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- 1. UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO National Guard Black Belt Training Module 22 Process Measurement UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO
- 2. UNCLASSIFIED / FOUO CPI Roadmap – Measure 8-STEP PROCESS 6. See 1.Validate 2. Identify 3. Set 4. Determine 5. Develop 7. Confirm 8. Standardize Counter- the Performance Improvement Root Counter- Results Successful Measures Problem Gaps Targets Cause Measures & Process Processes Through Define Measure Analyze Improve Control TOOLS •Process Mapping ACTIVITIES • Map Current Process / Go & See •Process Cycle Efficiency/TOC • Identify Key Input, Process, Output Metrics •Little’s Law • Develop Operational Definitions •Operational Definitions • Develop Data Collection Plan •Data Collection Plan • Validate Measurement System •Statistical Sampling • Collect Baseline Data •Measurement System Analysis • Identify Performance Gaps •TPM • Estimate Financial/Operational Benefits •Generic Pull • Determine Process Stability/Capability •Setup Reduction • Complete Measure Tollgate •Control Charts •Histograms •Constraint Identification •Process Capability Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive. UNCLASSIFIED / FOUO
- 3. UNCLASSIFIED / FOUO Learning Objectives Understand the importance of measurement to process improvement Apply measures of central tendency and variation to process data Apply the concepts of common and special cause variation Apply Sigma Quality Level to processes Know how to measure the Voice of the Customer and Voice of the Business UNCLASSIFIED / FOUO 3
- 4. UNCLASSIFIED / FOUO Measurement Fundamentals Definition: The assignment of numbers to observations according to certain decision rules Measurement is the beginning of any science or discipline Without measurements, we do not know where we are going or if we ever got there – we do not even know where we are now! If it is important to the customer, we should measure it UNCLASSIFIED / FOUO 4
- 5. UNCLASSIFIED / FOUO Measurement Example The following data is the number of minutes it took Soldiers to resolve their AKO issues when calling the AKO Helpdesk. Take a few minutes to examine the data: Time of Day Minutes To Resolve Issue 0730 00 0731 11 0800 06 0845 14 0903 11 0925 58 0940 47 1006 16 1120 09 1145 48 1158 43 1205 53 1214 49 1310 09 1400 10 How should we summarize and present this data to understand the AKO Helpdesk’s overall performance? UNCLASSIFIED / FOUO 5
- 6. UNCLASSIFIED / FOUO Calculating the Mean An easy way of summarizing data is to calculate the arithmetic average (or “mean”) of the column of numbers Mathematically, we can express this as follows: n X i 1 X i n UNCLASSIFIED / FOUO 6
- 7. UNCLASSIFIED / FOUO Mean Example Lets go back to our AKO Helpdesk data: 0, 11, 6, 14, 11, 58, 47, 16, 9, 48, 43, 53, 49, 9, 10 What is the mean value? X-bar = (0 + 11 + 6 + 14 + 11 + 58 + 47 + 16 + 9 + 48 + 43 + 53 + 49 + 9 + 10) / 15 = 25.6 minutes UNCLASSIFIED / FOUO 7
- 8. UNCLASSIFIED / FOUO Measures of Central Tendency The Mean is a measurement of central tendency, that is, where the “center” of most of the data is. Another measure of central tendency is the Median. The Median is calculated by listing the data in ascending order and then finding the value that is in the middle of the list If we re-order our AKO Helpdesk data in ascending order, we get the following list: 0, 6, 9, 9, 10, 11, 11, 14, 16, 43, 47, 48, 49, 53, 58 The value which occurs in the middle of the list is 14 minutes – this is the Median The Median can be a fraction or decimal even if the data is all integers. If we had fourteen instead of fifteen data points (no 58) the median would have been (11 + 14) / 2 = 12.5 minutes UNCLASSIFIED / FOUO 8
- 9. UNCLASSIFIED / FOUO Central Tendency – The Whole Story? While it is important to know where the “center” of our data is, does it tell the whole story? What does this tell us about the AKO Helpdesk’s performance? What does is not tell us? Why is there a difference between the mean and median in our example? UNCLASSIFIED / FOUO 9
- 10. UNCLASSIFIED / FOUO Measures of Central Tendency Mean, Median and Summary for Minutes Mode A nderson-Darling N ormality Test A -S quared 1.29 Mode - most P -V alue < 0.005 M ean 25.600 frequently S tDev 20.870 V ariance 435.543 S kew ness 0.43325 occurring data Kurtosis N -1.78559 15 point M inimum 1st Q uartile M edian 0.000 9.000 14.000 3rd Q uartile 48.000 A histogram 0 10 20 30 40 50 60 M aximum 58.000 95% C onfidence Interv al for M ean shows data by 14.043 37.157 95% C onfidence Interv al for M edian frequency of 9.374 47.626 95% C onfidence Interv al for S tDev 9 5 % C onfidence Inter vals occurrence. It 15.279 32.914 Mean also shows the Median “distribution” and 10 20 30 40 50 “spread” and of the data UNCLASSIFIED / FOUO
- 11. UNCLASSIFIED / FOUO Measuring Variation Another important way of summarizing our data is by measuring the average “spread” or variation between each data point and the mean While the center of our process is important, knowing the spread is particularly important in service because each user is an individual and deserves to be provided with acceptable service Do you care that the average wait is 26 minutes if you are the one who had to wait 58 minutes? A commonly used term in statistics for measuring this variation is the standard deviation UNCLASSIFIED / FOUO 11
- 12. UNCLASSIFIED / FOUO Calculating the Standard Deviation The standard deviation gives us a feel for the overall consistency of our data set Mathematically, it is calculated as follows: n ( X i X )2 s i 1 n 1 UNCLASSIFIED / FOUO 12
- 13. UNCLASSIFIED / FOUO Standard Deviation Example From the previous example we know that the sample mean, x-bar, is 25.6 minutes Find the sample standard deviation: ( 0 - 25.6)2 = 655.36 (11 - 25.6)2 = 213.16 Subtotal (Sum of Squares) = 6097.60 ( 6 – 25.6)2 = 384.16 Divided by (n-1) = 14 (14 – 25.6)2 = 134.56 (11 – 25.6)2 = 213.16 Variance = 435.54 min2 (58 – 25.6)2 =1049.76 (47 – 25.6)2 = 457.96 Standard Deviation = 20.86 min (16 – 25.6)2 = 92.16 (Square Root of Variance) ( 9 – 25.6)2 = 275.56 (48 – 25.6)2 = 501.76 (43 – 25.6)2 = 302.76 (53 – 25.6)2 = 750.76 (49 – 25.6)2 = 547.56 ( 9 – 25.6)2 = 275.56 (10 – 25.6)2 =243.36 Subtotal = 6097.60 UNCLASSIFIED / FOUO 13
- 14. UNCLASSIFIED / FOUO Variance If we square the standard deviation, we get the Variance The Variance of a Data Sample is defined as follows: Sample = 2 Variance s The Variance of the Population from which the sample is drawn is defined as: Population Variance 2 The Variance is useful since we cannot add Standard Deviations together, but we can add Variances (more on this in future modules) UNCLASSIFIED / FOUO 14
- 15. UNCLASSIFIED / FOUO Min, Max, and Range A simple way of measuring the amount of consistency in a data set is by calculating Min, Max, and Range The Min is the smallest value in our data set; the Max is the largest value The Range is the difference between the Max and Min and gives us a feel for the “spread” in our data Using our AKO Helpdesk data, the Min = 0 minutes, the Max = 58 minutes, the Range is 58 - 0 = 58 minutes UNCLASSIFIED / FOUO 15
- 16. UNCLASSIFIED / FOUO Central Tendency and Variation A key concept in Lean Six Sigma is understanding how central tendency and variation work together to describe a process by summarizing its data: Central Tendency is where the “middle” of the process is – this is where we would expect most of the data points to be Variation tells us how much “spread” there is in the data – the smaller the variation, the more consistent the process Both a measure of central tendency and variation are necessary to describe a data set UNCLASSIFIED / FOUO 16
- 17. UNCLASSIFIED / FOUO Understanding Variation There will always be some variation present in all processes: Nature – Shape/size of leaves, snowflakes, etc. Human – Handwriting, tone of voice, speed of walk, etc. Mechanical – Weight/size/shape of product, etc. We can tolerate this variation if: The process is on target The variation is small compared to the process specifications The process is stable over time We need to recognize that sources of variation (especially Special Cause variation) should be minimized or, if possible, eliminated UNCLASSIFIED / FOUO 17
- 18. UNCLASSIFIED / FOUO Variation – Its Impact on Business Variation is the Enemy of Improvement Efforts In the 1998 GE annual report, Chief Executive Jack Welch clearly articulated a concern that had been troubling other CEOs: “We have tended to use all our energy and Six Sigma science to “move the mean”… The problem is, as has been said, “the mean never happens,” and the customer is still seeing variances in when the deliveries actually occur – a heroic 4-day delivery time on one order, with an awful 20-day delay on another, and no real consistency… Variation is Evil.” UNCLASSIFIED / FOUO 18
- 19. UNCLASSIFIED / FOUO Types of Variation Common Cause Variation This is the consistent, stable, random variability within the process We will have to make a fundamental improvement to reduce common cause variation Is usually hard to reduce Special Cause Variation This is due to a specific cause that we can isolate Special cause variation can be detected by spotting outliers or patterns in the data Usually easy to eliminate UNCLASSIFIED / FOUO 19
- 20. UNCLASSIFIED / FOUO Exercise: Your Signature First, write your name 5 times Next, write your name 5 times with the other hand Is the variability common or special cause? UNCLASSIFIED / FOUO 20
- 21. UNCLASSIFIED / FOUO Special Cause Variation Examples of Special Cause variation are: Uncommon occurrence or circumstance Soldiers out for training holiday or flu epidemic Xbar Chart of Supp2 Convoy vehicle flat tire 603 1 1 UCL=602.474 Procedure change 602 Base-wide electrical Sample Mean 601 power outage 600 _ _ X=600.23 599 Control Chart showing Special Cause variation 598 LCL=597.986 2 4 6 8 10 12 14 16 18 20 Sample UNCLASSIFIED / FOUO 21
- 22. UNCLASSIFIED / FOUO Common Cause Variation Some examples of Common Cause variation are: Experience of individual Soldiers Internet server speed fluctuations Soldier out on sick-call Xbar Chart of Supp1 600.5 Day to day unit issues UCL=600.321 600.0 Sample Mean Control Chart showing 599.5 _ _ X=599.548 variation due only to Common Cause 599.0 LCL=598.775 2 4 6 8 10 12 14 16 18 20 Sample UNCLASSIFIED / FOUO 22
- 23. UNCLASSIFIED / FOUO Understanding Accuracy and Precision If the pictures to the right represent weapons training by two recruits, which one is better? Green? Blue? (Green) Which one is more accurate (better average)? Which one is more precise (more consistency)? (Blue) UNCLASSIFIED / FOUO 23
- 24. UNCLASSIFIED / FOUO Weapons Training Example On average, the green target is centered on the bulls-eye, therefore more accurate Accuracy is a measure of “average distance from the target” (Green) However, the blue target is more consistent, therefore more precise Precision is a measure of “average distance from each other” (Blue) UNCLASSIFIED / FOUO 24
- 25. UNCLASSIFIED / FOUO Weapons Training Example How could the recruit using the green target improve performance? How could the recruit using the blue target improve performance? (Green) Which recruit do you think has a better chance of becoming an expert shooter? Typically, it is easier to shift the mean than to reduce variation (Blue) UNCLASSIFIED / FOUO 25
- 26. UNCLASSIFIED / FOUO Goal: Shift the Mean / Reduce Variation Too Much Spread Off Center Centered (Blue) (Green) Reduce On-Target Center Spread Process Result: Improved Customer Satisfaction and Reduced Costs UNCLASSIFIED / FOUO 26
- 27. UNCLASSIFIED / FOUO Introducing The Distribution Upto now, we have been using the mean and standard deviation to summarize the data generated from a process Another way we can summarize the data is by showing its distribution Thedistribution shows us the number of times (“frequency count”) a particular data value appears in our data set The “peak” of the distribution shows its central tendency; the “spread” of the distribution tells us about the degree of variation present in the data UNCLASSIFIED / FOUO 27
- 28. UNCLASSIFIED / FOUO The Distribution By examining the distribution, we can see patterns that are difficult to see in a simple table of numbers Different processes and phenomena will generate different distribution patterns Both common and special cause variation will be present in the distribution The examples shown are different types of distributions UNCLASSIFIED / FOUO 28
- 29. UNCLASSIFIED / FOUO Histogram A common graphical tool used to portray the distribution is the histogram The histogram is constructed by taking the # difference between the min and max observation and dividing it up into evenly spaced intervals The number of observations in each Histogram interval are then counted and their frequency plotted as the height of each bar The histogram is, in essence, a simplified view of the distribution that generated the plotted data UNCLASSIFIED / FOUO 29
- 30. UNCLASSIFIED / FOUO Exercise: Build a Histogram Note the height in inches of the tallest Frequency and shortest students in the class 12 Divide this range into 5 equally sized 10 intervals 8 Make a bar to show the number of 6 students in class who’s height falls within each interval 4 The resulting chart is a histogram 2 How would you describe the shape of Height our histogram? 56 60 64 68 72 76 (Inches) How much variation is present in our data? Common or Special Cause? UNCLASSIFIED / FOUO 30
- 31. UNCLASSIFIED / FOUO Interpreting Histogram Data Ifthe variation is common cause, it reflects the natural variation inherent in the process and will show higher frequencies around the central tendency and taper off toward the edges of the distribution. The underlying process generating Common Cause Variation the data is stable, and the value of each data point is random and consistent with the rest of the distribution. Outlier Ifthe variation is special cause, an observation will not “fit” the rest of the distribution (i.e, it is Special Cause - Outlier an outlier), or there will be a “pattern” in our data. In other words, there is an identifiable reason for why this variation exists. Special Cause - Bimodal UNCLASSIFIED / FOUO 31
- 32. UNCLASSIFIED / FOUO Exercise: Minitab Let’s use Minitab to help us analyze some data Open the Minitab data set called Red Beads Data.mtw Four teams of four people each sampled 50 beads from the same bead box Each team member drew 10 samples of 50 The samples were randomly drawn and the beads randomly replaced after drawn The data collected was the number of “red” beads counted out of the fifty beads sampled What do you think the histogram of this data will look like? UNCLASSIFIED / FOUO 32
- 33. UNCLASSIFIED / FOUO Exercise: Minitab 1. Let’s make a histogram of the data Select: Stat> Basic Statistics> Display Descriptive Statistics UNCLASSIFIED / FOUO 33
- 34. UNCLASSIFIED / FOUO Exercise: Minitab 2. Double click (select) C3 Red Beads to place it in the Variables box 3. Click on Graphs UNCLASSIFIED / FOUO 34
- 35. UNCLASSIFIED / FOUO Exercise: Minitab 4. Check the box for Histogram of Data 5. Click OK 6. Click OK UNCLASSIFIED / FOUO 35
- 36. UNCLASSIFIED / FOUO Exercise: Minitab This is a frequency histogram that shows us, for the entire 160 samples run, how many red beads 22 remained in the paddle each time For example, 22 times out of 160, there were 11 red beads in the paddle What type of variation is present? Common or Special Cause? 11 UNCLASSIFIED / FOUO 36
- 37. UNCLASSIFIED / FOUO Exercise: Minitab Notice that the Data in Session Window gives us information on both Central Tendency and Variation Descriptive Statistics: Red Beads Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Red Beads 160 0 10.684 0.239 3.029 4.000 8.026 11.000 13.000 Variable Maximum Red Beads 19.000 UNCLASSIFIED / FOUO 37
- 38. UNCLASSIFIED / FOUO Other Information from Minitab Standard Error of the Mean (SEMEAN) s Gives the standard error of the mean. It is calculated as n . Quartiles Every group of data has four quartiles. If you sort the data from smallest to largest, the first 25% of the data is less than or equal to the first quartile. The second quartile takes all the data up to the median. The first 75% of the data is less than or equal to the third quartile and 25% of the data is greater than or equal to the third quartile – the fourth quartile. The Inter Quartile Range equals Q3 - Q1, spanning 50% of the data UNCLASSIFIED / FOUO 38
- 39. UNCLASSIFIED / FOUO Exercise: Minitab 1. Let’s make a Box Plot of the data Select: Stat> Basic Statistics> Display Descriptive Statistics UNCLASSIFIED / FOUO 39
- 40. UNCLASSIFIED / FOUO Exercise: Minitab 2. When this dialog box comes up, double click on C3-Red Beads to place it in the Variables box. Then double click on C1-Teams to place it in the By Variables box. Finally, click on Graphs. UNCLASSIFIED / FOUO 40
- 41. UNCLASSIFIED / FOUO Exercise: Minitab 3. Select Boxplot of Data, click on OK and then click on OK again UNCLASSIFIED / FOUO 41
- 42. UNCLASSIFIED / FOUO Exercise: Minitab Displayed are 4 boxplots, one for each team One way of interpreting a box plot is “looking down at the top of a histogram” This is a good way to see how spread and centering differ from one team to another UNCLASSIFIED / FOUO 42
- 43. UNCLASSIFIED / FOUO Exercise: Minitab Notice that Team 1 has 2 Outliers Notice also that team 4 has a slightly wider spread (i.e., larger standard deviation) than team 1 with a narrower spread (i.e., smaller std. deviation) UNCLASSIFIED / FOUO 43
- 44. UNCLASSIFIED / FOUO Exercise: Minitab As before, the session Descriptive Statistics: Red Beads window gives us all the Variable Team N N* Mean SE Mean StDev Minimum Q1 Median numbers Red Beads 1 40 0 11.325 0.426 2.693 6.000 10.000 11.000 2 40 0 10.200 0.482 3.048 4.000 8.000 10.000 As we would have 3 40 0 10.700 0.495 3.131 5.000 8.000 11.000 4 40 0 10.511 0.509 3.220 5.185 7.307 10.802 figured from the box Variable Team Q3 Maximum plot, team 4 has a Red Beads 1 13.000 19.000 slightly larger standard 2 12.750 17.000 3 13.000 16.000 deviation than team 1 4 12.987 16.573 UNCLASSIFIED / FOUO 44
- 45. UNCLASSIFIED / FOUO Exercise: Minitab 1. Now let’s make a Dotplot of the data Select Graph> Dotplot UNCLASSIFIED / FOUO 45
- 46. UNCLASSIFIED / FOUO Exercise: Minitab 2. Next select One Y and With Groups, since we have only one Y variable but four teams. Then click on OK. UNCLASSIFIED / FOUO 46
- 47. UNCLASSIFIED / FOUO Exercise: Minitab 3. Double click on C3-Red Beads to place it in the Graph Variables box 4. Double click on C1-Team to place it in the Categorical Variables box. Then click on OK. UNCLASSIFIED / FOUO 47
- 48. UNCLASSIFIED / FOUO Exercise: Minitab Displayed are the Four Dotplots, one for each team This is a good way to see how spread and centering differ from one team to another. Also, the scale remains the same. UNCLASSIFIED / FOUO 48
- 49. UNCLASSIFIED / FOUO Introducing the Normal Distribution In our Red Bead example, you may have noticed that the data in our histogram took on the shape of a bell shaped curve If we measure process performance over time, many processes tend to follow a Normal Distribution or bell shaped curve: Average ƒ(x) = Y Frequency Variation x The Normal distribution is important in statistics because of the relationship between the shape of the curve and the standard deviation () UNCLASSIFIED / FOUO 49
- 50. UNCLASSIFIED / FOUO Properties of the Normal Distribution One way of demonstrating the relationship between the standard deviation sigma () and the shape of the curve is to use sigma as a “measuring rod” to describe how far we are away from the mean The special properties of the normal distribution allow us to calculate the area underneath the curve based upon how many sigmas (or standard deviations) we are away from the mean: -3 -2 -1 +1 +2 +3 +/-1 =68.27% +/-2 =95.45% +/-3 =99.73% UNCLASSIFIED / FOUO 50
- 51. UNCLASSIFIED / FOUO Properties of the Normal Distribution Another property of the normal distribution is the area under the curve gives us the probability of a data point being drawn from this portion of the distribution This special property enables us to predict process performance over time Essentially all of the area (99.73%) of the normal distribution is contained between -3 sigma and +3 sigma from the mean. Only 0.27% of the data falls outside 3 standard deviations from the mean: -3 -2 -1 +1 +2 +3 +/-3 = 99.7% UNCLASSIFIED / FOUO 51
- 52. UNCLASSIFIED / FOUO Process Performance There are two aspects to process performance: Efficiency – Time and cost associated with executing the process Cycle time (processing time, on-time delivery, responsiveness, etc.) Cost (number of resources required, capital equipment, etc.) Effectiveness – Quality of the output of the process Level of output (calls answered, orders processed, etc.) Defects (accuracy, mistakes, errors, etc.) Customer Satisfaction Improving both the efficiency and effectiveness of process performance will enable us to reduce costs and better satisfy customers UNCLASSIFIED / FOUO 52
- 53. UNCLASSIFIED / FOUO Process Capability Process capability measures whether or not a process is capable of meeting customer requirements It is a quantifiable comparison of a process’ performance (Voice of the Process) vs. the customer requirements or “specifications” (Voice of the Customer) Most measures have some desired value (“target”) and some acceptable limit of variation around the desired value The extent to which the “expected” values fall within these limits determines how capable the process is of meeting its requirements UNCLASSIFIED / FOUO 53
- 54. UNCLASSIFIED / FOUO Understanding Acceptable Performance “Acceptable Performance” by definition is that which is acceptable to the customer: Target – The desired or nominal value of a characteristic Tolerance – An allowable deviation from the target value where performance is still acceptable to the customer Specifications – Boundaries where performance outside of these limits is not acceptable to the customer LSL = Lower Spec Limit USL = Upper Spec Limit UNCLASSIFIED / FOUO 54
- 55. UNCLASSIFIED / FOUO A Graphical View of Process Performance LSL Target USL USL Traditional View Tolerance • Target • Pass/Fail Cost LSL Target USL Correct View • Target • Service Break Points – Less than 1: Delighted Cost – 1 to 2: Very Satisfied – 2 to 3: Satisfied 3 2 1 1 2 3 UNCLASSIFIED / FOUO 55
- 56. UNCLASSIFIED / FOUO Satisfying Customer Requirements Specification Limits establish the boundaries for acceptable process performance. Performance outside these boundaries is “unacceptable.” They are “defects.” They are typically described by an Upper Specification Limit (USL) and Lower Specification Limit (LSL) For example, what are the spec limits for the temperature of this room? How LOW can the temperature get before you become uncomfortable or dissatisfied? This is the LSL. How HIGH can the temperature get before you become uncomfortable or dissatisfied? This is the USL. UNCLASSIFIED / FOUO 56
- 57. UNCLASSIFIED / FOUO What Reduced Variation Looks Like SQL = 3.0 SQL = 6.0 Target Target 1 Standard Deviation 1 Standard Deviation LSL USL LSL USL Process Process Center Center 3 3 3 6 Current process has 3 standard Improved process (reduced deviations between target and USL variation) has 6 standard deviations between target and USL NOTE: Illustrations do not include the 1.5 Sigma Shift, the discussion of which is beyond the scope of this lesson UNCLASSIFIED / FOUO 57
- 58. UNCLASSIFIED / FOUO Process Capability Is Sigma Quality Level Sigma is a Greek letter and a statistical unit of measurement that describes the variability or spread of data (the standard deviation of a population) Six Sigma refers to a methodology of continuous improvement where the goal is to improve process performance to meet customers’ requirements Sigma Quality Level is a measure of process performance with respect to customer requirements Note: Another approach to measuring process capability, Cp and Cpk, is shown in the Appendix and will be discussed in a future module. UNCLASSIFIED / FOUO 58
- 59. UNCLASSIFIED / FOUO Sigma Quality Level and Process Capability If we measure the performance of a process… Mean Standard Deviation …and know the customer’s Specification Limits, then: We can calculate Sigma Quality Level…which tells us how many “defects” we can expect over time (process capability) Understanding process capability will help us: Establish a baseline of current performance Measure on-going performance to determine level of improvement and then monitor and control performance to maintain the gain UNCLASSIFIED / FOUO 59
- 60. UNCLASSIFIED / FOUO Sigma Quality Level (SQL) and Defects per Million Opportunities (DPMO) SQL Yield DPMO 2 69.2% 308,537 3 93.32% 66,807 4 99.379% 6,210 5 99.977% 233 6 99.9997% 3.4 A 3 SQL process will fail to meet customer requirements 7% of the time UNCLASSIFIED / FOUO 60
- 61. UNCLASSIFIED / FOUO Process Capability: Invoice Example Errors made in preparing customer invoices has led to unacceptable delays in receiving customer payments A review of the last 100 prepared invoices revealed that 15 of them required corrections before they could be sent to customers However, there were three types of errors associated with the invoices and several invoices had more than one error: Incorrect address Wrong amount Mismatch of account number In total, there were 19 different defects on the 15 faulty invoices What is the Sigma Quality Level? UNCLASSIFIED / FOUO 61
- 62. UNCLASSIFIED / FOUO Process Capability: Invoice Example There are two ways to determine Sigma Quality Level (SQL), depending on the type of data measured: Continuous or Variable Data – Data that can take on any value (e.g., average cycle time of a process or room temperature) We calculate SQL using mean, standard deviation, and specification limits Discrete or Attribute Data – Data that typically can result in one of two possible outcomes (e.g., pass/fail, defective/acceptable) For this Invoice Example case, we calculate Defects Per Million Opportunities UNCLASSIFIED / FOUO 62
- 63. UNCLASSIFIED / FOUO Calculating Sigma Quality Level Based on Defects Per Million Opportunities (DPMO) 1. Determine number of defect or error opportunities per unit O= 3 2. Determine number of units N= 100 processed 3. Determine total number D= 19 of defects made 4. Calculate Defects D DPO = = 0.063 per Opportunity NxO 5. Calculate DPMO DPMO = DPO x 1,000,000 = 63,333 6. Look up the S.Q.L. in the Sigma Quality Level = ~3 Table (see next slide) UNCLASSIFIED / FOUO 63
- 64. UNCLASSIFIED / FOUO Sigma Quality Level (SQL) Conversion Table Yield Yield DPMO DPMO SQL Sigma Yield Yield DPMO DPMO SQL Sigma Yield Yield DPMO DPMO SQL Sigma 6.6% 934,000 0 69.2% 308,000 2 99.4% 6,210 4 8.0% 920,000 0.1 72.6% 274,000 2.1 99.5% 4,660 4.1 10.0% 900,000 0.2 75.8% 242,000 2.2 99.7% 3,460 4.2 12.0% 880,000 0.3 78.8% 212,000 2.3 99.75% 2,550 4.3 14.0% 860,000 0.4 81.6% 184,000 2.4 99.81% 1,860 4.4 16.0% 840,000 0.5 84.2% 158,000 2.5 99.87% 1,350 4.5 19.0% 810,000 0.6 86.5% 135,000 2.6 99.90% 960 4.6 22.0% 780,000 0.7 88.5% 115,000 2.7 99.93% 680 4.7 25.0% 750,000 0.8 90.3% 96,800 2.8 99.95% 480 4.8 28.0% 720,000 0.9 91.9% 80,800 2.9 99.97% 330 4.9 31.0% 690,000 1 93.3% 66,800 3 99.977% 230 5 35.0% 650,000 1.1 94.5% 54,800 3.1 99.985% 150 5.1 39.0% 610,000 1.2 95.5% 44,600 3.2 99.990% 100 5.2 43.0% 570,000 1.3 96.4% 35,900 3.3 99.993% 70 5.3 46.0% 540,000 1.4 97.1% 28,700 3.4 99.996% 40 5.4 50.0% 500,000 1.5 97.7% 22,700 3.5 99.997% 30 5.5 54.0% 460,000 1.6 98.2% 17,800 3.6 99.9980% 20 5.6 58.0% 420,000 1.7 98.6% 13,900 3.7 99.9990% 10 5.7 61.8% 382,000 1.8 98.9% 10,700 3.8 99.9992% 8 5.8 65.6% 344,000 1.9 99.2% 8,190 3.9 99.9995% 5 5.9 99.99966% 3.4 6 UNCLASSIFIED / FOUO 64
- 65. UNCLASSIFIED / FOUO How Do We Improve a Process? Desired Current LSL USL Lets say that you have this situation How do you go about improving it? UNCLASSIFIED / FOUO 65
- 66. UNCLASSIFIED / FOUO Shift Mean and Reduce Variability CPI Improvements Reduce Process Cycle Time and Improve Lean Six Sigma Reduces Process Cycle Time, Improving Consistency On- Time Delivery Performance for Tier One Auto Supplier (Average Cycle Time Reduced from 14 days to 2 days, (Average Reduced from 14 Days to 2 Days, Variance from 2 Days to 4 Hours) Variation Reduced from 2 days to 4 hours) 90% 80% 70% 60% % Distribution 50% 40% Distribution 30% Mean Delivery Time Reduced 20% Time Variation Reduced 10% 0% 0 2 4 6 8 10 12 14 16 18 20 Lead-Time (days) UNCLASSIFIED / FOUO 66
- 67. UNCLASSIFIED / FOUO “As Is” Baseline Statistics Template Summary for Workdays A nderson-Darling N ormality Test A -S quared 12.65 The current process P -V alue < 0.005 M ean 44.814 - Example - S tDev V ariance 61.251 3751.674 has a non-normal distribution with the S kew ness 2.87329 Kurtosis 9.54577 N 118 M inimum 1.000 P-Value < 0.05 1st Q uartile 12.000 Mean = 44 days M edian 22.000 0 60 120 180 240 300 360 3rd Q uartile 52.000 M aximum 365.000 Median = 22 days 95% C onfidence Interv al for M ean 33.647 55.981 95% C onfidence Interv al for M edian 17.000 29.123 95% C onfidence Interv al for S tDev Std Dev = 61 days 9 5 % C onfidence Inter vals 54.308 70.246 Mean Range = 365 days Median 20 30 40 50 60 Required Deliverable UNCLASSIFIED / FOUO
- 68. UNCLASSIFIED / FOUO Takeaways Now you should be able to: Explain the importance of measurement to process improvement Given process data, calculate a measure of central tendency and variation and describe what they tell us Identify and contrast special cause and common cause variation Given process data, calculate a Sigma Quality Level and describe what it tells us Explain what is meant by VOC and VOP UNCLASSIFIED / FOUO 68
- 69. UNCLASSIFIED / FOUO What other comments or questions do you have? UNCLASSIFIED / FOUO
- 70. UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO National Guard Black Belt Training APPENDIX UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO
- 71. UNCLASSIFIED / FOUO Process Capability Ratio – Cp Process Capability Ratio (Cp) is the ratio of total variation allowed by the specification to the total variation actually measured from the process Use Cp when: The mean can easily be adjusted (i.e., in many transactional processes the resource level(s) can easily be adjusted with no/minor impact on quality), AND The mean is monitored (so operators will know when adjustment is necessary – doing control charting is one way of monitoring) Typical goals for Cp are greater than 1.33 (or 1.67 for high risk or high liability items) If Cp < 1 then the variability of the process is greater than the specification limits. UNCLASSIFIED / FOUO 71
- 72. UNCLASSIFIED / FOUO Process Capability Ratio – Cp (Cont.) Cp = Allowed variation (Specification) or Cp = USL – LSL Normal variation of the Process 6 Where is “within” rather than pooled 99.7% of values -3 +3 Process Width LSL T USL UNCLASSIFIED / FOUO 72
- 73. UNCLASSIFIED / FOUO Process Capability Ratio – Cpk This index accounts for the dynamic mean shift in the process – the amount that the process is off target USL x x LSL Where is “within” C pk Min or rather than pooled 3σ 3σ Calculate both values and report the smaller number Notice how this equation is similar to the Z-statistic Z xx Cpk Z 3 s UNCLASSIFIED / FOUO 73
- 74. UNCLASSIFIED / FOUO Process Capability Ratio – Cpk (Cont.) Ratio of 1/2 total variation allowed by spec. to ½ the actual variation, with only the portion closest to a spec. limit being counted Use when the mean cannot be easily adjusted (i.e., in transactional processes where there is little flexibility, that is, where certain skill/expertise is not readily adjusted) Typical goals for Cpk are greater than 1.33 (or 1.67 if safety related) For sigma estimates use: R/d2 [short term] (calculated from X-bar and R chart) s= S (xi – x)2 [long term] (calculated from all data points) n-1 Long term: When the data has been collected over a time period and over enough different sources of variation that over 80% of the variation is likely to be included UNCLASSIFIED / FOUO 74

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