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ANALYZE PHASEANALYZE PHASE
Potential Problem AreaPotential Problem Area Lack of participation from the Lack of participation from the
team membersteam members And inadequate data for making And inadequate data for making
decisions and monitoring the decisions and monitoring the processprocess
Black belts should be prepared to Black belts should be prepared to spend time either researching old spend time either researching old records or collecting new records or collecting new information on the processinformation on the process
Purpose of the Analyze Purpose of the Analyze PhasePhase
Evaluate and reduce the variables, Evaluate and reduce the variables, using graphical analysis and using graphical analysis and hypothesis testinghypothesis testing
Identify the vital few factors in order Identify the vital few factors in order to identify the root cause of the to identify the root cause of the defectsdefects
Help to quantify the performance Help to quantify the performance gap and the benefits of improving the gap and the benefits of improving the processprocess
Analyze Phase ToolsAnalyze Phase Tools Histograms: Bar graph that displays the Histograms: Bar graph that displays the
relative frequency of continuous data relative frequency of continuous data valuesvalues
Box Plots: Basic graphing tool that Box Plots: Basic graphing tool that displays five points that represent the displays five points that represent the centering, spread, and distribution of a centering, spread, and distribution of a set of continuous dataset of continuous data The plot consists of a box, whiskers, and The plot consists of a box, whiskers, and
outliers and shows the maximum value, the outliers and shows the maximum value, the minimum value, the median, the 75th minimum value, the median, the 75th percentile and the 25th percentilepercentile and the 25th percentile
Analyze Phase ToolsAnalyze Phase Tools Dot Plots:Dot Plots:
Simple graphical display of data Simple graphical display of data points of a noncontinuous variable, points of a noncontinuous variable, with each observation represented with each observation represented by a dot placed above a horizontal by a dot placed above a horizontal line marked with a range of valuesline marked with a range of values
Analyze Phase ToolsAnalyze Phase Tools Dot Plots:Dot Plots:
The display is similar to a histogram The display is similar to a histogram ( with a horizontal axis), but the ( with a horizontal axis), but the axis is divided into more classesaxis is divided into more classes
Ideally, each distinct observation Ideally, each distinct observation would have its own plotting positionwould have its own plotting position
Useful for comparing distributionsUseful for comparing distributions
Analyze Phase ToolsAnalyze Phase Tools Interval Plots: Great graphical tool to Interval Plots: Great graphical tool to
compare two factorscompare two factors The graph shows the spread of data around the The graph shows the spread of data around the
means of groups by plotting confidence means of groups by plotting confidence intervalsintervals
A confidence interval for specific statistics gives A confidence interval for specific statistics gives us a range of values around the statistic where us a range of values around the statistic where the true statistic can be expected to be located the true statistic can be expected to be located within a given level of certaintywithin a given level of certainty
The calculation of confidence intervals is based The calculation of confidence intervals is based on the assumption that the variable is normally on the assumption that the variable is normally distributed in the populationdistributed in the population
Analyze Phase ToolsAnalyze Phase Tools Scatter PlotScatter Plot
Shows a correlation between two Shows a correlation between two variables, X and Yvariables, X and Y
Shows a graphical relationship Shows a graphical relationship between the dependent variable and between the dependent variable and the independent factorthe independent factor
But just because there is a But just because there is a relationship does not mean there is relationship does not mean there is causationcausation
Analyze Phase ToolsAnalyze Phase Tools Scatter PlotScatter Plot
Useful for investigating the Useful for investigating the influence of one factor at a time influence of one factor at a time over the output or CTQ you suspect over the output or CTQ you suspect to be vitalto be vital Helps to prove or disprove a hypothesis Helps to prove or disprove a hypothesis
you might have formulated about the you might have formulated about the problemproblem
Analyze Phase ToolsAnalyze Phase Tools Time Series PlotsTime Series Plots
Sequence of measurements, taken at Sequence of measurements, taken at successive points in timesuccessive points in time
Includes a wide range of exploratory and Includes a wide range of exploratory and hypothesis-testing methods that have two hypothesis-testing methods that have two main goals:main goals:
Understand the phenomenon represented by Understand the phenomenon represented by the measurementsthe measurements
Predict future values of the variable tracked in Predict future values of the variable tracked in the time seriesthe time series
Analyze Phase ToolsAnalyze Phase Tools Time Series PlotsTime Series Plots
Most time series patterns can be Most time series patterns can be described in terms of two basic described in terms of two basic categories: trend and seasonalitycategories: trend and seasonality Trend analysis is a time series that Trend analysis is a time series that
showsthe data, the fitted trend line, and showsthe data, the fitted trend line, and forecasts ( linear, quadratic, forecasts ( linear, quadratic, exponential, S-curve)exponential, S-curve)
Seasonality is a time series pattern that Seasonality is a time series pattern that shows a basic repetitive pattern over a shows a basic repetitive pattern over a long period of timelong period of time
Analyze Phase ToolsAnalyze Phase Tools Multivari AnalysisMultivari Analysis
Graphical analysis technique used to identify Graphical analysis technique used to identify and quantify dominant sources of variation in and quantify dominant sources of variation in a process when the Y’s are continuous and a process when the Y’s are continuous and the X’s under investigation are discretethe X’s under investigation are discrete
Data collection is passive in that the process Data collection is passive in that the process is monitored in its natural, unchanged stateis monitored in its natural, unchanged state
Can be used to assess capability, stability, Can be used to assess capability, stability, and graphical relationships between X’s and and graphical relationships between X’s and Y’sY’s
Analyze Phase ToolsAnalyze Phase Tools Multivari studies should continue until Multivari studies should continue until
the full range of the output variable is the full range of the output variable is observed and all treatment observed and all treatment combinations have been capturedcombinations have been captured
If all treatment combinations have been If all treatment combinations have been observed and Y has not varied through observed and Y has not varied through its full range, the X’s are not critical to its full range, the X’s are not critical to YY
Objective: to reduce the large number of Objective: to reduce the large number of possible causes of variation to a smaller possible causes of variation to a smaller family of variationfamily of variation
Analyze Phase ToolsAnalyze Phase Tools Multivari AnalysisMultivari Analysis
Basic steps in multivari analysisBasic steps in multivari analysis Step 1: Call a team meetingStep 1: Call a team meeting Step 2:Select the potential X’s to include in the Step 2:Select the potential X’s to include in the
studystudy Step 3: Establish a sampling planStep 3: Establish a sampling plan Step 4: Plan the method for collecting the dataStep 4: Plan the method for collecting the data Step 5: Collect the dataStep 5: Collect the data Step 6: Analyze the resultsStep 6: Analyze the results
Analyze Phase ToolsAnalyze Phase Tools Hypothesis TestingHypothesis Testing
A null hypothesis (H0) states the A null hypothesis (H0) states the assumption that there is no difference in assumption that there is no difference in parameters for two or more populations, parameters for two or more populations, that any observed difference in samples is that any observed difference in samples is due to chance or a sampling errordue to chance or a sampling error
A null hypothesis is used to check whether the A null hypothesis is used to check whether the new processs mean differs from the old process new processs mean differs from the old process meanmean
The beta risk is the probability of accepting the The beta risk is the probability of accepting the null hypothesis (H0) as true when it is actually null hypothesis (H0) as true when it is actually falsefalse
Analyze Phase ToolsAnalyze Phase Tools Hypothesis TestingHypothesis Testing
An alternate hypothesis ( Ha or H1) An alternate hypothesis ( Ha or H1) is any hypothesis that differs from a is any hypothesis that differs from a given null hypothesisgiven null hypothesis
It states that the observed It states that the observed difference or relationship between difference or relationship between two populations is real, that it is not two populations is real, that it is not the result of chance or a sampling the result of chance or a sampling errorerror
Analyze Phase ToolsAnalyze Phase Tools Analysis of VarianceAnalysis of Variance
Purpose: to test for significant Purpose: to test for significant differences between or among two or differences between or among two or pore means by comparing variances pore means by comparing variances within groups and variances between within groups and variances between and among groupsand among groups
ANOVA used to calculate the amount ANOVA used to calculate the amount of variation in a process and of variation in a process and determine if it is significant or if it is determine if it is significant or if it is caused by random noisecaused by random noise
Analyze Phase ToolsAnalyze Phase Tools Two types of analysis of variance:Two types of analysis of variance:
One’Way ANOVA allows comparison One’Way ANOVA allows comparison of several groups of observations, all of several groups of observations, all of which are independent but of which are independent but possibly with a different mean for possibly with a different mean for each groupeach group
Two-Way ANOVA studies the main Two-Way ANOVA studies the main effects of two factors separately and effects of two factors separately and sometimes together ( the effects of sometimes together ( the effects of their interaction)their interaction)
Analyze Phase ToolsAnalyze Phase Tools Analysis of VarianceAnalysis of Variance
If a factor is a common cause and it If a factor is a common cause and it contributes significantly to contributes significantly to variability in the output, the team variability in the output, the team has an opportunity to improve the has an opportunity to improve the process by controlling the factorprocess by controlling the factor
Analyze Phase ToolsAnalyze Phase Tools Analysis of VarianceAnalysis of Variance
If the primary sources of variation If the primary sources of variation are special causes, uncontrollable, are special causes, uncontrollable, and they are significant, the team and they are significant, the team might recommend redesigning the might recommend redesigning the process to withstand that variability process to withstand that variability to the degree possible or that the to the degree possible or that the project be abandonedproject be abandoned
Ascertain and Prioritize the Ascertain and Prioritize the Vital Few Causes of Vital Few Causes of
VariationVariation At this point the team screens At this point the team screens
potential causes for change in the potential causes for change in the target Y and identifies the vital few target Y and identifies the vital few X’sX’s
In most processes there are six or In most processes there are six or fewer factors that most affect the fewer factors that most affect the quality of outputs in that processquality of outputs in that process Whe you isolate these factors you know Whe you isolate these factors you know
what basic adjustments you need to make what basic adjustments you need to make to markedly improve the processto markedly improve the process
Ascertain and Prioritize the Ascertain and Prioritize the Vital Few Causes of Vital Few Causes of
VariationVariation To estimate the impact of each X on Y To estimate the impact of each X on Y
and prioritize the causes, the black belt and prioritize the causes, the black belt will develop theories about possible will develop theories about possible causes and the use data to confirm or causes and the use data to confirm or disprove those theoriesdisprove those theories
To verify its findings the team then To verify its findings the team then gathers additional data and might gathers additional data and might conduct experiments on the process, conduct experiments on the process, making certain changes to see if the making certain changes to see if the problems disappearproblems disappear
Ascertain and Prioritize the Ascertain and Prioritize the Vital Few Causes of Vital Few Causes of
VariationVariation To determine the key input To determine the key input
variables that cause the target variables that cause the target output variables to vary and then output variables to vary and then to prioritize those inputs, the to prioritize those inputs, the team can use ANOVA, analysis of team can use ANOVA, analysis of means (ANOM), F-test ,t-test, chi means (ANOM), F-test ,t-test, chi square test and/or design of square test and/or design of experimentsexperiments
Ascertain and Prioritize the Ascertain and Prioritize the Vital Few Causes of Vital Few Causes of
VariationVariation The team might check its findings The team might check its findings
by using an association matrixby using an association matrix This matrix helps prioritize possible This matrix helps prioritize possible
solutions to develop for the root solutions to develop for the root causes associated with the highest-causes associated with the highest-priority outputspriority outputs
• List the root causes across the top and the List the root causes across the top and the possible solutions down the left sidepossible solutions down the left side
• Then mark in each cell the potential of each Then mark in each cell the potential of each solution to reduce or eliminate the effects of solution to reduce or eliminate the effects of each root causeeach root cause
Transform the Gaps into Transform the Gaps into Improvement ProjectsImprovement Projects
Team members prioritize the Team members prioritize the opportunities to impose the opportunities to impose the processprocess• Which problems should they solve to Which problems should they solve to
achieve the greatest gains?achieve the greatest gains? Then they generate alternatives, Then they generate alternatives,
evaluate those alternatives, and evaluate those alternatives, and select the best solutionsselect the best solutions
Transform the Gaps into Transform the Gaps into Improvement ProjectsImprovement Projects
They identify any potential problems They identify any potential problems and obstacles they might encounter and obstacles they might encounter in implementing those solutionsin implementing those solutions
They decide on the people and the They decide on the people and the resources that will be necessary to resources that will be necessary to improve the processimprove the process
Finally translation of the Finally translation of the improvement opportunity into improvement opportunity into financial termsfinancial terms
Review the Project with the Review the Project with the ChampionChampion
Key Questions:Key Questions: Does the team understand the root Does the team understand the root
causes of the variation and verify causes of the variation and verify them?them?
Are there any significant factors to be Are there any significant factors to be further investigated in the Improve further investigated in the Improve Phase?Phase?
Are the Project and financial Are the Project and financial statements still valid?statements still valid?
Review the Project with the Review the Project with the ChampionChampion
Key Questions:Key Questions: Have the problem and goal statements Have the problem and goal statements
been updated to reflect the additional been updated to reflect the additional knowledge gained from the Analyze knowledge gained from the Analyze phase?phase?
Have any additional benefits been Have any additional benefits been identified that will result from closing identified that will result from closing all or most of the gaps?all or most of the gaps?
Conduct an Analyze Conduct an Analyze Phase- Gate Review Phase- Gate Review