Virtual DoE – Design of Experiment application

to Software Modelling to improve product reliability

Leonid Boim – CEO, Reliability System Engineer @

B.L. – Reliability and Quality Engineering Ltd., Israel

leonid.boim@bl-rqe.co.il

Presented at 13th National Conference of the Israel Society for Quality,

November 2015

Contents

• BL-RQE company overview

• Design Objective definition

• DoE model

• Analysis results

• Conclusions and Recommendations

2

B.L. – Reliability and Quality Engineering Ltd.

Consultation and Project executing at Specialized Fields of Expertise:

• System Reliability and Safety Assessment

• Product Design and Production Quality Assurance programs management

• Enterprise Quality System establishment, maintenance and auditing

3

B.L. – Reliability and Quality Engineering Ltd. (continued)

Design-for-Reliability and Six-Sigma tools application:

• Reliability modeling and prediction (RBD, MTBF)

• Failure Mode Effects and Criticality Analysis (FMEA/FMECA, DFMEA/PFMEA)

• Fault Tree Analysis (FTA)

• Component Stress Derating Analysis

• Circuit Tolerance Analysis

• Design of Experiments (DoE)

• HALT/ATL and ESS/HASS design

• FRACAS/CAPA process implementation

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This Case Study Highlights

• Statistical Design of Experiment (DoE) for Mechanical Computer Added Design (CAD).

• Based of CAD simulation (“virtual experiment”) of mechanical properties of the component with Final Elements analysis (by COSMOSXpess module of the Solid Works software).

• DoE was done using JMP software.

• Performed early in product design phase.

5

Electrical Contact Design

6

Ring Leaf

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Contact Design Requirements

The leaf displacement shall be between 0.5 to 0.6 mm, when 40 g force is applied to the leaf.

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Design Challenges

• Concept Realization Phase: difficult to define optimal “working point” (dimensions, material) - due-to dependence on multiple parameters.

• Design Verification Phase: difficult to measure force and displacement physically (before part assembly) – due-to small part dimensions.

Traditional approach – “Trials-and-Errors”

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How to Avoid the Difficulties? 1. First stage: Simulate the part displacement by

COSMOSXpress software (instead of measurements).

2. Second stage: Design series of “Virtual experiments” using Statistical DoE approach:

– Run simulation for each set of parameters (factors).

– Use all runs to fit linear model.

3. Third stage: Verify DoE results by real test

Minimize Trials-and-Errors attempts

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Displacement Simulation by COSMOSXpress

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Simulation Results – One Run

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DoE Model Definition

Y – response function (Leaf displacement),

µ – response average,

A, B, ... – model factors (Leaf dimensions, part material),

i – model parameters (to be determined by experiment),

– random error.

BABAY ABBA

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DoE Targets

1. Fit simple linear model including the main effects of the factors and the interactions between them.

2. Learn the part properties using the model.

3. Find particular values of dimensions and material to meet the design requirements.

4. Define less sensitive zones of parameters (determine optimal tolerances).

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Model Factors and Levels

1. Leaf WIDTH (W = 0.6 or 0.8mm)

2. Leaf BENDING (B = 0.3 or 0.7mm)

3. Contact THICKNESS (T= 0.1 or 0.15 mm)

4. Leaf NOTCHING (Yes/No)

5. Contact material HARDNESS (Steel or Brass): 1.9 or 1.0E+11 [N/m^2]

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DoE set-up overview

• The model was developed for five factors: 4 continuous and 1 categorical (yes/no) each one with two levels.

• Full factorial design: 25x1 = 32 different runs without replications (virtual experiment only - simulation, but may be additional runs with different meshing (Final Element structure) partition will give estimate for pure error ? - TBD)

• All parameters were changed simultaneously - use all runs to fit a simple linear model (main effects and interactions).

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Input data for DoE Analysis

# Bending,

mm

Width,

mm

Thickness,

mm

Hardness,

N/m^2

Notches,

(No/Yes)

Displacement

(Y), mm

1 0.3 0.6 0.1 1.9e+11 No notches 0.2461

2 0.7 0.6 0.1 1.9e+11 No notches 0.2208

3 0.3 1 0.1 1.9e+11 No notches 0.2398

4 0.7 1 0.1 1.9e+11 No notches 0.2158

... ... ... ... ... ... ...

31 0.3 1 0.15 1.0e+11 Notched 0.1621

32 0.7 1 0.15 1.0e+11 Notched 0.1457

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JMP Run – Visual Overview D

ispl

acem

ent

0.1

0.2

0.3

0.4

0.5

0.6

0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 0.6 0.8 Width

0.3 0.7 0.3 0.7 0.3 0.7 0.3 0.7 0.3 0.7 0.3 0.7 0.3 0.7 0.3 0.7 Bending

No notches Notched No notches Notched No notches Notched No notches Notched Notches

AISI 304 Brass AISI 304 Brass Material

0.1 0.15 Thickness

Variability Chart for Displacement

Variability Gage

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JMP Calculation Sequence

1.Start with full model fitted: 5 factors with all possible high order (3-, 4-, 5-) interactions (31 parameters fitted).

2.Then exclude low effects (less then 0.004 mm response).

3. Re-calculate the reduced model for all 5 factors and 2nd order interactions.

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Pareto plot of Estimates (i)

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Interactions Profiler

0.1

0.15

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Prediction Profiler

For target displacement of 0.55 mm (desirability = 1), the predicted parameters are:

• Critical: Thickness = 0.1 ± 0.02 mm, Hardness = 1E+11 (Brass), Notches = Yes.

• Non-critical: Bending 0.4 ± 0.1 mm, Width 0.65 ± 0.05 mm.

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Model Verification by Test • COSMOSXpress disclaimer:

The design decisions should not be based solely on the simulation data. Use this information in conjunction with experimental data and practical experience.

• For the following reference design parameters:

– Thickness = 0.1 mm, Width = 0.8 mm, Bending = 0.3 mm, No notches, Material hardness = 1E+9 N/m^2 (Brass)

– Model result: 0.43±0.01 mm

– Real displacement: ≥0.5 mm (relative error ~16%)

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Conclusions 1. Specific results – contact displacement:

– mostly dependent on thickness and material,

– weak dependence from width and bending,

– for soft material (brass) the thickness is more affecting displacement (interaction).

2. General – DoE applied to CAD simulation can predict part properties, define parameters and optimize tolerances prior to part manufacturing – similar to real experiment - minimizing “trial-and-error” attempts – shortening project schedule.

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Recommendations

• Pure error simulation – replications with different meshing (Final Element structure)

• Adding second requirement (internal stress limitation) – parameters optimization and trade-off between stress and target displacement (by Prediction Profiler).

• Continue DoE for different CAD models and Real Experiments verifications (electrical, RF, mechanical, etc.).