 Signal-to-Noise Ratios 171 11.3 Taguchi Analysis 172 11.4 Outer Arrays 175 11.5 Discussion 177 11.6 Exercises 177 11.7 Ideas on Analysis 179 11.7.1 A modeling approach 179 Appendix A: Multivariate Control Charts 181 A.1 Statistical Testing Background 182 A.2 Multivariate Individuals Charts 183 A.3 Multivariate Means T 2 Charts 185 A.4 Multivariate Dispersion Charts 186 References 187 Index 191 Preface Industrial Statistics is largely devoted to achieving, maintaining, and improving quality. Industrial Statistics provides tools to help in this activity. But management is in charge of the means of pro- duction, so only management can achieve, maintain, or improve quality. In the early 20th century Japan was renown for producing low quality products. After World War II, with influence from people like W. Edwards Deming and Joseph M. Juran, the Japanese began an emphasis on producing high quality goods and by the 1970s began out-competing American automobile and electronics manufacturers. Deming had had previous unsuccessful experiences in America with implementing (statistical) quality programs and had decided that the key was getting top management to buy into an overall program for quality. While the basic ideas of quality management are quite stable, actual implementations of those ideas seem subject to fads. When I first become interested in Industrial Statistics, Total Quality Management (TQM) was all the rage. That was followed by Six-Sigma which seems to have run its course. Lean seems to have been next up and even that seems to be passing. Lean Six-Sigma is what I see being pushed most in 2021. I expect a new fad to arise soon. Wikipedia has separate entries for Quality Management, Quality Management Systems (QMS), and TQM. I cannot tell that there is much difference between them other than what terminology is in vogue. The American Society for Quality (ASQ) has four major topics on their list for learning • Quality Management • Standards • Six-Sigma • Lean 0.1 Standards Standards refers to standards for quality management. The International Organization for Standard- ization (ISO - not an acronym in any of English, French or Russian) produces the 9000 series standards for Quality Management. The key document seems to be ISO 9001:2015 which specifies requirements for quality management. This was reviewed and confirmed in 2021. Other key stan- dards are ISO 9000:2015 on fundamentals and vocabulary and ISO 9004:2018 for continuous im- provement of quality. See https://www.iso.org/iso-9001-quality-management.html and https://www.iso.org/standard/62085.html. 0.2 Six-Sigma Six-Sigma is an entire management system that began at Motorola and was famously exploited by General Electric (GE). It is named after a very good idea related to control charts but has been extrapolated far beyond that. The basic idea of control charting is that with a process that is under control, virtually all of the output should fall within three standard deviations of the mean. (For technical reasons when determining control status this idea is best applied to the average of small groups of observations that are combined for some rational reason [rational subgroups].) Indeed, this idea is the basis for an operational definition of what it means to have a process under control. (For those with xiii xiv PREFACE some probability background you can think of it as an operational definition of what it means to be independent and identically distributed (iid).) The interval from the mean minus three standard deviations up to the mean plus three standard deviations is known as the process capability interval. Typically a product has some specification interval within which the product is required to fall. If the process capability interval is contained within the specification interval we are good to go. The standard deviation is typically denoted by the Greek letter sigma (s). The fundament idea behind Six-Sigma is striving to get the much larger interval from the mean minus six standard deviations (six-sigma) up to the mean plus six standard deviations within the specification interval. To do this may require cutting product variability in half. In such a case, if your process is on target (the middle of the specification interval) you will have very little variability and even if your process strays off of the target a bit, you can remain within the specification limits. But the overall Six-Sigma program is vastly more complicated. David Wayne (http://q-skills.com/Deming6sigma.htm) says “Six Sigma, while purport- ing to be a management philosophy, really seems more closely related to Dr. Joseph Juran’s more project-oriented approach, with a deliberate, rigorous technique for reaching a problem resolution or an improvement. Dr. Deming’s approach is more strategic, theoretical and philosophical in na- ture, and does not carry the detailed explicitness of the Six Sigma approach.” My memory (I am still looking for an exact reference) is that Deming was critical of Six-Sigma for being overly focused on financial issues. (Not surprisingly, this emphasis on financial issues seems to have made Six-Sigma more popular with top management.) Hahn, Hill, Hoerl, and Zinkgraf (1999) and Montgomery and Woodall (2008) present overviews of Six-Sigma from a statistical viewpoint. The panel discussion Stenberg et. al. (2008) also discusses Six-Sigma quite a bit. 0.3 Lean Lean is a program for eliminating waste based on Toyota’s program for doing so. It is often pre- sented as a cycle similar to the Shewhart Cycle: Plan, Do, Study, Act that is discussed in Section 1.3.
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