INTRODUCTION TO SIX SIGMA APPLICATIONS What is Six Sigma? A Philosophy Customer Critical To Quality (CTQ) Criteria Breakthrough Improvements Fact-driven, Measurement-based, Statistically Analyzed Prioritization Controlling the Input & Process Variations Yields a Predictable Product A Quality Level 6s = 3.4 Defects per Million Opportunities A Structured Problem-Solving Approach Phased Project: Measure, Analyze, Improve, Control A Program Dedicated, Trained BlackBelts Prioritized Projects Teams - Process Participants & Owners POSITIONING SIX SIGMA THE FRUIT OF SIX SIGMA Sweet Fruit Design for Manufacturability Process Entitlement Bulk of Fruit Process Characterization and Optimization Low Hanging Fruit Seven Basic Tools Ground Fruit Logic and Intuition UNLOCKING THE HIDDEN FACTORY VALUE STREAM TO WASTE DUE TO THE INCAPABLE CUSTOMER PROCESSES PROCESSES WHICH WASTE SCATTERED THROUGHOUT PROVIDE PRODUCT VALUE THE VALUE STREAM IN THE CUSTOMER’S EYES • EXCESS INVENTORY •FEATURES OR • REWORK CHARACTERISTICS THE • WAIT TIME CUSTOMER WOULD PAY • EXCESS HANDLING FOR…. • EXCESS TRAVEL DISTANCES • TEST AND INSPECTION Waste is a significant cost driver and has a major impact on the bottom line. Common Six Sigma Project Areas Manufacturing Defect Reduction Cycle Time Reduction Cost Reduction Inventory Reduction Product Development and Introduction Labor Reduction Increased Utilization of Resources Product Sales Improvement Capacity Improvements Delivery Improvements The Focus of Six Sigma…. All critical characteristics (Y) are driven by factors (x) which are “upstream” from the results….
Attempting to manage results (Y) only causes increased Y = f(x) costs due to rework, test and inspection… Understanding and controlling the causative factors (x) is the real key to high quality at low cost. SIX SIGMA COMPARISON Six Sigma Traditional Focus on Prevention Focus on Firefighting Low cost/high throughput High cost/low throughput Poka Yoke Control Strategies Reliance on Test and Inspection Stable/Predictable Processes Processes based on Random Probability Proactive Reactive Low Failure Rates High Failure Rates Focus on Long Term Focus on Short Term Efficient Wasteful Manage by Metrics and Analysis Manage by “Seat of the pants” “SIX SIGMA TAKES US FROM FIXING PRODUCTS SO THEY ARE EXCELLENT, TO FIXING PROCESSES SO THEY PRODUCE EXCELLENT PRODUCTS” Dr. George Sarney, President, Siebe Control Systems IMPROVEMENT ROADMAP Objective Phase 1: •Define the problem and Measurement verify the primary and secondary measurement Characterization systems. Phase 2: Analysis •Identify the few factors Breakthrough which are directly Strategy influencing the problem.
Phase 3: Improvement •Determine values for the few contributing factors Optimization which resolve the Phase 4: problem. Control •Determine long term control measures which will ensure that the contributing factors remain controlled. 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. WHY STATISTICS? THE ROLE OF STATISTICS IN SIX SIGMA. WE DON’T KNOW WHAT WE DON’T KNOW LSL T USL IF WE DON’T HAVE DATA, WE DON’T KNOW IF WE DON’T KNOW, WE CAN NOT ACT IF WE CAN NOT ACT, THE RISK IS HIGH IF WE DO KNOW AND ACT, THE RISK IS MANAGED IF WE DO KNOW AND DO NOT ACT, WE DESERVE THE LOSS.
Harry TO GET DATA WE MUST MEASURE DATA MUST BE CONVERTED TO INFORMATION INFORMATION IS DERIVED FROM DATA THROUGH STATISTICS WHY STATISTICS? THE ROLE OF STATISTICS IN SIX SIGMA. Ignorance is not bliss, it is the food of failure and the breeding ground for loss. Harry LSL T USL Years ago a statistician might have claimed that statistics dealt with the processing of data…. Today’s statistician will be more likely to say that statistics is concerned with decision making in the face of uncertainty.
Bartlett WHAT DOES IT MEAN? 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 Random Chance or Certainty…. Which would you choose….? The Focus of Six Sigma…. All critical characteristics (Y) are driven by factors (x) which are “downstream” from the results…. Attempting to manage results (Y) only causes increased Y = f(x) costs due to rework, test and inspection… Understanding and controlling the causative factors (x) is the real key to high quality at low cost.
INTRODUCTION TO PROBABILITY DISTRIBUTIONS Why do we Care? An understanding of Probability Distributions is necessary to: •Understand the concept and use of statistical tools. •Understand the significance of random variation in everyday measures. •Understand the impact of significance on the successful resolution of a project. IMPROVEMENT ROADMAP Uses of Probability Distributions Project Uses Phase 1: •Establish baseline data Measurement characteristics.
Characterization Phase 2: •Identify and isolate Analysis sources of variation. Breakthrough Strategy Phase 3: •Demonstrate before and Improvement after results are not random chance. Optimization Phase 4: •Use the concept of shift & Control drift to establish project expectations. KEYS TO SUCCESS Focus on understanding the concepts Visualize the concept Don’t get lost in the math….
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.
Types of Measures Measures where the metric is composed of a classification in one of two (or more) categories is called Attribute data. This data is usually presented as a “count” or “percent”. Good/Bad Yes/No Hit/Miss etc. Measures where the metric consists of a number which indicates a precise value is called Variable data.
Time Miles/Hr COIN TOSS EXAMPLE Take a coin from your pocket and toss it 200 times. Keep track of the number of times the coin falls as “heads”. When complete, the instructor will ask you for your “head” count. COIN TOSS EXAMPLE Results from 10,000 people doing a coin toss 200 times.
Results from 10,000 people doing a coin toss 200 times. Count Frequency Cumulative Count 600 10000 C umulative Frequency 500 Cumulative Percent Frequency 400 Cumulative Frequency 300 5000 200 100 0 0 70 80 90 100 110 120 130 70 80 90 100 110 120 130 "Head Count" Results from 10,000 people doing a coin toss 200 times. Cumulative count is simply the total frequency Cumulative Percent count accumulated as you move from left to 100 right until we account for the total population of Cumulative Percent 10,000 people. 50 Since we know how many people were in this population (ie 10,000), we can divide each of the cumulative counts by 10,000 to give us a curve with the cumulative percent of population.
0 70 80 90 100 110 120 130 "Head Count" COIN TOSS PROBABILITY EXAMPLE Results from 10,000 people doing a coin toss 200 times Cumulative Percent This means that we can now 100 predict the change that certain values can occur Cumulative Percent based on these percentages. 50 Note here that 50% of the values are less than our expected value of 100. 0 This means that in a future 70 80 90 100 110 120 130 experiment set up the same way, we would expect 50% of the values to be less than 100. COIN TOSS EXAMPLE Results from 10,000 people doing a coin toss 200 times.
Count Frequency 600 We can now equate a probability to the 500 occurrence of specific values or groups of values. Frequency 400 300 For example, we can see that the 200 occurrence of a “Head count” of less than 100 74 or greater than 124 out of 200 tosses 0 70 80 90 100 110 120 130 is so rare that a single occurrence was "Head Count" Results from 10,000 people doing a coin toss 200 times. not registered out of 10,000 tries. Cumulative Percent On the other hand, we can see that the 100 chance of getting a count near (or at) 100 Cumulative Percent is much higher.
With the data that we now have, we can actually predict each of 50 these values. 0 70 80 90 100 110 120 130 "Head Count" COIN TOSS PROBABILITY DISTRIBUTION PROCESS CENTERED ON EXPECTED VALUE % of population = probability of occurrence 600 If we know where SIGMA (s ) IS A MEASURE 500 OF “SCATTER” FROM THE we are in the EXPECTED VALUE THAT Frequency population we can 400 CAN BE USED TO equate that to a CALCULATE A PROBABILITY 300 OF OCCURRENCE probability value. This is the purpose 200 of the sigma value s 100 (normal data). 0 70 80 90 100 110 120 130 NUMBER OF HEADS 58 65 72 79 86 93 100 107 114 121 128 135 142 SIGMA VALUE (Z) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 CUM % OF POPULATION .997 WHAT DOES IT MEAN? Common Occurrence Rare Event 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….
Probability and Statistics • “the odds of Colorado University winning the national title are 3 to 1” • “Drew Bledsoe’s pass completion percentage for the last 6 games is .78% for the first 5 games” • “The Senator will win the election with 54% of the popular vote with a margin of +/- 3%” • Probability and Statistics influence our lives daily • Statistics is the universal lanuage for science • Statistics is the art of collecting, classifying, presenting, interpreting and analyzing numerical data, as well as making conclusions about the system from which the data was obtained. Sample (Certainty Vs. Uncertainty) A sample is just a subset of all possible values sample population Since the sample does not contain all the possible values, there is some uncertainty about the population. Hence any statistics, such as mean and standard deviation, are just estimates of the true population parameters.
Descriptive Statistics Descriptive Statistics is the branch of statistics which most people are familiar. It characterizes and summarizes the most prominent features of a given set of data (means, medians, standard deviations, percentiles, graphs, tables and charts. Descriptive Statistics describe the elements of a population as a whole or to describe data that represent just a sample of elements from the entire population Inferential Statistics Inferential Statistics Inferential Statistics is the branch of statistics that deals with drawing conclusions about a population based on information obtained from a sample drawn from that population. While descriptive statistics has been taught for centuries, inferential statistics is a relatively new phenomenon having its roots in the 20th century.
We “infer” something about a population when only information from a sample is known. Probability is the link between Descriptive and Inferential Statistics WHAT DOES IT MEAN? WHAT IF WE MADE A CHANGE TO THE PROCESS? Chances are very 600 And the first 50 good that the trials showed process distribution 500 “Head Counts” has changed. In greater than 130? Frequency 400 fact, there is a probability greater 300 than 99.999% that 200 it has changed. s 100 0 70 80 90 100 110 120 130 NUMBER OF HEADS 58 65 72 79 86 93 100 107 114 121 128 135 142 SIGMA VALUE (Z) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 CUM % OF POPULATION .997 USES OF PROBABILITY DISTRIBUTIONS Primarily these distributions are used to test for significant differences in data sets.
To be classified as significant, the actual measured value must exceed a critical value. The critical value is tabular value determined by the probability distribution and the risk of error. This risk of error is called a risk and indicates the probability of this value occurring naturally. So, an a risk of .
