1 Statistics and Six Sigma ProgramsThe modern global business environment is …ercely competitive. No companycan a¤ord to “stand still” if it hopes to stay in business. Every healthy com-pany has explicit strategies for constantly improving its business processes andproducts. To the extent that all sensible improvement strategies must involveempirical evidence, statistics is (at least) implicit in these strategies.A particularly popular form of corporate improvement emphasis currentlygoes under the name “Six Sigma.” The name originated at Motorola Corpora-tion in the late 1980’s. Six Sigma programs at General Electric, AlliedSignaland Dow Chemical (among other leading examples) are widely touted as at leastpartially responsible for important recent growth in pro…ts and company stockvalues. The purpose of this brief section is to outline some main elements of theSix Sigma movement and indicate the relevance of statistics.The name “Six Sigma” is popularly used in at least three di¤erent ways. Itrefers to:1. a goal for business process performance,2. a strategy for achieving that performance for all of a company’s processes,and3. an organizational, training and recognition program designed to supportand implement the strategy referred to in 2.As a goal for process performance, the “Six Sigma” name has a connection tothe normal distribution. It means that if a (normal) process mean is set 6¾inside engineering speci…cations (even should it inadvertently drift a bit, say byas much as 1:5¾) the process produces essentially no unacceptable results. Asa formula for organizing and training to implement universal process improve-ment, Six Sigma borrows from the culture of the martial arts. Properly trainedand e¤ective individuals are designated as “black belts,” “master black belts”and so on. These individuals with advanced training and demonstrated skillslead company process improvement teams.Here, our primary interest is in item 2 in the foregoing list. Most Six Sigmaprograms use the acronym MAIC and the corresponding steps1. Measure2. Analyze3. Improve4. Controlas a framework for approaching process improvement. The Measure step re-quires …nding appropriate responses to observe, identifying corresponding mea-surement systems, and collecting initial process data. The Analyze step involves1Table 1: MAIC and StatisticsElement Statistical TopicsMeasure²Measurement Concepts²Data Collection Principles²Regression and Linear Calibration²Modeling Measurement Error²Inference in Measurement Precision StudiesAnalyze²Descriptive Statistics²Normal Plotting and Capability Indices²Statistical Intervals and Testing²Con…dence Intervals and TestingImprove²Regression Analysis and Response Surface Methods²Probabilistic Tolerancing²Con…dence Intervals and Testing²Factorial and Fractional Factorial AnalysisControl²Shewhart Control Chartsproducing data summaries and formal inferences adequate to make clear initialprocess performance. After seeing how a process is operating, there comes anImprovement e¤ort. Often this is guided by experimentation and additionaldata collected to see the e¤ects of changes implemented. Further, there is typi-cally an emphasis on variation reduction (improvement in process consistency).Finally, the Six Sigma 4-step cycle culminates in process Control. This meansprocess watching/monitoring through the routine collection and attention toprocess data. The point is to be sure that improvements made persist overtime.The Six Sigma MAIC cycle is full of places where statistics is important.Hopefully this will be obvious as we make out way through this course. Table1 shows in detail where standard statistical concepts and methods …t into theMAIC