Tolerance Analysis/PPAP

Product Design and Analysis

Six Sigma

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Objectives

• Basic theory and statistics behind six sigma

• How six sigma affects design

• Detailed use of six sigma in design and product support

• Relationship between Six Sigma/Tolerance Analysis and Design Approval

• Provide further reading for additional learning (Additional Information)

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Overview

• Originally created as a process improvement tool

• Six Sigma (6σ) strives for perfection

• Provides techniques and tools to improve capability and reduce defects

• Ensures 99.9997% of all products produced in a given process are within design limits (Assuming a 1.5 sigma shift in nominal is taken into account)

• Provides a proactive approach to design– Focuses on prevention of issues

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Basics

• Define– Determine Customer requirements– Set baseline

• Measure– Develop measurement and collection

process– Collect data

• Analyze– Review data– Determine root cause (if necessary)– Determine potential improvements

• Improve– Validate potential improvements– Implement improvements

• Control– Monitor improvements– Assess effectiveness– Determine needed Adjustments

Standard 6σTheory

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Basics

Design for 6σ (DFSS)

• Define

• Measure

• Analyze

• DESIGN– Implement design to meet customers

needs

• VALIDATE– Test design against customer needs

• All DFSS methods use the same types of design tools. Examples include:– Quality Function Deployment– Failure Modes and Effects Analysis

(FMEA / PFMEA)– Design of Experiments (DOE)SAMPLE

Basics

• Focuses on a shift of nominal and reduction in variation

• Based upon Average ( ) and Standard Deviation (σ or s) of a sample– Assumes a normal distribution over

time– Assumes a large sample size

( )

1

2

1

−

−=∑=

n

xxn

ii

σ

6σ Statistics

x

n

xx

n

ii∑

== 1

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Basics

• Key process factors include Cp and Cpk

– Directly linked (Cp) to defects and 6σ

• Cp determines if the process can fit within its limits (tolerances)– Ratio defining the process spread

(width)

• Cpk determines how close the process is to its center (nominal)– Capability is spread AND location

– Cpk = Minimum of Cpu and Cpl

Statistics - Cp and Cpk

( )σ6

LSLUSLCp−

=

( )σ3

xUSLCpu−

=( )

σ3LSLxCpl

−= [1]

[1] – Statistical Process Control. 2000-2009. MoreSteam.com. <http:// http://moresteam.com/toolbox/t402.cfm>SAMPLE

Basics

Cp and Cpk Distribution

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Basics

• DPPM = Defective parts per million

• DPHU = Defects per hundred units

• DPMO = Defects per million opportunities

( )6101××

×=

oudDPMO

Process / Defect Metrics

( )6101××

=

tddDPPM

100×

=

udDPHU

Does NOT take into account the complexity of the “system”

Provides a Direct link to statistical control

and 6σ

ConversionSAMPLE

Design and 6 Sigma

• Part level manufacturing validation

• Statistical Process Control (SPC) used as method for process validation– Includes Cp and Cpk

• Used to validate and improve design at a subsystem level

• Constraint Matrix

• Tolerance Analysis

MANUFACTURING DESIGN

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Design and 6 Sigma

SPC is Process control ensuring a process is stable over time

• Two types of process control issues– Common Cause are Predictable causes accounting for 85% of all issues

• Changes to common cause items require a PROCESS change

– Special Cause are Sporadic causes accounting for 15% of all issues• Special causes cannot be prevented by process

– Deal with the EVENT, not the process

– Engineer can only lessen the effect with proper CONTINGENCY PLANNING

• Only Common Cause variation is taken into account during sigma calculations (See causes, below/right)

Manufacturing

“causes”SAMPLE

Design and 6 Sigma

• Part level validation– Focuses on producing a part

within limits

• Supplier SPC Use/Charting– Long term data gathering– True process control over time

• Engineering SPC Use/Charting– Short term data analysis– Predicted process control based

on small sample size• Typically 30 pieces from 300

MFG Use

Sample Size Example

[1]

[1] – Statistical Process Control. 2000-2009. MoreSteam.com. <http:// http://moresteam.com/toolbox/t402.cfm>SAMPLE

Design and 6 Sigma

• Theoretical tools to validate and improve design at part and subsystem levels

• Preventative design approach– Utilizes part production methods and

part interaction to predict design quality

– Constraint Matrix• Defines the interaction between every

part in an assembly

• Aids in determining tolerance loop for the Tolerance Analysis (TA)

– Tolerance Analysis• Closed loop analysis determining

variation between chosen items

Design / Mechanical Sub-Assy(s)

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Design and 6 Sigma

• How do parts interact?

• What parts and gaps are critical?

• What items are included in a tolerance loop?

• What is the nominal gap between each part?

• Matrix provides individual part interaction and nominal gap, but no link to tolerance loop

• Bubble Chart (not shown) provides visual map of part interaction and clear path for tolerance loop

Design - Constraint Matrix

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Design and 6 Sigma

• Critical Items– Is the loop correct?– Are the correct tolerances used?– Is the nominal gap correct?– Are user defined limits included?– Is the calculated sigma value

adequate?• Strive for six sigma wherever

possible

• Final sigma value is engineering judgment

– HOWEVER, deviations to very low sigma levels are dangerous and require detailed analysis and technical explanation for proper consideration

Design - Tolerance Analysis

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Design and 6 Sigma

• Tolerance analysis will help define critical dimensions to include on drawings– Any feature / dimension used in a tolerance analysis must be included on the part

drawings and documented in a Production Part Approval Process (PPAP) document– Part and drawing changes affecting TA items should be analyzed prior to change to

ensure they do not negatively affect quality

• Tolerance Analyses are critical in determining assembly capabilities, including– Tolerances of visual gaps– Proper function of latches and mechanisms

• SPC items are used to determine process capability (not necessarily tied to TA items)– Select critical dimensions flagged as SPC to provide overall process capability– Any PPAP measurements near upper or lower limits must be accompanied by SPC

analysis to demonstrate adequate process control and to maintain proper quality

• Low sigma values / low SPC values directly relate to poor quality.

6σ / PPAP Relationship

Poor Quality CostSAMPLE

BACKUP

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Conversion Charts

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Cost of Quality

• Lower sigma levels mean more defects and poor quality

• Poor quality comes at a cost– Refer to comparison at right to see

an estimated cost impact of poor quality on company sales

SigmaDefects Per Million

OpportunitiesCost of Poor

Quality Notes6 Sigma 3.4 defects < 10% of sales World Class5 Sigma 233 defects 10-15% of sales4 Sigma 6,210 defects 15-20% of sales Industry Average3 Sigma 66,807 defects 20-30% of sales2 Sigma 308,537 defects 30-40% of sales Non-Competitive1 Sigma 690,000 defects

Six Sigma Quality Level Comparison

Source: Harry, pg 61SAMPLE

1.5 Sigma Shift

... 6 sigma actually translates to about 2 defects per BILLION opportunities, and 3.4 defects per million opportunities, which we normally define as 6 sigma, really corresponds to a sigma value of 4.5.

Where does this 1.5 sigma difference come from?

• Motorola determined, through years of process and data collection, that processes vary and drift over time – what is commonly called “Long-Term Dynamic Mean Variation”. This variation typically falls between 1.4 and 1.6.– Early in the project cycle, the standard deviation and sigma value of the

process is measured. This early measurement is considered a short-termvalue, as it can only be attributed to common cause variation. A full project and the associated collection of process data covers a much longer period of time (years, rather than months). This long term data contains both common cause AND special cause variation. Because short term data does not contain this special cause variation, it will typically yield a higher process capability than is realistic long-term.

• The difference is the 1.5 sigma shift…SAMPLE

MFG Example

• Sample sizes should contain a minimum of 30 pieces to provide any significant information

• The larger the sample size, the smaller the opportunity for error

Statistical example “significance”

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Additional Information

Further Six Sigma Reading:

• http://moresteam.com/toolbox/index.cfm

• http://www.isixsigma.com/library/content/six-sigma-newbie.asp

• Six Sigma: The Breakthrough Management Strategy Revolutionizing the World’s Top Corporations, Mikel Harry and Richard Schroeder, 2000

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