Javier Garcia - Verdugo Sanchez - Six Sigma Training - W2 Statistical Process Control (SPC)

d PCIntroduction in SPC

St ti ti lStatistical

Process

Control

Week 2

Knorr-Bremse Group

SPC Helps You…

At the process control:

Y ill i if t i ti d b• You will recognize if current process variations are caused by common causes and if the process is stable in order to avoid over reaction.

At the analysis:

• To identify sources of variation and subsequent determination of actions to eliminate these sources or at least to reduce the variation.

Further applications of these ideas:Further applications of these ideas:

• Report on the state of control

• Monitoring for maintenance purposes

D t i th it d f ff t d t h f th• Determine the magnitude of effects due to changes of the process

• Discover sources of variation

Knorr-Bremse Group 11 BB W2 SPC 08, D. Szemkus/H. Winkler Page 2/37

Content

• Introduction to SPC

• Creating SPC charts

• Different types of SPC charts

• Exercises in Minitab

• Sub grouping strategy


Definition of SPC

“An approach, to adjust a process “An approach, to adjust a process

on a target value with minimal on a target value with minimal

variation due to the detection and variation due to the detection and

elimination of the sources of elimination of the sources of

i ii ivariation.variation.


Types of charts• X-Bar & R Charts

• Individual Charts & Moving Range charts (IXMR)g g ( )

• P- Charts (& NP charts)

C Ch t (& U h t )• C- Charts (& U charts)

• More 'advanced' charts are available.

Control Limits reflect thevariation 'built' into theprocess

Metric

process.

ControlLimits


Time

Selection of the correct Control Chart

Type of DataCount or Classification

(Attribute Data)Measurement(Variable data)

Count ClassificationCount Classification

Incidences orNonconformance

Defectives ornonconforming

itNonconformance

units

Portion of Number of Number of defective units per subgroup

defective units per subgroup

DPU in each subgroup

defects in each

subgroup

Sample size constant

Sample size variable


Sample size variable


Sample size = 1Sample size

variable

PChart

NPChart

UChart

CChart

Xbar/RChart

Xbar/SChart

Xi/mRChart


ChartChartChartChart Chart ChartChart

Introduction SPC• Measurements display variation.

• There is a model (the common cause - special cause model) that• There is a model (the common cause - special cause model) that differentiates this variation into either:

i bl i ti th t d t " i l"– assignable variation or that are due to "special" sources, or

– common cause variation.

• This is the Shewhart or Deming model.

• Control charts are used to distinguish the variation.

• A metric that is in control implies a stable, predictable amount of p , pvariation (of common cause variation). This does not mean a "good" or desirable amount of variation.

• A metric that is out-of-control implies an unstable, unpredictable amount of variation. It is subject to both common AND special


causes of variation.

Components of a control chart

X-bar Chart for timeUpper control limit

32

X bar Chart for time

UCL=31,48M ( b )

31

Me

an

Mean (x-bar), Process center

30

29

Sam

ple

Mean=29,96

28

LCL=28,43

20100

Sample NumberLower control limit

Specification limits (lower and upper) are given by the customer, control limits are independent of specification limits!


control limits are independent of specification limits!

Guidelines and Thoughts• Control limits are calculated from a time series of the metric.

• Different formulas are available, depending on the type of data.

• Control limits should not be recalculated each time data is collected.

• The observed metrics (and so the control limits) are a function of the sampling and sub grouping plan.

• Variation due to 'assignable cause' is often the easiest variation to reduce.

• The most commonly monitored metrics are the 'Ys'.

• These metrics may be a function of one process or many processes.y p y p

• Control limits are not related to standards! Nor are they specifications. Control limits are a measure of what the process does/has done. It is pthe present/past tense, not the future (what we want the process to do).

• Control limits identify the extent of variation that now exists so that we do


ynot overreact to 'random' variation.

X-bar and R Chart, Definitions

– X: an individual measurement

– n: the numbers of observations within a subgroup

X : the average of a subgroup– X : the average of a subgroup

– X : the average of the averagesX : the average of the averages

– R: the range of a subgroupg g p

– R: the average of the ranges

– A2, d2, D3, D4: ‚constants' used for control charts


X-bar and R Chart, Definitions

• X-bar & R charts are a way of displaying variable data.

E l f i bl d t Width Di t T t W i ht– Examples of variable data: Width, Diameter, Temperature, Weight, Time, Etc.

• R chart

– Displays changes in the "within" subgroup dispersion of the process data.

– Asks "Is the variation in the measurements within subgroups g pconsistent?"

• X-bar chart

– Shows changes in the average value of the process.

– Asks "Is the variation between the averages of the subgroups more than that predicted by the variation within the subgroups?"


D i i li l S li l i li

Creating a X-bar and R Chart• Determine an appropriate sampling plan. Sampling location, sampling

frequency, and size of subgroup. Always be able to answer: What do you want to know? What potential sources of variation are captured within subgroup? Between subgroup?

• Sample: (Take a set of readings at each specified interval of time and/or p ( g pfrom each suspected source of variation).

• Calculate the average and range for each subgroup.g g g p

• Plot the data. (Both the averages and the ranges).

• After '20' or more sets of measurements, calculate control limits for the range chart.

• If the range chart is not in control, take appropriate action

• If the range chart is in control, calculate control limits for the X- bar chart.g ,

• If the X-bar chart is not in control, take appropriate action.


• If both charts are in control, take appropriate action.

„Out of control“ identification

UCL+ 3 sigma limits Zone A

+ 2 i li it Zone B

UCL

+ 2 sigma limits Zone B

+ 1 sigma limit Zone CAverage

Zone B

- 1 sigma limit Zone CAverage

- 3 sigma limits Zone ALCL

- 2 sigma limits Zone B

2 0100

LCL

Control limits are based on three times sigma


g

„Out of control“ identification

• One or more data points fall outside the control limits (UCL or LCL)One or more data points fall outside the control limits (UCL or LCL)

• Two out of three consecutive points fall within (the same) Zone A

• Four out of five consecutive points fall within (the same) Zone B

• Nine consecutive points fall on the same side of the average

• Six consecutive points are either increasing or decreasing

• Fourteen consecutive points are alternating up and down

• Fifteen consecutive points fall within Zone Cs


Exercise X-bar Chart with Minitab Stat

>Control ChartsFile: SPC.mtw

>Variable Charts for Subgroups

>Xbar…

File: SPC.mtwColumn: Mean

9,5

9,0

UCL=9,353

Xbar Chart of Mean

le M

ea

n

8,5

8,0__X=7,967

Sa

mp

l

7,5

7,0

X 7,967

Sample2018161412108642

6,5 LCL=6,581


Exercise X-bar R Chart with Minitab

Try with the columns mean 1 and group 1

Stat

>Control Charts1 and group 1>Variable Charts for Subgroups

>Xbar-R…

n

9

UC L=9,353

Xbar-R Chart of Mean

Sa

mp

le M

ea

n

8

7

__X=7,967

Sample2018161412108642

7

LC L=6,581

e R

an

ge

4,8

3,6

2 4_R=2 403

UC L=5,082

Sa

mp

le

2018161412108642

2,4

1,2

0,0

R=2,403

LC L=0


Sample2018161412108642

Exercise with Random Data

Calc

>Random Data

100 data points with a mean = 70 and standard deviation = 2>Random Data

>Normal

standard deviation 2

Prepare an X-bar R chart and a Individual X moving range chart. Activate all tests and comment on the results.


Exercise, Individuals with Minitab Stat

>Control Charts File: SPC.mtw>Variable Charts for Individuals

>Individuals…

Column: Individual


Exercise, Individuals with Minitab

If needed including the 11

UCL=10,526

I Chart of Individual

moving range chart

al V

alu

e

10

9

Ind

ivid

ua 8

7

6

_X=7,880

Observation2018161412108642

6

5LCL=5,234

ue

10,8

9,6

UC L=10,526

I-MR Chart of Individual

Ind

ivid

ua

l V

alu

8,4

7,2

6,0

_X=7,880

LC L=5,234StatObservation

2018161412108642

an

ge

3

2

UC L=3,250

>Control Charts

>Variable Charts for IndividualsM

ov

ing

Ra

2018161412108642

2

1

0

__MR=0,995

LC L=0

>I-MR…


Observation

Control Charts for Variable Data

Chart Type Purpose Application Subgroup Size RemarksChart Type Purpose Application Subgroup Size Remarks

Average (X bar) Monitor the avg. of a characteristic

over timeWhen more than 3 units can be

sampled per time framen < 11;

usually 3 - 5Insensitive to shifts smaller than 2 Sigma whenn = 4 to 6.

Range (R) Monitor the variability of a characteristic over time

Used with the X bar charts whensample size is < 11

n < 11; usually 3 - 5

None

Standard Deviation (S)

Monitor the variability of a characteristic over time

Used with the X bar charts whensample size is > 10.

n >10

Increased sensitivity due to increased sample size.Use when tight control is necessary and/or when sampling cost is not a factor.

Prod ction areas that req ireIndividual & Moving Range

(I & MR)

Monitor the variability of anindividual characteristic over time.

Production areas that require long periods of time to obtain asingle sample or when a single

sample is meaningful.

n = 1Must make sure normal distribution requirements are satisfied.

ExponentiallyUsed in areas where rational

subgroup is n = 1 or when it isNot a Shewhart Chart. Does not react to largeshifts as quickly Also able to produce forecastedExponentially

Weighted MovingAverage (EWMA)

Monitor small shifts in the process

subgroup is n = 1 or when it is necessary to detect small shiftsin the process, or when data is

not normally distributed

n > 1shifts as quickly. Also able to produce forecasted results. Smoothes data to emphasize trends. Uses weights to emphasize the importance of recent data

Cumulative Sum Not a Shewhart Chart Same sensitivity asCumulative Sum(CUSUM)

Similar to EWMA Use for specialized applications n > 1Not a Shewhart Chart. Same sensitivity as EWMA. Difficult for manual charting.


Control Charts for Attribute Data

Chart Type Purpose Application Subgroup Size Remarks

Number ofMonitor the Number of defectives in a

subgroup

Fixed subgroup size which eliminates the need to redo the Subgroup size must be

Not effective when defect level is lowNumber ofDefective (np)

subgroup

Number of Units rejected

control limits for each subgroup.

More convenient than the p chart

g pfixed

n usually > 49

Not effective when defect level is low.Alternatives need to be considered

Monitor the fraction of defectives Usually used at quality control pointsVariable subgroup size

t b l h tes /

No

FractionDefective (p)

Monitor the fraction of defectivesin a subgroup

Units Rejected / Units Inspected

Usually used at quality control points where 1 or more product attributes

are inspected and result in a pass/fail condition for the unit.

must be large enough to have a high prob. that at least 1 defect is present

in the subgroup n usually > 49

Not effective when defect level is low and/or when subgroup size is too small. Not appropriate if a single defect will put the chart out of control.

Ye

Number ofDefects per

Subgroup (c)

Monitor the Number ofdefects in a subgroup

Employed to monitor the Numberof defects in a unit

Subgroup size is 1 unit that could have multiple defects.

c > 5

Ineffective control when defect level is small.

un

ts

Average Number of Defects per Units

(u)

Monitor the avg. Numberof defects in a unit

Employed to monitor theaverage Number of defects in a unit.

Subgroup size may vary.

Ineffective control when defect level is small.

Control limits must be calculated individuallyfor each subgroup if subgroup size is varying.

Co

u


SPC, Starting Activities

• Environment Top management has to provide an environment• Environment – Top management has to provide an environment, that supports the activities from all employees.

• Process – Define the target process, where everybody involved can expect a benefit.

• Characteristics – Define a goal where an improvement is beneficial.

• Process improvement teams – Define a team for every critical processprocess.

• Measurement systems – Choose measurement systems and y yequipment easy to handle and precise enough. Investigate measurement system for measurement errors.


Summary

• Introduction to SPC

• Creating SPC charts

• Different types of SPC charts

• Exercises in Minitab

• Sub grouping strategy


Appendix to SPC:pp

- Calculation of Control limitsCalculation of Control limits

Others- Others


Exercise

Practice of calculation of limits. Consider the following data set:

Exercise: Lot Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 Range X barExercise:

The following data set is from 20 different lots of rotating fans. One fan was taken from each lot

Lot Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 Range X bar

1 11,1 9,4 11,2 10,4 10,1

2 9,6 10,8 10,1 10,8 11,0

3 9,7 10,0 10,0 9,8 10,4

4 10 1 8 4 10 2 9 4 11 0 2 6 9 82One fan was taken from each lot and 5 blades were selected “randomly” and measured. Complete the table and plot the

4 10,1 8,4 10,2 9,4 11,0 2,6 9,82

5 12,4 10,0 10,7 10,1 11,3 2,4 10,90

6 10,1 10,2 10,2 11,2 10,1 1,1 10,36

7 11,0 11,5 11,8 11,0 11,3 0,8 11,32

charts. Then, answer the questions:

1. Where is within subgroup

8 11,2 10,0 10,9 11,2 11,0 1,2 10,86

9 10,6 10,4 10,5 10,5 10,9 0,5 10,58

10 8,3 10,2 9,8 9,5 9,8 1,9 9,52

11 10,6 9,9 10,7 10,2 11,4 1,5 10,56g pvariation located? What is the source of the “within” variation?

2. Where is subgroup variation

12 10,8 10,2 10,5 8,4 9,9 2,4 9,96

13 10,7 10,7 10,8 8,6 11,4 2,8 10,44

14 11,3 11,4 10,4 10,6 11,1 1,0 10,96

15 11,4 11,2 11,4 10,1 11,6 1,5 11,142. Where is subgroup variation located? What is the source of the variation “between” subgroup?

16 10,1 10,1 9,7 9,8 10,5 0,8 10,04

17 10,7 12,8 11,2 11,2 11,3 2,1 11,44

18 11,9 11,9 11,6 12,4 11,4 1,0 11,84

19 10,8 12,1 11,8 9,4 11,6 2,7 11,14

3. What question is this sub grouping strategy asking? What is the answer?

19 , , , , , , ,

20 12,4 11,1 10,8 11,0 11,9 1,6 11,44

File: Blade xls


File: Blade.xls

Exercise; Calculating the Control Limits

• Calculate the control limits and label the charts.2

• Provide an estimate of Within Subgroup

• Comment on Between Subgroup

2σ̂2σ̂Between Subgroup

Formulas:Sample

SizeA2 D3 D4 d2

CL X A R

UCL D R

X = ± 2

2 1,880 - 3,267 1,1283 1,023 - 2,574 1,6934 0,729 - 2,282 2,059

UCL D R

LCL D R

R

R

=

=4

3

5 0,577 - 2,114 2,3266 0,483 - 2,004 2,5347 0,419 0,076 1,924 2,7048 0 373 0 136 1 864 2 847

⎞⎛ R

8 0,373 0,136 1,864 2,8479 0,337 0,184 1,816 2,97010 0,308 0,223 1,777 3,078

(If the range chart is in control)⎟⎟⎠

⎞⎜⎜⎝

⎛=σ

2d

Rˆ


Exercise; Calculating the Control Limits

Add in the Limits and Centerline

Range Chart X-bar Chart

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1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20


Exercise

• Note that provides an estimate of the variation captured R

d2

within subgroup (if the range chart is in control).

When does provide of an estimate of all the variation in the

2

R• When does provide of an estimate of all the variation in the

charts?d2

• When does provide of an estimate of all the variation in the

process?

Rd2

process?

• In process investigations, why do we not usep g , y

( )1

2

−= ∑ −

ns

XXi

as an estimate of variation?

1n


Diagnosing the Causes of Variation

What does an IN-CONTROL chart tell you about the process? What does an OUT-OF-CONTROL chart tell you?

We can use control charts and the related control limits to view and evaluate some of the potential causes of variation within a pprocess.

This view of the process can be used to estimate theThis view of the process can be used to estimate the improvement opportunity if the identified cause or causes of variation could be removed (or reduced).

The technique that we use is called: rational sub groupingrational sub grouping

Rational sub grouping means that we have some kind of “rationale” for how we sub group. In other words, we are conscious of the question we are asking with our sub groupingconscious of the question we are asking with our sub grouping strategy and will take appropriate action based on the results (or answer) the control charts provide.


Rational Sub Grouping

The total variation of any system is composed of multiple causes:

set up proceduresset-up procedures

Products or process conditions

maintenance processes

B b i d h h l f h f hBy sub-grouping data such that samples from each of these separate conditions are placed in separate sub-groups we can explore the nature of the variation of the system or equipmentexplore the nature of the variation of the system or equipment.

The goal is to establish a subgroup (or sampling strategy) small enough to exclude systematic non random influencesenough to exclude systematic non-random influences.

The intended result is to generate data exhibiting only common f ( ) ( fcause variation within groups of (n) items and special cause (if it

exists) variation between groups.


Sampling Strategies

• Now that we have discussed sub grouping, we need to mention SAMPLING. It is not always convenient to do 100% sampling.

• Sampling Plans: A Control Chart is only as useful as the sampling strategy used to collect the data.

• Consider a process where all measurements on a key characteristic are available. Consider the output from this hypothetical process below.

Center Line (R)

Upper Control Limit

Range Chart Examines Variation Within Subgroups

Ce e e ( )

Upper Control Limit

X Chart Examines Variation In Process•••

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Center Line (X)

Lower Control Limit

TIME


Sampling Strategies, Exercise

Consider the impact of various sampling plans on the hypotheticalConsider the impact of various sampling plans on the hypothetical data streams shown on the following pages.

• Before turning to each situation, suggest sampling plans you might use.

• Draw the control charts that would result from your sampling scheme.

• How would charts look for different sampling and sub grouping strategies? (Space is provided for you to suggest and drawstrategies? (Space is provided for you to suggest and draw charts for 2 suggested sampling schemes.)


Sampling Strategies, Example 1

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TIME

Upper Control Limit

Range Chart

Charts resulting from suggested sampling plan.

Upper Control Limit

Range Chart


Center Line (R)

X Chart

Center Line (R)

X Chart

Center Line (X)

Upper Control Limit

X Chart

Center Line (X)

Upper Control Limit

X Chart

Lower Control Limit Lower Control Limit



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Upper Control Limit

Range Chart


Upper Control Limit

Range Chart


Center Line (R)

X Chart

Center Line (R)

X Chart

Center Line (X)

Upper Control Limit

X Chart

Center Line (X)

Upper Control Limit

X Chart




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Upper Control Limit

Range Chart


Upper Control Limit

Range Chart


Center Line (R)

Upper Control Limit

Center Line (R)

Upper Control Limit

Center Line (X)

Upper Control Limit

X Chart

Center Line (X)

Upper Control Limit

X Chart

( )

Lower Control Limit

Center Line (X)

Lower Control Limit



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Charts resulting from suggested sampling plan. Charts resulting from suggested sampling plan.

Upper Control Limit

Range Chart

Upper Control Limit

Range Chart

g gg p g p

Center Line (R)

X Chart

Center Line (R)

X Chart

Center Line (X)

Upper Control Limit

Center Line (X)

Upper Control Limit



Expansion of Sub Grouping

Examine the hypothetical process output again. The '•' indicate output from one machine. The '*' indicate output from a second machine.

Exercise:Exercise:

Describe the sampling plan necessary to detect differences in machinemachine.

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Engineering

Javier Garcia - Verdugo Sanchez - Six Sigma Training - W2 Statistical Process Control (SPC)