Six Sigma 5 - Control

7/27/2019 Six Sigma 5 - Control

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industrial engineering ui - where the science of engineering and management blends TEKNIK INDUSTRIUNIVERSITAS INDONESIA

D M A I C

Control

Control

Six Sigma Road Map


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D M A I C

Control

QFDProcess Mapping

Measurement Systems

Benchmarking/Baselining

Yield & SigmaBasic Quality Tools

Design of Experiments

Brainstorm & Workout

Control Charts

Procedures

Training

ProductProduct

oror

ServiceService

1 Select CTQ Characteristics

2 Define Performance Standards

3 Validate Measurement System

4 Establish Product Capabili ty5 Define Performance Objectives

6 Identify Variation Sources

7 Screen Potential Causes

8 Discover Variable Relationships9 Establish Operating Tolerances

10 Validate Measurement System

11 Determine Process Capabil ity

12 Implement Process Controls

MMeasureeasure

IImprovemprove

CControlontrol

AAnalyzenalyze

StrategyStrategy CookbookCookbook Tools &Tools &

ConceptsConcepts

DDefineefine Define the problem Select cross-functional team Define team charter

Moving into the Control Phase


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Control: Main Objectives/Deliverables

To make sure that ourprocess stays in control after the solution

has been implemented.

To quickly detect the out of control state and determine the

associatedspecial causes so that actions can be taken to correct

the problem before nonconformances are produced.

Develop and implement control system

Determine improved process capability

Given the planned capability for controlling the Xs, what will

be the new and improved capability for the process CTQ(s)?

Process Before

Improvement

LSL USL

Process After

Improvement

LSL USL


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Control

Maintaining Control

Keep Xs within tolerance by using appropriate

controls (Risk Management, Mistake Proofing, etc.)

Apply control charts to Xs to monitor and control

variation.

Understand implications on existing quality plans due tomodification of current control systems.

Establish transition plan for maintaining control of

improved process (training plan, audit plan, etc.).


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What is a Process Control System? A process control system

strategy for maintaining the improved process performance

over time

identifies the specific actions and tools required for

sustaining the process improvements or gains

A control system may incorporate

Risk Management

Mistake-proofing devices

Statist ical process control (SPC)

Data collection plans

Ongoing measurements

Audit plans

Response or Action plans

Product drawings

Process documentation

Process ownership


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Why is a Process

Control System Important? Defines the actions, resources, and responsibilit iesneeded to make sure the problem remains corrected and thebenefits from the solution continue to be realized.

Provides the methods and tools needed to maintain the

process improvement, independent of the current team.

Ensures that the improvements made have been

documented (often necessary to meet regulatoryrequirements).

Facilitates the solution's full-scale implementation by

promoting a common understanding of the process and plannedimprovements.


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Key Steps in

Developing a Process Control System1. Complete an implementation plan.

Plan and implement the solution and develop a method to controleach vital X or key sources of variation

Define all possible areas that may require action in order to

control the process X and then determine the appropriate course

ofaction to take

2. Develop a data collection plan to confirm that your solution

meets your improvement goals. Establish ongoing measurements needed for the project Y and

create a response plan to follow in case process performance falls

below established standards


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3) Communicate your strategy.

Document the process and control plan to ensure process

standardization and the continuation of the solution's benefits

4) Train Personnel.

5) Run the new process and collect the data to confirm

your solution.

Key Steps (contd)

Th M i C t l M h i


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Three Main Control Mechanisms

Risk

Management

Risk

Management

SPCSPC

MistakeProofingMistakeProofing

Control

PotentialProblems

Avoid

PotentialProblems

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Determine the probability and impact of each riskpresented by the planned process change.

Link the probability and impact of occurrence to the risk,then determine the abatement action.

Assign ownership and determine timing for eachabatement action.

Risk Management

Recommended tool

Failure Modes & Effects Analysis (FMEA)

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Mistake Proofing Helps to sustain a solution by eliminating the possibility thatan X can be set outside the desired level or configuration...or

Warns the process operator before the X goes outside limitsso preventative action can be taken.

Mistake proofing can be used alone or with either riskmanagement or statistical process control to sustain a solution.

D M A I C


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Control charts can be used to monitor Xs and quicklydetect a change in the process due to special cause

variation.

Very helpful when your Xs cannot be mistake proofed or

easily controlled within the required tolerance range.

Statistical Process Control

Tool we will look at Shewhart control charts,

as an introduction to SPC

D M A I C


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Introduction to Statistical Process Control (SPC)

(Recommended reference: Montgomery, Doug (2001).Introduction to StatisticalQuality Control, 4th edition, John Wiley & Sons, New York, NY.)

From Montgomery:

SPC a powerful collection of problem-solving tools useful in

achieving process stability and improving capability through

the reduction of variability.

SPC can be applied to any process. Its seven major tools (often

referred to as the magnificent seven) are:

Histogram or stem-and-leaf display

Check sheet

Pareto chart Cause-and-effect diagram

Control chart

Scatter diagram

Defect concentration

diagram

Focus of

remaininglectures

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Concepts/definitions:

Common cause variability Inherent or natural variability in a

process, which is the cumulative effect of essentially unavoidable

causes.

Assignable cause or special cause variability - above and

beyond the natural process variability. In a manufacturing process,this often comes from improperly adjusted machines, operator error

or defective raw material. This may result in a shift in the process

mean, an increase in the process variability, or both.

Statistical process control charts are used to detect the presence

of an assignable causes, by detecting a shift in the mean of

the parameter being monitored, an increase in its variance,or both.

D M A I C


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Statistical basis of the Control Chart

Sample number or time

Sam

plequalitycharacteristic

Upper control limit (UCL)Usually center line + 3s, where

s is the standard error of the

quality characteristic being plotted.

Lower control limit (LCL)Usually center line - 3s, where

s is the standard error of the

quality characteristic being plotted.

Center line avg value of the

sample quality characteristicwhen the process is in control

When the process is in control, all points should fall within the UCL

and LCL, in an essentially random pattern.

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Relationship between control charts and hypothesis testing

Some similarities:

Suppose the sample quality characteristic being plotted (vertical axis) is

. If the current value of plots between the control limits, then we conclude

that the process mean is in control; that is, it is equal to some value 0 . Ifexceeds either limit, we conclude that the process mean is out of control; that

is, it is equal to some value 1 0.

Type I and II errors apply to performance of control charts- Type I error is concluding that an in-control process is out of control

- Type II error is concluding that in out-of-control process is in control

Some differences:

When testing statistical hypothesis, usually check for validity of

assumptions. Control charts are used to check for departure from an assumed

state.

Assignable cause can result in different types of shifts in process parameters

(e.g. sustained shift or abrupt temporary shift or steady drift).

X

X

X

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Samplequalitycharacteristic Upper control limit (UCL)

Lower control limit (LCL)

Center line

Detect a process shift and correct it, before it ever exceeds the

specification limits (ie results in unacceptable quality)

Controlling the process parameter within specification/tolerance

Upper specification limit (USL)

Lower specification limit (LSL)

Sample number or time

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Process improvement using a control chart

ProcessProcess

Measurement SystemMeasurement System

Input Output

Detect assignable cause

Identify root cause

of the problem

Implement

corrective action

Verify and

follow up

D M A I C


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Guide to Univariate Process Monitoring and Control

Continuous or Discrete data?

Sample size Data type

ContinousDiscrete (attribute)

Shift sizeto detect

n>1 n=1fraction Defects (count)

large small large small large small large small

SXRX,, Cusum

EWMACusumEWMA

CusumEWMA

Using p

Cusum

EWMAUsing c,u;

time between

events

cu

pnp

X (individuals)

MR

Shift sizeto detect

Shift sizeto detect

Shift sizeto detect

Assumption: Process data is not autocorrelated

Shewhart control chartsDr. Walter Shewhart, Bell Labs, 1920s

(


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Sensitizing rules for Shewhart control charts

1. One or more points outside of the control limits.2. Two of 3 consecutive points outside the 2-sigma warning limits but still

inside the control limits.

3. Four of 5 consecutive points beyond the 1-sigma limits.

4. A run of 8 consecutive points on one side of the center line.5. Six points in a row steadily increasing or decreasing.

6. Fifteen points in a row in zone C.

7. Fourteen points in a row alternating up and down.

8. Eight points in a row on both sides of the center line with none in zone C.9. An unusual or nonrandom pattern in the data.

10. One or more points near a warning or control limit.

estern

lectric

ules

+ 1 s.e.

-1 s.e.

Zone C

-2 s.e.

+ 2 s.e.

+ 3 s.e.

-3 s.e.

D M A I C


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Control

Guide to Univariate Process Monitoring and Control

Continuous or Discrete data?

Sample size Data type

Continuous Discrete (attribute)

Shift sizeto detect

n>1 n=1fraction Defects (count)

large small large small large small large small

SXRX,, Cusum

EWMACusumEWMA

CusumEWMA

Using p

Cusum

EWMAUsing c,u;

time between

events

cu

pnp

X (individuals)

MR

Shift sizeto detect

Shift sizeto detect

Shift sizeto detect

Assumption: Process data is not autocorrelated

Shewhart control chartsDr. Walter Shewhart, Bell Labs, 1920s

(


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Control

Shewhart control charts for a continuous Y or X

Need to monitor both the mean and variability of the variable (Y

or X).

Assume n > 1, for every sample collected over time

Monitor to control the process mean ( chart)

Monitor S (sample std dev) or R (sample range) to control the

process variability. (S chart or R chart)

Typically use an S chart if n >10-12 or if n varies from sample to

sample.

R chart is more commonly used than an S chart.

X X

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Control

Constructing the and R chartsX

Statistical basis:

Assume that X, the process parameter to be monitored, is normallydistributed with mean and std deviation , both known.

Assume that we are collecting m samples of size n from the processover time. The sample data can be summarized by and

ri for i= 1, m.

Therefore,

ix

=+


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Typically, and are unknown, so they must be estimated fromthe sample data.

Unbiased estimator for is mix

m

xi

i ,...,1,1

==

Unbiased estimator for is , where

and d2 is listed for various sample sizes in Appendix Table VI of

Montgomerys SQC book (reference given in Control 2.ppt).

2d

R miRm

Ri

i ,...,1,1

==

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Constructing the chartX

Centerline = X

LCL =

=

ndRX2

3nd

RX2

3+UCL =

=RAX 2 RAX 2+

Where A2 is found in Appendix Table VI.

See Piston ring example from handout (Montgomery, pages 213-215).


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C l


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Constructing the and R charts in MinitabX

Piston ring example:

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C l


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Select

Xbar-R

chart

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C t l


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C t l


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252015105Subgroup 0

74.015

74.005

73.995

73.985

SampleM

ean

X=74.00

3.0SL=74.01

-3.0SL=73.99

0.05

0.04

0.03

0.02

0.01

0.00SampleR

ange

R=0.02324

3.0SL=0.04914

-3.0SL=0.00E+

Xbar/R Chart for x1-x5

Minitab output:


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P-chart example (with Minitab)

See example 6-1 in Montgomery, pages 288-290 of handout.

N=50 for each of the 30 samplesSampl e Di

num1 122 153 8

4 105 46 77 168 99 1410 1011 512 6

13 1714 1215 22

16 817 1018 5

19 1320 1121 2022 1823 2424 1525 926 1227 7

28 1329 930 6

Sampl e Di

num

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Minitab input:

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Since our n was constant for all samples,it can be entered as a constant here.

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3020100

0.5

0.4

0.3

0.2

0.1

0.0

Sample Number

Proportion

P Chart for Di

1

1

P=0.2313

3.0SL=0.4102

-3.0SL=0.05243

Minitab output:

Six Sigma 5 - Control

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