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Six Sigma Green Belt Core Data Displays -6 -4 -2 0 2 4 6 Sigma Quality Management 1 Six Sigma Green Belt Variation in Product or Service Leaving the World of Averages and Entering the World of Dispersion Coin Toss Exercise: Flip 1 2 3 4 5 6 7 8 9 10 Result (H or T) 2 Data and Statistics Concepts Six Sigma Green Belt Nature of Data – Measurement vs. Count Data Single Point Measures of Performance •Central Tendency •Variability 3 Central Tendency Measure Mean Description & Use The Average of a set of numbers. The most commonly used measure of the data’s center. Remember, when you calculate an average, about half of the raw data will be above and half will be below the average - this does not translate into one half good and one half bad!! Median The midpoint of a set of numbers placed in rank order. The median is a preferred measure of the data's center when there are very large or small values, i.e. when the data is skewed. Mode The most frequently appearing number(s) in a set of data. Useful when data displays wide variation, perhaps due to mixed processes. Six Sigma Green Belt How to Calculate n x x i i 1 n where: is the symbol for "sum of" n is the number of data, and xi are the data values for an odd number of data: x( n1)/ 2 for an even number of data: x n 2 1 x n 2 2 For the data set: 1,2,2,3,3,3,3,4,4,5,5,6,7 three is the mode 4 Variability Measure Range Description & Use The difference between the largest and smallest values in a data set. Variance The sum of the squared differences of the data from the mean, divided by the number of data less one. Forms the basis for the standard deviation. Standard Deviation The square root of the variance. This is the “best” measure of variability, since it considers all the data from the sample. The Standard Deviation can be thought of as a “distance” measure - showing how far the data are away from the mean value. Six Sigma Green Belt How to Calculate R xmax xmin n s2 (x x ) 2 i i 1 n 1 s s2 5 Line Graphs Six Sigma Green Belt 1. Draw a vertical and a horizontal axis on a piece of graph paper. 2. Label the vertical axis with the variable being plotted. 3. Label the horizontal axis with the unit of time or order in which the numbers were collected (i.e. Day 1, 2, 3, . . ., Customer 1, 2, 3, . . . etc.). 4. Determine the scale of the vertical axis. The top of this axis should be about 20 percent larger than the largest data value. The bottom of this axis should be about 20 percent lower than the smallest data value. This let’s you see the best picture of the process’ variability. Label the axis in convenient intervals between these numbers. 5. Plot the data values on the graph number by number, preserving the order in which they occurred. 6. Connect the points on the graph. 7. (Optional) Calculate the mean of the data and draw this as a solid line through the data. This turns the line graph into a run chart - trends and patterns are often easier to see with a run chart. 6 Six Sigma Green Belt Line Graph Errors per 1000 Orders 10 8 Errors 6 4 2 0 1 3 5 7 9 11 13 15 17 19 Orders (1000) 7 Six Sigma Green Belt Run Chart Defects/Unit Good Defects 18 16 14 12 10 8 6 4 2 0 1 3 5 7 9 11 13 15 17 19 21 23 25 Data Collected: 7/29-8/3 A. J. Carr Unit Number 8 Six Sigma Green Belt Interpretation Mean (Center Line) 1 3 5 7 9 11 13 15 17 19 Mean 1 3 5 7 9 11 13 15 17 19 Mean Also: Extreme Values 1 3 5 7 9 11 13 15 17 19 9 Decisions in the Face of Variation Six Sigma Green Belt Correct Decisions: 1. Only Common Cause Variation Present 2. Common and Assignable Cause Variation Present Errors: 1. Just Common Cause Variation Present – NOT! 2. Assignable Cause Variation Present – NOT! 10 Six Sigma Green Belt Variation Decision - Summary “Our” Interpretation “True” Situation Only Common Causes Only Common Causes Common Plus Assignable Causes Correct Decision – If Process is Not Capable, Act to Understand Process Variables and Improve Process Wrong Decision – You Are Ignoring Possible Opportunities to Eliminate Assignable Causes from the Process Common Plus Assignable Causes Wrong Decision – You are Overreacting to Point -to-Point Variation! Correct Decision – Understand and Eliminate Assignable Causes from Process 11 Six Sigma Green Belt Bar Chart Examples 100 90 80 Sales Volum es by Region by Qtr 70 60 50 40 30 Missing Patient Documentation by Nursing Unit Percentage Missing 30 (%) Date: Nov, Dec By: F.N. Gale, RN East West North 20 10 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr 20 10 3West 3 North 2 North 2 West Unit Megawat t Hours Elect ricit y Product ion Growt h by Year and Fuel Gas Coal Oil Nuclear Year 12 Six Sigma Green Belt “Bad” Bar Chart Percent 98 Survival Rate - Open Heart Surgery by Hospital Three “Worst” 97 D H I Hospital 13 Six Sigma Green Belt Pie Chart Pie Chart of PC Printer Errors - Model PH-6 Garbled Font 6 Other 12 Low Memory Wrong 12 Font 48 Extra Sheet Fed 18 Paper Jam 32 14 Six Sigma Green Belt Radar Chart Power 1 0.9 0.8 Handling 0.7 0.6 Comfort 0.5 0.4 0.3 0.2 0.1 0 Style Safety Price Economy 15 Chart Comparison Six Sigma Green Belt Chart Line Graph Advantages Makes trends and data variation over time easy to track. Good for highlighting changes in some variable. Can be used to track more than one variable at a time. Disadvantages Can lead to “overreaction” to changes that aren’t really there. Control charts are the best tools for studying variation. Bar Chart Good for comparing one category to another. Many different styles can be constructed (stacked bar, “3dimensional” bar chart, etc.) Easy to construct. Sometimes inappropriately used for tracking data over time. Similar danger to overreaction as line graph. Pie Chart Useful for showing relative proportion of each Should not be used for tracking data over time. category to the whole. Several layers of stratification can be shown on one graph. Radar Chart Useful for showing performance of many variables or Not useful for tracking data over time, although characteristics on one chart. Useful for comparing “before & after” comparisons can be made. two or more products/services across many characteristics. 16