【正文】 The National Graduate School of Quality Management v7 ? 60 COIN TOSS POPULATION DISPERSION 1 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 7 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 Number of occurrences What are some of the ways that we can easily indicate the dispersion (spread) characteristic of the population? Three measures have historically been used。The National Graduate School of Quality Management v7 ? 53 COIN TOSS CENTRAL TENDENCY 1 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 7 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 Number of occurrences What are some of the ways that we can easily indicate the centering characteristic of the population? Three measures have historically been used。The National Graduate School of Quality Management v7 ? 45 ?Common Occurrence ?Rare Event WHAT DOES IT MEAN? What are the chances that this “just happened” If they are small, chances are that an external influence is at work that can be used to our benefit…. 169。The National Graduate School of Quality Management v7 ? 37 Focus on understanding the concepts Visualize the concept Don?t get lost in the math…. KEYS TO SUCCESS 169。The National Graduate School of Quality Management v7 ? 29 PLANT RESTRUCTURE ? Defect counts remain too high for the plant to be profitable. ? The two best performing production workers will be retained and the two worst performing production workers will be laid off. ? Your performance will be based solely on your ability to produce white beads. ? Your defect quota is no more than 10 off color beads allowed per paddle. 169。The National Graduate School of Quality Management v7 ? 21 ?Sales Receipts ?On Time Delivery ?Process Capacity ?Order Fulfillment Time ?Reduction of Waste ?Product Development Time ?Process Yields ?Scrap Reduction ?Inventory Reduction ?Floor Space Utilization WHAT DOES IT MEAN? Random Chance or Certainty…. Which would you choose….? 169。The National Graduate School of Quality Management v7 ? 13 The Focus of Six Sigma….. Y = f(x) All critical characteristics (Y) are driven by factors (x) which are “upstream” from the results…. Attempting to manage results (Y) only causes increased costs due to rework, test and inspection… Understanding and controlling the causative factors (x) is the real key to high quality at low cost... 169。The National Graduate School of Quality Management v7 ? 5 Day 4 Agenda ? Team Report Outs on Practicum Application ? Design of Experiments ? Wrap Up Positives and Deltas 169。The National Graduate School of Quality Management v7 ? 2 Day 1 Agenda ? Wele and Introductions ? Course Structure ? Meeting Guidelines/Course Agenda/Report Out Criteria ? Group Expectations ? Introduction to Six Sigma Applications ? Red Bead Experiment ? Introduction to Probability Distributions ? Common Probability Distributions and Their Uses ? Correlation Analysis 169。The National Graduate School of Quality Management v7 ? 10 POSITIONING SIX SIGMA THE FRUIT OF SIX SIGMA Ground Fruit Logic and Intuition Low Hanging Fruit Seven Basic Tools Bulk of Fruit Process Characterization and Optimization Process Entitlement Sweet Fruit Design for Manufacturability 169。The National Graduate School of Quality Management v7 ? 18 Measurements are critical... ?If we can’t accurately measure something, we really don’t know much about it. ?If we don’t know much about it, we can’t control it. ?If we can’t control it, we are at the mercy of chance. 169。The National Graduate School of Quality Management v7 ? 26 STANDING ORDERS ? Follow the process exactly. ? Do not improvise or vary from the documented process. ? Your performance will be based solely on your ability to produce white beads. ? No questions will be allowed after the initial training period. ? Your defect quota is no more than 5 off color beads allowed per paddle. 169。The National Graduate School of Quality Management v7 ? 34 Learning Objectives ? Have a broad understanding of what probability distributions are and why they are important. ? Understand the role that probability distributions play in determining whether an event is a random occurrence or significantly different. ? Understand the mon measures used to characterize a population central tendency and dispersion. ? Understand the concept of Shift Drift. ? Understand the concept of significance testing. 169。The National Graduate School of Quality Management v7 ? 42 COIN TOSS PROBABILITY EXAMPLE 1 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 7 0 1 0 0 5 0 0 C u m u l a t i v e P e r c e n t R e s u l t s f r o m 1 0 , 0 0 0 p e o p l e d o i n g a c o i n t o s s 2 0 0 t i m e s C u m u l a t i v e P e r c e n t This means that we can now predict the change that certain values can occur based on these percentages. Note here that 50% of the values are less than our expected value of 100. This means that in a future experiment set up the same way, we would expect 50% of the values to be less than 100. 169。The National Graduate School of Quality Management v7 ? 50 WHAT DOES IT MEAN? 6 5 4 3 2 1 0 1 2 3 4 5 6 NUMBER OF HEADS s SIGMA VALUE (Z) CUM % OF POPULATION 58 65 72 79 86 93 100 107 114 121 128 135 142 .003 .135 1 3 0 1 2 0 1 1 0 1 0 0 9 0 8 0 7 0 6 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0 F r e q u e n c y And the first 50 trials showed “Head Counts” greater than 130? WHAT IF WE MADE A CHANGE TO THE PROCESS? Chances are very good that the process distribution has changed. In fact, there is a probability greater than % that it has changed. 169。The National Graduat