javier garcia - verdugo sanchez - six sigma training - w2 multi - vari studies

Multi-Vari-Studies110

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Week 2

Knorr-Bremse Group

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About this Module

Now we combine our knowledge of ANOVA and regression for Multivari studies. In practice almost always different factors ( i d ib i ) h Af hi d l(continuous and attributive) appear together. After this module you know how to proceed evaluating complex questions. We will rehear some already trained techniques with Minitab and at the same time

C t t

some already trained techniques with Minitab and at the same time you will improve handling the software.

Content

• Overview Multivari-StudiesOverview Multivari Studies

• Planning Multivari-Studies

• Collecting data

• Analysis of data

Structured approach and final report

Knorr-Bremse Group 10 BB W2 Multivari Studies 08, D. Szemkus/H. Winkler Page 2/34

• Structured approach and final report

The DMAIC Cycle

ControlMaintain

DefineMaintain

ImprovementsSPC

Control Plans

Project charter (SMART)

Business Score CardQFD VOC

D Documentation QFD + VOC

Strategic GoalsProject strategy

C M

MeasureB li A l iImprove

AIBaseline Analysis

Process MapC + E Matrix

M t S tAnalyze

ImproveAdjustment to the

OptimumMeasurement System

Process CapabilityDefinition of

critical InputsFMEA

pFMEA

Statistical TestsSimulation FMEA

Statistical Tests

Multi-Vari StudiesRegression

Tolerancing


Regression

A View into the Tool Box

Example• Different operators.• Different machines

Tools• Box plotsGeneral tools Different machines

• Different shifts

Noise inputsNoise inputs

p• Diagram of main

effects & interaction• ANOVAs, T-test

C & E - MatrixFMEA

Results

(Discrete)(Discrete),

Results Outputs

Y1 Y2ProcessControllable

InputsY1, Y2 …

Noise inputsNoise inputs(C ti )(C ti )

Example

• Temperature

• Pressure

Tools• Measurements

Examples• Ambient temperature

(Continuous)(Continuous)

Tools

Pressure

• Time

Tools

Measurements system

• Process capabilityp

• Air pressure• Relative Humidity

• Raw material condition

Tools• Scatter plots• Correlation

• Correlation• Regression• ANOVA

capability


• RegressionANOVA

Multivari-Studies

• Method of characterizing the baseline capability of a process as it runs during normal production.

• The data recording is passive as the process in his natural condition is recorded.

• The data are analysed to determine process capability and stability. The relations between inputs and outputs are assessed.

M lti i t di h ld ti til th f ll f th t t• Multivari studies should continue until the full range of the output variable is recorded (from Low to High as observed in the short-term capability or historic data)term capability or historic data)

• You will get valuable information if you :

– are available on the shop floor (at least for the first time)p ( )

– run Minitab evaluation as soon as first results are available. (Corrections can be done later)

– have a minimum of 30 values for the final evaluation

• If the range of the output (Delta) is to small ?! .... You should think about running a DOE


about running a DOE.

Reporting Results

• Description

– Objectives

– Input and output variables measured

– Sampling plan

– Process Settings

• Stability and Capability

– Trend/Control Charts

– Capability analysis

• Histograms• Histograms

• Cp, Cpk, Sigma

• Analysis of Rational Subgroupsy g p

• Significant relationships among variables

– Box plots, Scatter plots, etc.

– Statistical Analysis

• Conclusions


• Recommendations for further studies

Data Recording

This example: Contamination.mtw is already known from week 1.

We have data of 2 days (in total 16). We want to carry out an evaluation first of all to y ( ) ylearn from the first available results.

Day Shift Sample time Temp Pressure Contamination %

1 1 1 91 48 21 1 1 91 48 2

1 1 2 97 52 2

1 1 3 88 44 2

1 1 4 87 43 1

1 2 1 109 50 61 2 1 109 50 6

1 2 2 98 45 4

1 2 3 103 55 3

1 2 4 99 49 5

2 1 1 111 55 12 1 1 111 55 1

2 1 2 103 53 1

2 1 3 106 54 4

2 1 4 93 55 0

2 2 1 101 46 52 2 1 101 46 5

2 2 2 93 48 4

2 2 3 97 54 1

2 2 4 99 49 3

In this form the data should be prepared for the evaluation with Minitab


Minitab.

Sampling Plan• A good sampling plan will capture all relevant sources of noise

variability.

– Lot-to-Lot, Batch-to-Batch

– Different Shifts, Operators, Machines or processes

Different ra materials or prod cts– Different raw materials or products

• Sample Size: rule of thumb: 30p

• Input variables do not always have to be measured for each sample; many inputs are more or less constant over the samplingsample; many inputs are more or less constant over the sampling period (e.g. humidity).

Q ti I it th hil t d bl h k l t t kQuestions: Is it worthwhile to double check samples or to stock samples? Is it helpful to carry out the above mentioned changes

specifically?


specifically?

Sample Size

DeltaStDev

Samplesα 5% β10%

Reminder

Th l i d d th l l0,5 840,6 580 7 43

βThe sample size depends on the level of significance and the difference (measured in StDev) you like to 0,7 43

0,8 330,9 26

( ) ydetect.

Based on the recommendation of 30 1,0 211,1 171,2 15

Based on the recommendation of 30 samples you can detect differences of 1 StDev.

1,3 121,4 111 5 9

If you have small differences (like 0,5 StDev) you should think about running 1,5 9

1,6 81,7 71 8 6

) y ga DOE instead of a Multivari Study.

But do not forget that process type 1,8 61,9 62,0 5

But do not forget that process type, time to result and cost of the study are important factors as well.


Major Focus

Basic principle for the procedure

Examine the discrete noise variables first!Examine the discrete noise variables first!

Fl ct ations of the noise ariables often ca se ac te and– Fluctuations of the noise variables often cause acute and chronic mean shifting and changes in the variation which lead to process instability.p y

– If possible, we must remove these sources of variation before we turn to the important controllable input variablesbefore we turn to the important, controllable input variables systematically.

I l lif i l d b i i bl ft ll– In real life signals caused by noise variables often cover all other signals. Then don't try to evaluate the other variables. The results of such studies will sidetrack you and harm ymore than they help.


The First Evaluation Steps

A -Squared 0,42P-V alue 0,282

Mean 2,7500StDev 1 7701

A nderson-Darling Normality Test

Summary for Contamination %

As usual we start with the description in basics statistics,

bili d1st Q uartile 1,0000Median 2,50003rd Q uartile 4,0000

StDev 1,7701V ariance 3,1333Skewness 0,26787Kurtosis -1,01125N 16

Minimum 0,0000

process stability and process capability.

65432103rd Q uartile 4,0000Maximum 6,0000

1,8068 3,6932

1,0000 4,0000

1,3076 2,7396

95% C onfidence Interv al for Mean

95% C onfidence Interv al for Median

95% C onfidence Interv al for StDev95% Confidence Intervals

Median

Mean

4,03,53,02,52,01,51,0

Process Capability of Contamination %

10

8

6

UCL=8,60

I Chart of Contamination %

LB USL

LB 0Target *USL 8Sample Mean 2,75

Process DataPp *PPL *PPU 0,99Ppk 0,99

O v erall C apability

Process Capability of Contamination %

6

4

2n

div

idu

al V

alu

e

_X=2,75

Sample Mean 2,75Sample N 16StDev (O v erall) 1,77012

Ppk 0,99C pm *

15131197531

0

-2

-4

In

LCL=-3,1086420

PPM < LB 0 00O bserv ed Performance

PPM < LB *Exp. O v erall Performance


15131197531Observation

PPM < LB 0,00PPM > USL 0,00PPM Total 0,00

PPM < LB *PPM > USL 1509,01PPM Total 1509,01

Box plots for Day, Shift and Time

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Boxplot of Contamination %

6


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Sample time

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Indication for a strong shift impact

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21Shift

Diagram of Main Effects Stat

>ANOVA4

Day Shift

Main Effects Plot for Contamination %Data Means

>Main Effect Plot…

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Response = Contamination

Factors = Day, Shift, Time

4

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Me

Sample time

4321

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Interval Plot of Contamination %

Stat

>ANOVA5

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Interval Plot of Contamination %95% CI for the Mean

>Intervalplot…4

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Categorical Variable = Shift21

1

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Confidence Interval 95%21

Shift

Diagram of Interactions

Stat

>ANOVA


Factors = Day, Shit, Time

>Interaction Plot…

y

21 4321

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Interaction Plot for Contamination %Data Means

4

2Day

12

Day

0

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2Shift

12

Shift

0

Sample timeSample time


ANOVA; Evaluation with Many FactorsStat

>ANOVA

>General Linear Model

General Linear Model: Contamination % versus Day; Shift; Sample time

>General Linear Model…

Factor Type Levels ValuesDay fixed 2 1; 2Shift fixed 2 1; 2S l ti fi d 4 1 2 3 4Sample time fixed 4 1; 2; 3; 4

Analysis of Variance for Contamination %, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PSource DF Seq SS Adj SS Adj MS F PDay 1 2,2500 2,2500 2,2500 **Shift 1 20,2500 20,2500 20,2500 **Sample time 3 3,5000 3,5000 1,1667 **Day*Shift 1 1,0000 1,0000 1,0000 **Day Shift 1 1,0000 1,0000 1,0000 Day*Sample time 3 1,2500 1,2500 0,4167 **Shift*Sample time 3 15,2500 15,2500 5,0833 **Day*Shift*Sample time 3 3,5000 3,5000 1,1667 **Error 0 * * *Error 0 Total 15 47,0000

General Linear Model (GLM) allows to evaluate unbalanced observations for main


effects and interactions

Reduce Model to Significant FactorsGeneral Linear Model: Contamination % versus Shift; Sample time

Factor Type Levels ValuesShift fixed 2 1; 2Sample time fixed 4 1; 2; 3; 4

Analysis of Variance for Contamination %, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PShift 1 20,250 20,250 20,250 20,25 0,002S l ti 3 3 500 3 500 1 167 1 17 0 381Sample time 3 3,500 3,500 1,167 1,17 0,381Shift*Sample time 3 15,250 15,250 5,083 5,08 0,029Error 8 8,000 8,000 1,000Total 15 47,000

S = 1,00000 R-Sq = 82,98% R-Sq(adj) = 68,09%

Now we have a proper calculation... Is it meaningful???

Is there an interaction between shift and sample time? ...Possible if the operators draw the samples and so influence the study. This is rather

unlikely but happens as an exception, however. Use your practical experience to decide.


p

The Multivari Chart

Multi-Vari Chart for Contamination % by Day - Sample time

Stat

>Quality Tools

6

21 21

1 2 3 412

Day

Multi Vari Chart for Contamination % by Day Sample time>Multvari Chart…

5

4

na

tio

n %

3

2

1

Co

nta

min

21

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21Shift

Panel variable: Sample time

Time 3 is responsible for the significant interaction.

Th i fl f th hift d i t l i thi h t


The influence of the shift dominates also in this chart.

The Continuous Factors

6 S 1,70983R-Sq 12,9%R-Sq(adj) 6,7%

Fitted Line PlotContamination % = - 6,203 + 0,09095 Temp

6 S 1,75255R-Sq 8,5%R-Sq(adj) 2,0%

Fitted Line PlotContamination % = 9,000 - 0,1250 Pressure

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q( j) ,

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q( j) ,

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Why do we see a weak correlation between these factors and the impurity?

1101051009590

0

Temp5654525048464442

0

Pressure

The regression equation isContamination % = - 0,97 + 0,203 Temp - 0,326 Pressure

Why do we see a weak correlation between these factors and the impurity?

Predictor Coef SE Coef T PConstant -0,966 5,116 -0,19 0,853Temp 0,20330 0,06047 3,36 0,005Pressure -0,3259 0,1024 -3,18 0,007

S = 1,33015 R-Sq = 51,1% R-Sq(adj) = 43,5%

Analysis of VarianceSource DF SS MS F PRegression 2 23,999 12,000 6,78 0,010


Regression 2 23,999 12,000 6,78 0,010Residual Error 13 23,001 1,769Total 15 47,000

Catapult Multivari-Study

Ball type

Rubber band Tension Point4 4

Rubber band

56

Rubber band Attachment point

Stop position

Tension Point

34

2

3

4

2

2345

1

2

Release angle1

2

12

356


Catapult Multivari-Study• Each shift shoots 6 time. Catapult shooting takes the whole day

(2 shifts per day)

• The following SOP’s are currently in place:

• Standard Setupp

• The 2 Rubber bands are changed every 9 shots

• 1 Operator per Shift1 Operator per Shift

• 1 Observer per Shift

3 B ll T h d l ith h t• 3 Ball-Types changes randomly with every shot

• To decide what ball to use, use Minitab’s random number generator

• Perform the Multivari Study for a 3-day period (36 shots)

• Change set-up as desired - remember to record the changes!!g p g

• Figure out which variables are the primary drivers of variability! Present results on Flip Chart.


p


Rules for effective data collection

• Carry out a test run to check your methods.

• Stick to the sampling plan• Stick to the sampling plan.

• Note any changes of the process conditions which are not part of the normal or initial process conditions.

• Control the measuring systems for the key processControl the measuring systems for the key process inputs.

R d ll l t• Record all unusual events.

• Enter the data in the data base fast.

• Lead logbook.



Recommended Database

Columns:

– Day

– Shift– Shift

– Operator

– Observer

– Rubber band

B ll T– Ball Type

– Distance


s a ce

Create the Minitab Worksheet

Calc

Use the menu „Simple Set of Numbers“ to create the columns

Calc

>Make pattern Data

>Simple Set of Numbers

To randomise the ball column use “random data” menu

Calc

>Random data

>Sample from columns


Reporting Results• Description

– Objectives

– Input and output variables measured

– Sampling plan

Process Settings– Process Settings

• Stability and Capability– Trend/Control Charts

– Capability analysis

• Histograms

• Cp, Cpk, Sigma

• Analysis of Rational Subgroups

• Significant relationships among variables• Significant relationships among variables– Box plots, Scatter plots, etc.

– Statistical Analysisy

• Conclusions• Recommendations for further studies


Conclusions

• Supported by data

• Shown in graphical and statistical format

• Not based on conjecture or intuition

M k f t h i l t d i t• Make sense from a technical standpoint

Data and Hard Evidence!!Data and Hard Evidence!!Data and Hard Evidence!!Data and Hard Evidence!!


Summary

• Overview Multivari Studies

• Reviewed Noise variables and Analysis Introduction

• Planning Multivari Studies

f f C• Identified methods for Data Collection

• Examples in Data Analysis• Examples in Data Analysis

• Discussed how to handle Noisy Data - Outliers andDiscussed how to handle Noisy Data Outliers, and Non-normal data

• Reviewed the format for a Final Report


Attachments: Multivari Studies

Roadmaps Details Sample Plan


Steps to a Capability Study - Phase I

1. Set the process to the “best” setup and record the Inputs.

2. Identify a reasonable way to create rational subgroups.

3. Run the product over a short period of time to remove as much p pexternal variation as possible (approx. 30 points).

4. Carefully observe the process and take plenty of notes.y p p y

5. Measure and record the Outputs.

6. Run Capability Analysis and review Normal Plot, Histogram and SPC Charts. Use both the pooled and the overall standard deviations.deviations.

8. Diagnose for Mean Shift and Variance Inflation.

9. Estimate Long-Term Capability.

10. Develop action plan based on diagnostics.


10. Develop action plan based on diagnostics.

Steps in Multivari - Phase II

Planning

1. Determine Objective

2. Identify Inputs and Outputs to be studiedy

3. Identify Measurement Systems for each variable

Which should be studied to assure capability?

4. Determine sampling plan

5. Determine data collection, formatting and storage procedure

6 D i ti f d d tti d t6. Description of procedure and settings used to run process

7. Team assigned and trained

8. Clear responsibilities assigned

9 O tli f d t l i t b f d


9. Outline of data analysis to be performed

Steps in Multivari - Phase II

Execution and Analysis

1. Run process and collect Data

2. Analyze data:

• Is the process stable, in control?

• Which are the key noise variables affecting the output variable?

• Which are the key controllable variables that influence the output variable?p

3. Validate Results with follow-up DOE

4. Conclusions

5. Reporting Results, Recommendations


p g

Sampling Plan• A good sampling plan will capture all relevant sources of noise

variability.

– Lot-to-Lot, Batch-to-Batch

– Different Shifts, Operators, Machines or processes

• Sample Size rule of thumb: 30

• Input variables do not always have to be measured for eachInput variables do not always have to be measured for each sample if the input is constant over the sampling period.

• Sampling designs help insure a representative sample of theSampling designs help insure a representative sample of the process without collecting extreme amounts of data

– Simple Random SampleSimple Random Sample

– Stratified Sampling

Cluster Sampling– Cluster Sampling

– Systematic Sampling


Sampling Plan

• Simple Random Sample

All possible samples of n units are equally likely– All possible samples of n units are equally likely

• Example: After each laminate press cycle, 10 random numbers from 1 to the number of panels are generated These panels arefrom 1 to the number of panels are generated. These panels are then evaluated with respect to the output measures.

• In continuous processes, using a SRS is very difficult because p , g ythere is no clear experimental unit.

• Stratified SampleStratified Sample

– Divide the population into homogeneous groups and randomly sample from every groupand randomly sample from every group

• Example: In fiber spinning, there are a large number of Blocks with each block having several spinnerets Randomly samplewith each block having several spinnerets. Randomly sample one spinneret from each block.

• This sample will effectively represent each block’s effect on the


This sample will effectively represent each block s effect on the variability of the output variables.

Sampling Plan

• Cluster Sample

– Divide the sample into smaller homogeneousDivide the sample into smaller homogeneous groups, then take random samples of each group.

• Example: Back to fibre spinning; usually there are a large• Example: Back to fibre spinning; usually there are a large number of blocks, each with a certain number of spinnerets. Number each block and randomly sample a subset of blocks. Then randomly sample spinnerets in the selected blocks.

• This represents block effects without sampling from all blocks.

• Systematic Sample

Start with a randomly chosen unit and sample– Start with a randomly chosen unit and sample every kth unit thereafter.

E l F l i t l th N b f• Example: For a laminate press cycle, the are N number of samples. Pick a number at random to start and then select every third panel to evaluate.


• This method is good because it’s simple.

Worksheet Sampling Plan

K e y O u t p u t s : V a r ia b le H o w M e a s u re d W h e n M e a s u re d

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N o is e V a r ia b le s : V a r ia b le H o w M e a s u re d W h e n M e a s u re dN o is e V a r ia b le s : V a r ia b le H o w M e a s u re d W h e n M e a s u re d

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C o n t ro l la b le In p u t s V a r ia b le H o w M e a s u re d W h e n M e a s u re d

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O ve ra l l S a m p l in g P la n :


javier garcia - verdugo sanchez - six sigma training - w2 multi - vari studies

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