02/25/06SJSU Bus David Bentley1 Chapter 12 – Design for Six Sigma (DFSS) QFD, Reliability analysis, Taguchi loss function, Process capability

02/25/06SJSU Bus David Bentley2 DFSS Activity Categories Concept development Design development Design optimization Design verification We’ll look at each of these in detail

02/25/06SJSU Bus David Bentley3 Concept Development Based on: Customer requirements Technological capabilities Economic considerations Tools Quality Function Deployment (QFD) Concept engineering

Rev. 11/25/02SJSU Bus David Bentley4 Quality Function Deployment (QFD) Structured approach for design Developed at Mitsubishi’s Kobe shipyards “House of quality” – built on relationships Customer requirements Design requirements Competitive assessment Technical assessment 4 layers: product, part, process, production (quality plans )

11/21/02SJSU Bus David Bentley5 The House of Quality Correlation matrix Design requirements Customer require- ments Competitive assessment Relationship matrix Specifications or target values Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

SJSU Bus David Bentley6 House of Quality Technical requirements Voice of the customer Relationship matrix Technical requirement priorities Customer requirement priorities Competitive evaluation Interrelationships THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/21/02SJSU Bus David Bentley7 QFD Example Operations Management, Seventh Edition, by William J. Stevenson Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.

02/25/06SJSU Bus David Bentley8 QFD Steps Identify/ prioritize customer requirements 2. Determine technical requirements 3. Relate customer requirements to technical requirements 4. Compare ability to meet requirements against competitive products

02/25/06SJSU Bus David Bentley9 QFD Steps Set targets for technical requirements and determine capability 6. Look for high opportunity requirements to satisfy customer 7. Continue QFD process to the next level.

SJSU Bus David Bentley10 QFD Levels technical requirements component characteristics process operations quality plan THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

02/25/06SJSU Bus David Bentley11 Concept Engineering Understand customer environment Convert into requirements Deploy learning into operations Generate concepts Select appropriate concept

02/25/06SJSU Bus David Bentley12 Design Development Product and process performance issues Focus on ability to meet requirements in operations Tools Tolerance design and process capability Design failure mode and effects analysis (DFEA) Reliability prediction

02/25/06SJSU Bus David Bentley13 Tolerance Design - 1 Specification Translation of customer requirements into design requirements Consists of nominal value and tolerances Nominal value Ideal dimension or target value for meeting customer requirement Tolerance Allowable variation above and/or below nominal value Recognizes natural variation (common causes)

02/26/05SJSU Bus David Bentley14 Tolerance Design - 2 Consider tradeoff between costs and performance Too tight tolerances = unnecessary cost Too loose tolerances = not meeting customer requirements End result: too loose or too tight is going to cost you money!

02/26/06SJSU Bus David Bentley15 DFMEA Design failure and effects analysis (DFMEA) Identify all the ways failures can occur Estimate effects of the failures Recommend changes in design

SJSU Bus David Bentley16 THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

Rev. 02/25/06SJSU Bus David Bentley17 Reliability Prediction Generally defined as the ability of a product to perform as expected over time Formally defined as the probability that a product, piece of equipment, or system performs its intended function for a stated period of time under specified operating conditions THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley18 Types of Failures Functional failure Failure that occurs at the start of product life due to manufacturing or material detects “DOA” or “infant mortality” Reliability failure Failure after some period of use THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM (Mod 11/11/02 DAB)

11/11/02SJSU Bus David Bentley19 Types of Reliability Inherent reliability – predicted by product design (robust design) Achieved reliability – observed during use THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM (Mod 11/11/02 DAB)

11/11/02SJSU Bus David Bentley20 Reliability Measurement Failure rate ( ) – number of failures per unit time Alternative measures Mean time to failure Mean time between failures THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley21 Cumulative Failure Rate Curve THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley22 Failure Rate Curve “Infant mortality period” THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley23 Average Failure Rate THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley24 Reliability Function Probability density function of failures f(t) = e - t for t > 0 Probability of failure from (0, T) F(t) = 1 – e - T Reliability function R(T) = 1 – F(T) = e - T THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley25 Series Systems R S = R 1 R 2... R n 12n THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley26 Parallel Systems R S = 1 - (1 - R 1 ) (1 - R 2 )... (1 - R n ) 1 2 n THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/11/02SJSU Bus David Bentley27 Series-Parallel Systems Convert to equivalent series system AB C C D RARARARA RBRBRBRB RCRCRCRC RDRDRDRD RCRCRCRC AB C’ C’D RARARARA RBRBRBRB RDRDRDRD R C’ = 1 – (1-R C )(1-R C ) THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

02/25/06SJSU Bus David Bentley28 Design optimization Minimize variation in processes Seek robust design (Taguchi) Insensitive to process variations or the use environment Tools Taguchi loss function Optimizing reliability

11/21/02SJSU Bus David Bentley29 Loss Functions loss no loss nominal tolerance loss Traditional View Taguchi’s View THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

11/21/02SJSU Bus David Bentley30 Taguchi Loss Function Calculations L(x) = k(x - T) 2 Example: Specification =.500 .020 Failure outside of the tolerance range costs $50 to repair. Thus, 50 = k(.020) 2. Solving for k yields k = 125,000. The loss function is: L(x) = 125,000(x -.500) 2 Expected loss = k(  2 + D 2 ) where D is the deviation from the target. THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM

Rev. 02/26/06SJSU Bus David Bentley31 Optimizing Reliability Standardization Redundancy Physics of failure THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM (Mod 11/11/02 DAB)

02/25/06SJSU Bus David Bentley32 Design Verification Ensure that process capability meets the appropriate sigma level Meet specifications (AND customer requirements) Tools Reliability testing Measurement systems evaluation Process capability determination

Rev. 02/26/06SJSU Bus David Bentley33 Reliability Testing Life testing Accelerated life testing Environmental testing Vibration and shock testing Burn-in THE MANAGEMENT AND CONTROL OF QUALITY, 5e, © 2002 South-Western/Thomson Learning TM (Mod 11/11/02 DAB)

02/26/06SJSU Bus David Bentley34 Measurement System Evaluation Variation can be due to: Process variation Measurement system error Random Systematic (bias) A combination of the two

02/26/06SJSU Bus David Bentley35 Metrology - 1 Definition: The Science of Measurement Accuracy How close an observation is to a standard Precision How close random individual measurements are to each other

02/26/06SJSU Bus David Bentley36 Metrology - 2 Repeatability Instrument variation Variation in measurements using same instrument and same individual Reproducibility Operator variation Variation in measurements using same instrument and different individual

02/26/06SJSU Bus David Bentley37 R&R Studies Select m operators and n parts Calibrate the measuring instrument Randomly measure each part by each operator for r trials Compute key statistics to quantify repeatability and reproducibility

02/25/06SJSU Bus David Bentley38 R&R Spreadsheet Template

02/26/06SJSU Bus David Bentley39 R&R Evaluation Acceptable: < 10% Unacceptable: > 30% Questionable: 10-30%

02/26/06SJSU Bus David Bentley40 Calibration Compare 2 instruments or systems 1 with known relationship to national standards 1 with unknown relationship to national standards

41 Process Capability The range over which the natural variation of a process occurs as determined by the system of common causes Measured by the proportion of output that can be produced within design specifications

SJSU Bus David Bentley42 Types of Capability Studies  Peak performance study  How a process performs under ideal conditions  Process characterization study  How a process performs under actual operating conditions  Component variability study  Relative contribution of different sources of variation (e.g., process factors, measurement system)

SJSU Bus David Bentley43 Process Capability Study  Choose a representative machine or process  Define the process conditions  Select a representative operator  Provide the right materials  Specify the gauging or measurement method  Record the measurements  Construct a histogram and compute descriptive statistics: mean and standard deviation  Compare results with specified tolerances

44 Process Capability specification natural variation (a)(b) natural variation (c)(d)

45 Process Capability Index C p = UTL - LTL 6  C pl, C pu } UTL -  3  C pl =  - LTL 3  C pk = min{ C pu =

46 Process Capability Ratios Non-centered process (general case): choose c pk = the lower of: Upper spec – process mean c pu = or 3  Process mean – lower spec c pl =  SJSU Bus. 142 David A. Bentley 09/30/02

47 Process Capability Ratios Centered process (special case): specification width c p = process width Upper spec – lower spec =  SJSU Bus. 142 David A. Bentley 09/16/02

48 Process Capability Requirements Process must be normally distributed Process must be in control Process capability result: > 1.34 = capable < 1.33 = not capable = 1.33 = barely capable > 5 or 10 is “overkill”, excessive resource use SJSU Bus. 142 David A. Bentley 0/24/06

Rev. 02/26/06SJSU Bus David Bentley49 Process Capability Spreadsheet Template