Quantify and Verify Causes Six Sigma Fundamentals Continuous Improvement Training Six Sigma Fundamentals Continuous Improvement Training Six Sigma Simplicity

ObjectiveObjective  GB certification criteria: “Quantify and verify the effect of the critical x's on the y”

Basic process 1. Focus on some X’s 2. Select and gather data points for each graph 1. Understand Variation in Y 2. Draw Histogram of Y 3. Understand Variation in X 4. Draw Histogram of X 5. Plot X vs Y 6. (BB will in addition plot X vs other X’s and combinations of X’s vs Y) 3. Review with the team 1. Verify - Can we see a link between the process and the data? 2. Quantify – how big a change in Y do the verified X’s cause 3. If it depends gather more data and make a decision 4. Repeat within budget and until you have enough quantified X’s 1. Focus on some X’s 2. Select and gather data points for each graph 1. Understand Variation in Y 2. Draw Histogram of Y 3. Understand Variation in X 4. Draw Histogram of X 5. Plot X vs Y 6. (BB will in addition plot X vs other X’s and combinations of X’s vs Y) 3. Review with the team 1. Verify - Can we see a link between the process and the data? 2. Quantify – how big a change in Y do the verified X’s cause 3. If it depends gather more data and make a decision 4. Repeat within budget and until you have enough quantified X’s

Why verify potential causes?  People’s opinion on potential causes might be different or wrong  Need to determine and confirm the deeper causes with the biggest impact resulting in the problem  Develop solutions for the verified causes  People’s opinion on potential causes might be different or wrong  Need to determine and confirm the deeper causes with the biggest impact resulting in the problem  Develop solutions for the verified causes

Where to begin?  With the list of possible causes ask the team where they would like to begin the search. This ensures high acceptance. With practice you can quickly eliminate non-X’s. From your initial list n/3 can be very helpful.  This is a good time to consult a black belt  With the list of possible causes ask the team where they would like to begin the search. This ensures high acceptance. With practice you can quickly eliminate non-X’s. From your initial list n/3 can be very helpful.  This is a good time to consult a black belt

Process and Data Doors  There are two methods - 1) Process Is there any logical link between the suggested cause and the output? 2) Data Can it be shown consistently that if the suggested cause changes Y changes  You can start with either method. Causes are eliminated if they do not satisfy both  There are two methods - 1) Process Is there any logical link between the suggested cause and the output? 2) Data Can it be shown consistently that if the suggested cause changes Y changes  You can start with either method. Causes are eliminated if they do not satisfy both

Process Door : tools & techniques  SIPOC  Detailed sub-process mapping  Value Flow Analysis  VA, NVA, ENVA analysis  Brown Paper  Fishbone  XY Matrix  SIPOC  Detailed sub-process mapping  Value Flow Analysis  VA, NVA, ENVA analysis  Brown Paper  Fishbone  XY Matrix

Data Door : tools & techniques  Graphical Data  Time Plots  Understanding Variation  Histogram/ Capability  Superimpose X and Y Time plots  Variable X’s  Scatter plot X vs Y  Best fit line  Attribute X’s  Pareto  Effects Plot X vs Y  Box plot  Graphical Data  Time Plots  Understanding Variation  Histogram/ Capability  Superimpose X and Y Time plots  Variable X’s  Scatter plot X vs Y  Best fit line  Attribute X’s  Pareto  Effects Plot X vs Y  Box plot  Statistics  Has a metric moved?  Does X effect Y  + many more covered in weeks (modules) 3 and 4. For which you have a black belt

Data Door : terminology  Population  All of the units or individuals who exist and who will exist in the future  Sample  A subset of units or individuals drawn from the population, either at one time or over time  Observation  An individual measurement  Population  All of the units or individuals who exist and who will exist in the future  Sample  A subset of units or individuals drawn from the population, either at one time or over time  Observation  An individual measurement

Understanding Variation in X or Y The control chart enables us to identify possible special causes

Plot Y or X histogram  This enables use to identify whether the process is one process or many put together.  Usually we expect certain shapes to the process histogram if these shapes are not present then we suspect multiple processes or the measurement system.  This enables use to identify whether the process is one process or many put together.  Usually we expect certain shapes to the process histogram if these shapes are not present then we suspect multiple processes or the measurement system.

Expected shape Normality LSL USL I have a dream

Classes of non normality : Right skew Possibly multimodal or typical shape for lead time or a process with rework (with no overtime)

Classes of non normality : Left skew Possibly multimodal or typical shape for lead time (with overtime) or a process with a limit

Classes of multi modal non normality : Flat, Pointy, Multi modal, Bi modal

Non-normalityNon-normality  Identifying why data is not normal is a great step in solving problems  For these purposes, the actual distribution of data and the presence and location of outliers can be of great help in solving the problem.  If your only interest in the data is to find influential variables in the process or to solve problems with the process, then you will not gain anything by correcting the data.  Identifying why data is not normal is a great step in solving problems  For these purposes, the actual distribution of data and the presence and location of outliers can be of great help in solving the problem.  If your only interest in the data is to find influential variables in the process or to solve problems with the process, then you will not gain anything by correcting the data.

Lead time Verifying X’s

Exercise– lead times  You have been asked to work on reducing lead times by 20%  On the next page are the lead times for the last 20 orders.  You have been asked to work on reducing lead times by 20%  On the next page are the lead times for the last 20 orders.  As a team draw a histogram and run chart for the order lead times and identify possible causes  You have 20 minutes

Exercise - Lead times (weeks)  Note: When using the data door we need to repeat the 5 step process of Data Collection – The team quickly get this data for the orders shipped this month  3,5,4,2,4,3,4,1,20,4,2,2,4,1,5,4,2,3,4,2,3,2,4,1,3,3,4,16,4,2,4,4,3,3,3,2,2,2,3,3,4,4,4,1,3,4,4,3,1,2,2, 2,3,18,17,18,3,19,3,4,3,1,2,4,1,20,4,0,2,3,19,2,2, 19,4,3,4,5,3,4,2,3,5,2,34,3,1,17,5,4,4,20,4,2,3,4,3,4,3,3,4,3,4,18,2,2,17,3,17,4,2,3,2,2,3,3,3,3,3,1,3, 3,3,1,4,2,4,3,4,4,3,2,3,4,3,32,5,2,2,2,1,3,4,4,3,2,0,3,5,3,3,5,3,2,2,3,2,4,3,1,2,3,3,1,3,3,1,3,2,4,2,4,5, 3,19,4,4,18,1,4,3,3,2,3,4,4,2,4,2,4,4,3,3,3,5,5,3,4, 2,2,4,2,4,5,2,5,3,16,4,4,3,4,5,4,1,3,2,2,3,  Note: When using the data door we need to repeat the 5 step process of Data Collection – The team quickly get this data for the orders shipped this month  3,5,4,2,4,3,4,1,20,4,2,2,4,1,5,4,2,3,4,2,3,2,4,1,3,3,4,16,4,2,4,4,3,3,3,2,2,2,3,3,4,4,4,1,3,4,4,3,1,2,2, 2,3,18,17,18,3,19,3,4,3,1,2,4,1,20,4,0,2,3,19,2,2, 19,4,3,4,5,3,4,2,3,5,2,34,3,1,17,5,4,4,20,4,2,3,4,3,4,3,3,4,3,4,18,2,2,17,3,17,4,2,3,2,2,3,3,3,3,3,1,3, 3,3,1,4,2,4,3,4,4,3,2,3,4,3,32,5,2,2,2,1,3,4,4,3,2,0,3,5,3,3,5,3,2,2,3,2,4,3,1,2,3,3,1,3,3,1,3,2,4,2,4,5, 3,19,4,4,18,1,4,3,3,2,3,4,4,2,4,2,4,4,3,3,3,5,5,3,4, 2,2,4,2,4,5,2,5,3,16,4,4,3,4,5,4,1,3,2,2,3,

Lead time Exercise – continued  The team strongly believes that 2 X’s may be important in increasing the lead time Y  For the last 20 lead times they collect  X1 the Number of Days from order entry until the BOM is completed  X2 the number of days from order entry that the castings are received  The team strongly believes that 2 X’s may be important in increasing the lead time Y  For the last 20 lead times they collect  X1 the Number of Days from order entry until the BOM is completed  X2 the number of days from order entry that the castings are received

Lead time exercise Create with your team for both X’s 1. Y vs X 2. X run chart 3. X histogram 4. Y,X against time  Using the 8 graphs do you believe that the X’s may be significant? Create with your team for both X’s 1. Y vs X 2. X run chart 3. X histogram 4. Y,X against time  Using the 8 graphs do you believe that the X’s may be significant?

Production capacity Quantifying X’s

Plot X vs Y – Observed Effects Plot  The observed effects plot is a tool which can give us a way to quickly share the change in X’s effect on Y 1. Measure Y as a variable 2. Record X as an attribute – each different value X can have is called a level 3. Draw a dot plot for each level of X on the same Axis for Y 4. Identify the average value of Y for each level of X 5. Record the observed effect as the change in average value for Y  The observed effects plot is a tool which can give us a way to quickly share the change in X’s effect on Y 1. Measure Y as a variable 2. Record X as an attribute – each different value X can have is called a level 3. Draw a dot plot for each level of X on the same Axis for Y 4. Identify the average value of Y for each level of X 5. Record the observed effect as the change in average value for Y

Effect - definition  If you have 2 sets of data the effect of one set is the difference in the sets average  E.g. ( ) and (4 7 10)  Averages ( 3 ) and (7)  Effect between ( ) and (4 7 10) = -4  Effect between (4 7 10) and ( ) = 4  Key X’s create large significant effects in Y  If you have 2 sets of data the effect of one set is the difference in the sets average  E.g. ( ) and (4 7 10)  Averages ( 3 ) and (7)  Effect between ( ) and (4 7 10) = -4  Effect between (4 7 10) and ( ) = 4  Key X’s create large significant effects in Y

Example observed Effects Plot  Y = Shipments in number of units  What is the effect of the day of the week?  Y = Shipments in number of units  What is the effect of the day of the week?

Example Effects – day of week  On Monday Average = 4 units per day on Friday Average = 8.5 units per day  Effect of Friday against Monday = = 4.5 units  On Monday Average = 4 units per day on Friday Average = 8.5 units per day  Effect of Friday against Monday = = 4.5 units

Example Effects – day of week Average Average of all shipments 4.9 Mondays4= ( )/4 Fridays8.5 = ( )/4 Weekends 3.5 = ( )/8 Weekdays Including Fridays 5.5

Effects Graph For Day of Week  Note – dotted line is overall average  Red marks show average for each level (day)  Which Day(s) have the biggest effect upon the shipments?

Pareto of Effects  If, you take the absolute effect between the effect of a day and the overall average shipments you can draw a Pareto which orders the magnitude of the effects. (Eg. Overall average = 4.9 units / day, average on Friday = 8.5 units  If you could do what ever you do on a Friday on a Thursday how many more shipments would you expect each week?  Would the team be better to focus on the Effect of Weekend working patterns instead?

Exercise Effects Plot  Y = Shipments in number of units  Draw the effects graph for effect of the week of the month week upon number of units shipped?  Is it bigger than the effect of Friday?  Y = Shipments in number of units  Draw the effects graph for effect of the week of the month week upon number of units shipped?  Is it bigger than the effect of Friday?

Variable data and Effects plots  Closer review of the shipments on a Friday in comparison to Thursday reveals a possible cause a different approach to overtime  So the team finds out how many hours overtime was worked  Closer review of the shipments on a Friday in comparison to Thursday reveals a possible cause a different approach to overtime  So the team finds out how many hours overtime was worked

Shipped vs Overtime  If Overtime is important how can we compare it with the other effects?

Effect of overtime  To calculate the effect of overtime we need to break overtime into 2 levels – e.g. 0 – 10 hours overtime and 10+ hours of overtime  The average number of shipments when 0-10 hours of overtime are worked is 3.6,  The average number of shipments when 10+ hours of overtime are worked is 9.6.  The effect of working more than 10 hours overtime = _______ shipments per day  Is this effect bigger than that of Fridays?

What is a “Significant” effect? Are the shipments on Day 3 Wednesday or Day 1 Monday “significantly” different from each other? How sure are we of our decision?

Effects and Significance  Practical effect and significance  The amount of change, or improvement that will be of practical, economic, or technical value to you  The amount of improvement required to pay for the cost of making the improvement  Statistical effect and significance  The magnitude of effect or change required to distinguish between a true effect, change, or improvement and one that could have occurred by chance  We can use non graphical data analysis to help make decisions whether effects are significant when it is otherwise unclear  Practical effect and significance  The amount of change, or improvement that will be of practical, economic, or technical value to you  The amount of improvement required to pay for the cost of making the improvement  Statistical effect and significance  The magnitude of effect or change required to distinguish between a true effect, change, or improvement and one that could have occurred by chance  We can use non graphical data analysis to help make decisions whether effects are significant when it is otherwise unclear

Signal to Noise ‘Delta Sigma’ -The Ratio between  and   Delta (  ) or signal is the size of the effect between two means or one mean and a fixed value.  Sigma (  ) or noise is the sample standard deviation of the distribution of individuals of one or both of the samples under question.  If the variance of the data is large it is difficult to establish effects. We need larger sample sizes to reduce uncertainty.  Delta (  ) or signal is the size of the effect between two means or one mean and a fixed value.  Sigma (  ) or noise is the sample standard deviation of the distribution of individuals of one or both of the samples under question.  If the variance of the data is large it is difficult to establish effects. We need larger sample sizes to reduce uncertainty. X high X low Signal or Delta Noise or Sigma

Effects and Significance For normal data, statistical significance is all about effects. In general 1. Larger signal/noise ratio is more significant 2. Larger sample sizes are more significant 3. Larger effects are more significant For normal data, statistical significance is all about effects. In general 1. Larger signal/noise ratio is more significant 2. Larger sample sizes are more significant 3. Larger effects are more significant 1 3 2

Risk in deciding significance  We can get the decision as to whether an effect is significant wrong  Risk can be measured objectively e.g. % car crashes. Increase in cancer amongst smokers  We can get the decision as to whether an effect is significant wrong  Risk can be measured objectively e.g. % car crashes. Increase in cancer amongst smokers  To make CI decisions objective we ask Green Belts to use consistent risk levels  For a fuller understanding ask a black belt or refer to your location library

CIP Significance Risk Factors  The levels that we ask you to use are such that you will be right  95% of the time when you say an effect is significant you will be correct  90% of the time when you say that an effect is not significant you will be correct  The levels that we ask you to use are such that you will be right  95% of the time when you say an effect is significant you will be correct  90% of the time when you say that an effect is not significant you will be correct

Why 2 risks?  Ever sat at a road junction in your car?  When you take the turn you are comparing the risk of waiting for a safer moment to turn and the risk of sitting at the junction all day  However our response to risk is subjective. Just compare your driving to that of a taxi Crash Alpha Error Wait Beta Error Correct Decision Correct Decision True Conditions DangerousSafe Dangerous Safe Your decision

How to decide if effects are significant  You have two sets of data.  They have different average values.  This table shows how much data you need to identify if the effect is significant?  You have two sets of data.  They have different average values.  This table shows how much data you need to identify if the effect is significant? X high The Effect X low The Delta (  )

Does an X have a significant Effect?  The team is sure that a significant number of late General Arrangement Drawings (GA’s) is due to subcontractors.  You find that for the last 5 GA’s where there is no subcontractor involvement, the lead time is on average 5 days standard, deviation 1 day.  For the last 5 GA’s which required sub-vendor involvement the lead time was 7 days standard, deviation 1 day  Is the team right to believe that the impact of sub-vendors is significant?  What would you do next?

Practically significant X’s  You have gathered two sample sizes of  When Manchester United wins, production the following week is 100 seals, standard deviation 5.  When Manchester United looses, the production following week is 80 seals, standard deviation 5. Does the football team’s results have an impact on the production?  You have gathered two sample sizes of  When Manchester United wins, production the following week is 100 seals, standard deviation 5.  When Manchester United looses, the production following week is 80 seals, standard deviation 5. Does the football team’s results have an impact on the production?  Statistically there is a relationship between the numbers. But we should already have checked the process door – if no one related to the process cares whether Manchester United wins/ looses then the team should reject the idea.

Has a project had significant effect?  E.g 10 weeks before project. Metric from 10 measurements was average 20, standard deviation 12.  During the last 10 weeks average is 32, standard deviation 12.  Is the effect of the project significant?  E.g 10 weeks before project. Metric from 10 measurements was average 20, standard deviation 12.  During the last 10 weeks average is 32, standard deviation 12.  Is the effect of the project significant?  Delta / Sigma = (32- 20)/12 = 1  For Delta Sigma 1 the table shows you need a sample size of 23 to be sure. So it is unsafe to suggest that the project has had a real impact on the metric so far

ProportionsProportions

Proportions %  Proportions – values which can be expressed between 0 and 1 or 0% and 100%  Unfortunately when proportions are measured they are very susceptible to sample size. You may need a Black Belts assistance to identify, for your circumstances, how significant results are  Proportions – values which can be expressed between 0 and 1 or 0% and 100%  Unfortunately when proportions are measured they are very susceptible to sample size. You may need a Black Belts assistance to identify, for your circumstances, how significant results are

Samples and proportions  Lets assume a coin has an even chance of landing on heads or tails  If I flip it 100 times will I get 50 heads  Lets assume a coin has an even chance of landing on heads or tails  If I flip it 100 times will I get 50 heads Pair up and try it!

When is it safe to predict that the coin will land heads 50% of the time. How many tosses would we need to identify if the tossing process or, if the coin had changed? Number of times coin tossed Number of heads % heads

On time delivery  How many units do you have to record before you can predict that the on time delivery is 50% of the time?  How many units do you have to measure to notice whether the process that produces on time delivery has successfully changed from 50%?  How many units do you have to record before you can predict that the on time delivery is 50% of the time?  How many units do you have to measure to notice whether the process that produces on time delivery has successfully changed from 50%?

Practical application  Plant A produces 66% on time this month and 95% on time last month – How should we react?  Find out if the measurement is valid  Find out the sample size  Get a black belt to tell you whether this is statistically significant  If it is statistically significant and practically significant start to investigate potential X’s

Chi-Square testing  What comparing two samples is for continuous variables, Chi-squared is for proportions.  It enables us to identify when changes in Y occur and whether different X’s produce significantly different values in Y.  Its’ basis is to look at how much subsets of data are different from the whole, then to compare the effects with sample size.  What comparing two samples is for continuous variables, Chi-squared is for proportions.  It enables us to identify when changes in Y occur and whether different X’s produce significantly different values in Y.  Its’ basis is to look at how much subsets of data are different from the whole, then to compare the effects with sample size.

Chi-Square testing on Y’s  Ask a Black Belt  Inventory accuracy has been recorded from December to May and is observed to vary between 80% and 89%. Over the whole period the average inventory accuracy is 84%  Has there any evidence that the process has significantly changed?

Chi-Square testing on X’s  Ask a Black Belt  You are trying to improve on time delivery. The team suggests that the engineered product is performing worse than Parts. Is this true?

SummarySummary  Follow the process  Use your black belt  Result is that we will reduce conflict by sharing with the key stakeholders objective information, right 95% of the time, about what will and will not work in the improvement phase before we invest in change  Follow the process  Use your black belt  Result is that we will reduce conflict by sharing with the key stakeholders objective information, right 95% of the time, about what will and will not work in the improvement phase before we invest in change

DeliverablesDeliverables  Find enough the Key X’s to complete your project  Show from the Identified causes  which have no link to the process  which have an insignificant effect  and their effect on Y  Find enough the Key X’s to complete your project  Show from the Identified causes  which have no link to the process  which have an insignificant effect  and their effect on Y

Quantify and Verify Causes Six Sigma Fundamentals Continuous Improvement Training Six Sigma Fundamentals Continuous Improvement Training