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HSBC Six Sigma Black Belt Training Analyse

HSBC Six Sigma Black Belt Training Analyse. April 2006 Rev 1.0. Analyse Phase. Module 1. Recap of the Measure Phase. Module 2. Overview of the Analyse Phase. Module 3. Graphical Data Analysis. Module 4. Simple – Identify, Rank and Validate Key X’s - 5 Why - Cause and effect diagram

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HSBC Six Sigma Black Belt Training Analyse

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  1. HSBC Six Sigma Black Belt Training Analyse April 2006 Rev 1.0

  2. Analyse Phase Module 1 Recap of the Measure Phase Module 2 Overview of the Analyse Phase Module 3 Graphical Data Analysis Module 4 Simple – Identify, Rank and Validate Key X’s - 5 Why - Cause and effect diagram - Multi-voting Module 5 Validate the Vital Few - One sample methods - Two sample methods - Chi-Square Module 6 More Advanced – Identify, Rank and Validate Key X’s - ANOVA - Simple regression Advanced – Identify, Rank and Validate Key X’s - Introduction to design of experiments Module 7 Module 8 Tollgate

  3. 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice Methodology overview Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps:

  4. Analyse Phase Module 1 Recap of the Measure Phase Module 2 Overview of the Analyse Phase Module 3 Graphical Data Analysis Module 4 Simple – Identify, Rank and Validate Key X’s - 5 Why - Cause and effect diagram - Multi-voting Module 5 Validate the Vital Few - One sample methods - Two sample methods - Chi-Square Module 6 More Advanced – Identify, Rank and Validate Key X’s - ANOVA - Simple regression Advanced – Identify, Rank and Validate Key X’s - Introduction to design of experiments Module 7 Module 8 Tollgate

  5. Measure Phase Objectives Measure Phase • It’s critical we first understand data demographics for our project to determine sampling characteristics and data collection requirements • We won’t repeat all of Measure, instead just cover • Measurement System Analysis (MSA) • Data Collection • Sample Size Determination • Process Capability Before moving intoanalyse, let’s leverage our tools to betterexplore and explain our project data

  6. Measure Phase – Remove Measurement Variation Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps: 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice Pocket guide (pages 41-45)

  7. Measure Phase – Remove Measurement Variation • We completed Measurement System Analysis (MSA) last time • Review the details in the material on the intranet or on the course CD • Measurements should be • Precise/accurate • Repeatable • Reproducible • Stable over time • Have adequate resolution Measure Tollgate A. Collect or create inputs B. Determine the correct decision 4. Map and analysethe process C. Identify the decision makers 5. Remove measurement variation & collect data 6. Determine process capability D. Administer the assessment E. Analyse the outcomes and take action MSA is an essential first step to minimise measurementbias prior to sampling & data collection

  8. MSA – What Is It? • A measurement system is composed of all the components and the processes used to obtain quantitative information about a process characteristic • Typical components are • People – the assessors • Measurement tool(s) – the gage • Material – the actual item/process being measured • Method – procedures • Environment – external conditions • A measurement system analysis is the investigation into how all of these components work together to measure the information needed to understand the process Unfortunately, these components can bring their own level of variation to the process. MSA is analysis and control of measurement variation

  9. Repeatability Variation that occurs when repeated measurements are made of the same item under absolutely identical conditions Reproducibility Variation that occurs when different conditions are used to take measurements MSA Review OperatorB You’re a smooth operator… Let’s seeif your friends are as smooth as you! Ask me again, and I’ll tell you the same! OperatorC OperatorA Repeatability Reproducibility Our measures need to be reliable

  10. Step 1 – Create inputs Decide on the outputs to be evaluated (inputs) The inputs need to be Representative Equally represented in the set of outputs Correct decision should not be too obvious Sufficient sample size Ensure 50% of inputs are defect-free Determine number of inputs needed Step 2 – Determine standard Develop a standard Have two credible decision makers inspect or review each input Come to a consensus agreement with each other as to the correct disposition MSA Review

  11. Step 3 – Identify decision makers Identify the person or persons who are going to participate in the study These should be individuals who make the decisions within the process under study on a regular basis Selected decision makers have to meet the following guidelines Familiar process Same location Same time constraints Step 4 – Administer The structure of the assessment requires that each decision maker evaluate each item at least twice Process 1st person evaluates all of the samples in trial 1 2nd person does the same Once all the people have assessed, the samples are returned to the 1st person for an evaluation in trial 2 Then back to 2nd person Be aware of bias MSA Review

  12. Step 5 – Analyse outcome and take action Analyse outcome and take actions Assess Assessor effectiveness Overall MSA Biases Actions include Immediate corrections Refined definitions Training Gage recalibration Starting over MSA Review

  13. Measure Phase – Collect Data Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps: 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice Pocket guide (pages 22-52)

  14. Measure Phase – Collect Data Measure Tollgate A. Data demographics 4. Map and analysethe process Remember, must complete MSA prior to collecting or analysing data! 5. Remove measurement variation & collect data 6. Determine process capability B. Sampling Data collection begins with the end in mind. “What do you want to know?”

  15. Collect Data & Sampling Measure A1. Select what to measure Tollgate A2. Develop operational definitions A. Data demographics A3. Identify data sources 4. Map and analysethe process A4. Prepare data collection form A5. Implement and refine data collection 5. Remove measurement variation & collect data B1. Sample types and terminology 6. Determine process capability B2. Confidence B. Sampling B3. Sampling techniques B4. Sample size formulas/calculators Data demographics + sampling = Data collection

  16. Select What To Measure • Selecting what you need to measure is not always easy • Initially, you may have to simply count defects that show up in your process output (Y) • Then, go back to your process map and measure the performance of those process steps that seem to be contributing to output defects (suspect x’s) • Use a CTQ Tree format to identify measures • Use the XY Matrix to prioritise x’s Application availability (uptime) Systems Funding source Network availability (uptime) Market instructions Timely trades (Y) Advisor Origination Destination Equity of fixed income Security Lot size Market 1st Step: What are you going to measure?

  17. Develop Operational Definitions • Saying that your team will count the number of defects in a service is easy. But what do you mean by “defect” or “service”? • Without having precise definitions for the things you’re trying to measure, different people will count different things in different ways • To avoid this confusion, you need to have operational definitions • A clear, understandable description of what’s to be observed and measured, such that different people taking or interpreting the data will do so consistently 2nd Step: Create clear and understandable data definitions

  18. There are two main sources of data available to the team Data that is already being collected in your organisation and has been around for some time (usually called “historical” data) New data that your team collects Historical data can be handy, when you have it - it requires fewer resources to gather, it’s often computerised, and you can start using it right away But be warned! Existing data may not be suitable if It was originally collected for reasons other than process improvement It uses different definitions Data structure makes it hard to stratify (or database lacks sort capability) Identify Data Sources 3rd Step: Where are you going to get the data?

  19. What? Why? Who? How? When? Where? Measures Operational definition Formula Purpose Single person Collection method Dates/times Source of the data responsible frequency collection Prepare Data Collection Plan Actions taken to validate measurement system Sampling information Type of Data Discrete Continuous(please circle one) Sample size Collection time period 4th Step: Now that you know what you want… how do we plan to get it?

  20. Implement And Refine Data Collection • There are five steps in implementing and refining the data collection process • Review and finalise your data collection plans • Prepare the workplace • Test your data collection procedures • Collect the data • Monitor accuracy and refine procedures as appropriate Final Step: Are you sure that your plan will work? Have you tested it?

  21. Measure Phase – Determine Sample Size Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps: 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice Pocket guide (pages 47-51)

  22. Sample Types & Terminology • Samples are either judgmental or statistical • A judgmental sample is selected based upon the opinion of the analyst and the results may be used to make inferences only about those items from within the sample • A statistical sample is randomly selected from the entire population and the results may be used to make inferences about the entire population Judgmental vs Statistical sampling Judgmental sample Statistical sample • Sample is selected based on knowledge and experience • Only a subset of the population is included in the selection process • Sample is assumed to be representative of the population • Sample is selected randomly • Entire population is included in the selection process • Sample is representative of the population 1st Consideration – Do you need opinions or facts?

  23. Sample Types & Terminology Sampling is the process of collecting only a portion of available data either from a static data group (population) or on an ongoing basis (process), and drawing conclusions about the total population when the process is stable (statistical inference) • Population (N): The entire set of objects or activities for a process • The mean (μ) is the arithmetic average calculated for a population • The standard deviation (σ) is calculated for a population • Sample (n): A group that is part or subset of a population • The mean (x) of a sample • The standard deviation (s) of a sample The sample is a “window” into the population

  24. Sample Types & Terminology Population approach • Make probability statements about the population from the sample • “I have 95% confidence that the mean of the population is between 1.5 and 2.5 min” Process approach • Assess the stability of the population over time • Are shifts, trend, or cycles occurring? • Special or common cause? Population approach Process approach …the type of “window” you use depends on the population

  25. 10000 8000 6000 4000 Sample size 2000 0 -2000 0 .05 .1 .15 .2 Precision interval Confidence Level And Precision • Confidence is the probability that the actual population value being estimated will be contained within the precision interval of our estimate • The precision interval represents the total amount of sampling error that you should expect for any specific sample size • This chart shows the relationship between sample size and precision for estimating the proportion of defects in a transaction process (95% CL) Sample size and precision interval 2nd Consideration – How precise do you need to be?

  26. Population Sample X X X X X X X X X X Randomsampling X X X X X X Population B A A B Sample B B A B A B A A B B B C D D Stratified random sampling B D D D C C D D D Sampling Techniques • Random • Sample is selected in a purely random fashion • Each unit has the same chance of being selected • Stratified random • The population is segmented into more than one layer (stratum) and items are randomly selected within each layer • Every item in the population has a chance (not equal) of being included in the sample

  27. X X Sample Systematicsampling X X X X Preserve Time Order 09:30 09:45 10:00 10:15 XXXXX XXXXXXX XXXXXX XXXXXX Subgroupsampling Sample X X X X Preserve Time Order Sampling Techniques • Systematic • Samples are selected based on a pre-defined sequence and are selected as they’re being produced by the process • Subgroup • Sample n units every t hour (ex: 3 units every hour) • Calculate the mean (proportion) for each subgroup

  28. Sample Size Formula Data Variable/continuous Attribute/discrete 2 2 1.96s 1.96 [p(1-p)] n= n= d d n = ? s = 24.03 d = 2 n = ? d = .02 p = 5% n = sample size s = standard deviation d = precision p = proportion defective 1.96 = 95% Confidence Lastly, how much data do you need?

  29. Sample size n=54 Sample Size Calculators (JMP)

  30. Measure Phase – Determine Process Capability Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps: 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice Pocket guide (pages 86-92)

  31. Determine Process Capability • We covered capability last time. You can review the details in the material on the intranet or on the Course CD, or refer to pages 86-93 in the Pocket Guide • Process capability measures how much variation there is in a process relative to customer specification • As your data collection improves the picture of your process, go back and validate the process capability relative to customer specifications Measure Tollgate A. VOC 4. Map and analysethe process B. Determine Y 5. Remove measurement variation & collect data 6. Determine process capability C. Z, Sigma, Yield Process capability is the metric that our customers feel

  32. Determine Process Capability Identify process Define CTQ Define unit, defect, & defect opportunity Count units, opportunities, & defects Discrete orcontinuous data Discrete Continuous Calculate defect rate: Count defects per million opportunities Identify distribution set defect limits calculate yield Look up Sigma value in table Convert yield into short term sigma value

  33. Determine Process Capability • Step 1 – Use process measures to determine output (Y) • Step 2 – VOC data and analysis will determine customer specifications in terms of Y measure • Step 3 – Determine defects • Continuous data: Calculate z score and translate to sigma or yield • Discrete data: Calculate DPMO and translate to yield of sigma

  34. Analyse Phase Module 1 Recap of the Measure Phase Module 2 Overview of the Analyse Phase Module 3 Graphical Data Analysis Module 4 Simple – Identify, Rank and Validate Key X’s - 5 Why - Cause and effect diagram - Multi-voting Module 5 Validate the Vital Few - One sample methods - Two sample methods - Chi-Square Module 6 More Advanced – Identify, Rank and Validate Key X’s - ANOVA - Simple regression Advanced – Identify, Rank and Validate Key X’s - Introduction to design of experiments Module 7 Module 8 Tollgate

  35. Methodology Overview Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps: 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice

  36. Analyse Phase Objectives Analyse phase • In Analyse, you will use data collected in the define & measure phase to Module 4 Module 5 Module 6 Module 7    Identify sourcesof variation   Rank key causes of variation     Validate root causes Analyse requires us to identify the “likely suspects…”

  37. The Paths For The Analyse Phase 6. Determine process capability Simple “<2 Sigma” • Graphical data analysis • Brainstorming • Five-whys • Cause and effect diagram • Multi-voting • Process analysis - waste elimination(covered in measure) Measure Tollgate Process stable? Common cause strategy More advanced “2-3.5 Sigma” Yes All tools above and • Validating the vital few • 1 sample methods • 2 sample methods • Chi-Square • 1 and 2 way ANOVA • Simple regression No Special cause strategy • Quick hits • Waves of RIP’s • Fix obvious problems • Just do it! Advanced “>3.5 Sigma” All tools above and • DOE

  38. Analyse Phase Module 1 Recap of the Measure Phase Module 2 Overview of the Analyse Phase Module 3 Graphical Data Analysis Module 4 Simple – Identify, Rank and Validate Key X’s - 5 Why - Cause and effect diagram - Multi-voting Module 5 Validate the Vital Few - One sample methods - Two sample methods - Chi-Square Module 6 More Advanced – Identify, Rank and Validate Key X’s - ANOVA - Simple regression Advanced – Identify, Rank and Validate Key X’s - Introduction to design of experiments Module 7 Module 8 Tollgate

  39. Methodology Overview Define Measure Analyse Engineer Control Tollgate Tollgate Tollgate Tollgate Tollgate • Clarify problem • Achieve consistency between • Problem statement • Business case • Goals & objectives • Obtain unbiased view of the requirements • Agree on project timeline • Develop macro view of process(es) involved • Establish baseline • Stratify problem or opportunity to a component level specific enough to analyse • Establish key areas of the process where the data are collected • Establish valid data collection plan • Remove or account for measurement variation • Finalise problem statement • Identify the critical factors driving the requirement(s) (Y’s) • Identify improvement impact • Find root cause(s) of variation • Generate solution • Develop and test improvements • Complete pilot testing • “Should be” process • Develop cost/benefit • Develop/build implementation plan • Validate improvement • Establish new performance levels • Sustain good performance levels • Establish corrective & contingency action plan • Translate & transfer learnings • Celebrate! Steps: 1. Complete team charter 4. Map and analysethe process 7. Identify sourcesof variation 10. Generatesolution ideas 13. Implement solution 2. Specify customer requirements & MGP 5. Remove measurement variation & collect data 8. Rank key causesof variation 11. Select best fit solution 14. Monitor processand results 3. Complete high level process map 6. Determine process capability 9. Validate root causes 12. Test solution and confirm results 15. Replicate and share best practice

  40. Module Objectives By end of this module you should be able to • Catalogue the core tools available to graphically display data given the various combinations of continuous and discrete Y’s and x’s • Be proficient in executing each of the graphical analysis tools using JMP • Analyse tool output to identify sources of variation and candidates for further analysis

  41. In The Analyse Phase • Primary activities to assist in identifying variation • Graphical data analysis • Brainstorming • Five-whys • Cause and effect diagram Measure Tollgate A. Graphical data analysis 7. Identify sources of variation B. Brainstorming 8. Rank key causes of variation C. Five whys 9. Validate root causes D. Cause and effect diagram We have to first think “out of the box” before we can focus “inside the box…”

  42. Identifying Sources Of Variation • Define provided focus and scope through the Charter • Measure provided further focus through data collection and calculation of process capability • Now, we need to identify the major sources of variation • We’ll “filter” the results to answer the critical question... • What vital few process inputs and variables (x’s) have the greatest impact on process performance (Y)? We have so much data! We need good filters to sort through it all!

  43. Graphical data analysis Brainstorming Five- whys Cause and effect Process analysis Key “nuggets” (root causes) Identify Sources Of Variation • Variation can be identified using a variety of tools • Graphical data analysis • Brainstorming • Five-whys • Cause and effect diagramming • Also... process analysis (covered in Measure Phase) Our filters (tools) separate the vital few “nuggets” from the rest of the trivial many

  44. Stratification is a data analysis technique by which data are sorted into various categories Through the identification of specific factors, one can surface suspicious patterns and uncover differences in processes Important to “stratify the data” to focus and prioritise improvement efforts later in the Engineer Phase Data stratification helps to identify the impact of each x on Y Compares variation in Y with each individual x Results identify critical x(s) Concerned with the direction and magnitude of the relationship, not why one exists Graphical Data Analysis And Stratification Stratification is exploration

  45. Stratification will point to the factors that have the greatest impact on a problem May need to expand (or narrow) the problem and goal of your project Establish priorities for further analysis Provide clues regarding possible causes by comparing “good” and “bad” Common factors used for stratification: Type (What is occurring?) Timing (When it occurs?) Frequency (How often does it occur?) Where (Where in the process or location?) Who (Which business, department, employee, customer group?) Graphical Data Analysis And Stratification Goal of data stratification is to prioritise and focus efforts

  46. Total trade cycle time 140 130 120 110 100 90 80 70 0 10 20 30 Months starting January 2003 Fixed income Equity 140 140 130 130 120 120 110 110 100 100 90 90 80 80 70 70 0 10 20 30 0 10 20 30 Months starting January 2003 Months starting January 2003 Stratification Example

  47. Graphical Data Analysis Tool Selector Discrete Continuous X Y Discrete/counts Bar chart, Histogram, Pareto chart, Pie chart Bar chart, Histogram, Pareto chart Continuous Box plot, Multi-variability chart Scatter plot, Run chart*, Multi-variability chart * When plotting Y against time - always use a Run Chart

  48. Graphical Data Analysis Tool Selector Discrete Continuous X Y Discrete/counts Bar chart, Histogram, Pareto chart, Pie chart Bar chart, Histogram, Pareto chart Continuous Box plot, Multi-variability chart Scatter plot, Run chart*, Multi-variability chart • Discrete Y vs x: Generally, this type of data will focus on counts of defects or of specific output types • We can use simple tools like Pareto Charts and Pie Charts to identify any relationship between Y and x’s * When plotting Y against time - always use a Run Chart

  49. 160 100% N= 160 140 90% 85% 120 75% 75% 100 55% Number of errors 80 50% 60 40 25% 20 88 32 16 8 16 0 0 Typos Other Empty fields Missing pages Wrong fieldsentries Date Prepared Type of error Collected By Date Source Formula Pie Chart, Pareto Chart Pie chart Trade error rate by brokerage offices Pareto chart Pareto chart of loan application errors5/12 to 5/13/96 - Raleigh office

  50. Graphical Data Analysis Tool Selector Discrete Continuous X Y Discrete/counts Bar chart, Histogram, Pareto chart, Pie chart Bar chart, Histogram, Pareto chart Continuous Box plot, Multi-variability chart Scatter plot, Run chart*, Multi-variability chart • The Y is sometimes characterised as a discrete value, often as a defect (or non-defect) • The x being studied varies over a continuous range * When plotting Y against time - always use a Run Chart

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