Design robustness demonstration by DOE and Monte Carlo Simulation

Design Robustness Demonstration by

DOE and Montecarlo Methods.

Application to automotive Fuses

MTA - Ricardo González Luna

RGL 1

RGL 2

This work was originally Published in the Meet Minitab 2015 (Milan)

http://www.gmsl.it/materiale-e-presentazioni-meet-minitab-2015

/

http://www.gmsl.it/materiale-e-presentazioni-meet-minitab-2015/



MTA USA

MTA BRASIL

MTA MEXICO MTA INDIA MTA CHINA

MTA POLAND

MTA SLOVAKIA

HEADQUARTERS CODOGNOELECTRONICS ROLO

FRONT OFFICE FRANCEFRONT OFFICE GERMANY

FRONT OFFICE TURKEY

Production

R & D

SalesMTA is an Italian automotive

company with more than 1100 employees worldwide

(2015)RGL 3

MTA Electromechanic and Electronic Components

RGL 4

AGCO Group ARGO Group CNH GEHL JCB John Deere SDF Group

Cargotec Elgin Sweeper Freightliner Iveco Navistar Smith Electric

Aston Martin BMW Ferrari-Maserati FCA Ford GM Lamborghini Lotus Mahindra PSA Peugeot Citröen Renault – Nissan TATA Tesla Volvo Car Corporation Volkswagen

Aprilia BMW Motorrad Brammo Cagiva Ducati Derby Harley Davidson Husqvarna MBK Moto Guzzi MV Agusta Piaggio Yamaha

MTA Tier 1 Customers

MTA PRODUCES AUTOMOTIVE FUSES SINCE

1954RGL 5

RGL 6

FUNCIONALITY OF AN AUTOMOTIVE FUSE

1. Is the weakest link in the chain, to be able to protect the entire electrical system and specifically the wire

2. There are two kind of anomalies1. Short circuit2. Overload

3. Must also reliably supply the electrical current, flowing through himself, therefore causing heating and as a consequence, materials degradation.

RGL 7


Conditions of functionality:

1. If there is an anomaly, the fuse must act before the wire can be damaged, but….

2. The fuse never must blown if there is no anomaly and…..

3. Should heat as less as possible, under normal operating conditions

Statistical guarantee for functional characteristics is :• Demonstrate CpK>1,67,

OR• Test 100%.

But fuses test is destructive!!!

RGL 8

RGL 9


Joule EffectPIN=I2xR = I x Voltage drop

Conv

ectio

n

i

Rad

iatio

n

i

Conduction

Conduction

The physics of the fuse is the interaction among the thermal effects: Joule Heating, Heat dissipation, phase changes and resitivity variation with temperature.

RGL 11

WHY THIS WORK?

Customers wants the probability to

find a defective part well below 5ppm, and that Defect

Free does not rely just on End-of-Line

test

The Direction of the Company requires

that product quality is

guaranteed and does not incurs in

high costs of control and scrap

at End-of-Line test.

Therefore require a Capability Index

greater than 1,67!!

FAIL!!

12

SINTHESYS: Statistical Content of the Robustness Demonstration Method

Determine Transfer

Functions

DOE

Identify parameter distribution

Data Analysis

Evaluate design robustness

Capabi-lity

RGL 13

TRANSFER FUNCTION DETERMINATION

We want to understand the relationship between the values of the physical components that built the fuse

Width

BLOW TIMEFiThickn.

Length

Melting °CResistivity HEAT

Then Predict the effect of the natural variability of the physical characteristics

And his behavior:

The Transfer

Functions «Fi»

Transfer Function Determination

Use Engineering functions and solve mathematically

Design of Experiments (DOE)

14

OR

RGL 15

Select appropriate combination of parameters and find the functional results for those combinations. The results will serve to define mathematical functions through regression methods. Results can be obtained:

Experimentally By Numerical Methods

DOE obtains the effect of each single parameter, but also the effect of the combination of two or more of this parameters («interactions»)

Design Of Experiments (DOE):

RGL 15

RGL 16

X-Y Interaction means that effect of X is modified by the presence of YDOE

16

X-Y Interactions example

RGL 17

Define the variables that influences the system and their range of variation according to the goal of the DOE:◦ Identification of the influent parameters and interactions◦ Design optimization by selection of parameter’s values◦ Efect of the natural variation of the parameters

This requires a good technical knowledge about the system itself and must be carried out by system experts helped by DOE practitioners.

It is important to reduce the number of parameters to reduce time and cost. Also interesting from a practical view to choose those parameters that can be easily varied in an experimental method.

DOE

17

RGL 18

For example in our case the effect of the variation of Width and Thickness can be considered two similar ways to vary the of cross-section, therefore we choose to vary only the width, than can be more easily done using CAM samples made with numerically controlled instruments.

DOE PARAMETERS CHOICE

18

W

Th

RGL 19

We can also exclude interactions between the geometrical characteristics and the quantity of low melting temperature material add to the fuse (tin in this case).

To have a lower experimental uncertainty in the practical samples preparation method, we decided to investigate this effect with a regression to be add to the DOE.

The effect is within the experimental error, then it is reppresented as a Uniform Noise.

DOE PARAMETERS CHOICE

19

RGL 20

For example in our case the effect of the variation of Width and Thickness can be considered two ways to vary the of cross-Section, therefore we choose to vary only the width, than can be more easily done using CAM samples made with numerically controlled instruments.


20

RGL 21

Inserting the experimental results in the Minitab ® Software, we obtain easily which parameters and interactions have statistical significance in the results, and therefore must be used in the regression model.


21

Pareto Chart of Standardized Effects: For Blow Time, Width and Resistivity are significative with more than 95% Confidence. Length is also significative but less evident because experimental error mask somewhere it’s smaller effect

These are the parameters and interactions that influence measurable Resistance changes for the expected variation in production.

RGL 22

Residuals are the measured variation NOT explained by the significant parameters

The conclusions given by the DOE model are acceptable if the residuals are normally distributed, and have equal variance across all the regression range, and are independent from the experimental order◦ Normally Distributed◦ Do not show a trend versus the fitted value◦ Do not show a trend versus the order of measure


22

5002500-250-500

9990

50

10

1

Residual

Perc

ent

1600140012001000800

500

2500

-250

-500

Fitted Value

Resid

ual

6004002000-200-400

10,0

7,5

5,0

2,5

0,0

Residual

Freq

uenc

y

30282624222018161412108642

500250

0-250-500

Observation Order

Resid

ual

Normal Probability Plot Versus Fits

Histogram Versus Order

Residual Plots for t-150% [sec]

You can verify these hypothesis with the Residual Plots.

RGL 23


23

Minitab model supply also the coefficients for the transfer functions in form of Linear Combination (LC), then:

Blow time = LC [WxTh; L;Resistivity ; Normal_Noise]

Resistance = LC[WxTh;Resistivity; Uniform_Noise]

1,2851,215

1400

1300

1200

1100

1000

900

80015,31014,660 1,016740,97516

W

Mea

n of

t-15

0% [s

ec]

L resistività

Effetti principali tempo fusione 150%Fitted Means

Graphical reppresentation for parameter’s effect: for example increasing width implies a strong increase in Blow time.

Identify the practical distribution for all the construction parameters

24

Identify what are the distribution type closest to the historical values for each construction parameter

Minitab© and other software have applications to find the most suitable distributions

RGL 25

How is the resulting distribution for the functional values??

MONTE CARLO METHOD

Extract Randomly the values of each parameters and calculate the operating characteristics with the Transfer Functions

RGL 26

MONTE CARLO METHOD

26

𝑌 𝑗=F [ 𝑋 𝑖 ]

RGL 27

36003000250020001500100050090

Pp 4,70PPL 2,77PPU 6,62Ppk 2,77Cpm *

Cp 5,58CPL 3,29CPU 7,86Cpk 3,29

Potential (Within) Capability

Overall Capability

PPM < LSL 0,00 0,00 0,00PPM > USL 0,00 0,00 0,00PPM Total 0,00 0,00 0,00

Observed Expected Overall ExpectedDifetti

LSL USL

OverallWithin

Distribuzione del Tempo di Fusione e relativa Capability

DESIGN ROBUSTNESS

A simple Robustness analysis allow us to predict the number of defective parts, if the input parameters respect the distribution used in the simulation

27

By repeating the process hundreds thousands of times we obtain the distribution of the operating characteristics.

RGL 28

CONCLUSIONS

We want to demonstrate that if some geometrical and material parameters are under control, the whole production of an automotive fuse will respect the functional specifications

28

RGL 29

CONCLUSIONS1° Use DOE to obtain the mathematical relationship between construction parameters and operating results.2° Determine parameters distribution according to historical values3° Extract random values from the distributions and calculate the operating value that would be obtained for such fuse. Repeat the process till a suitable distribution is obtained (Monte Carlo simulation).4° Analyce this distribution Robustness against the operating limits and predict the number of defects

29

RGL 30

https://it.linkedin.com/in/ricardogonzalezluna

https://ricardogonzalezluna.wordpress.com

[email protected]

Ricardo Gonzalez Luna

Thank You!!




https://ricardogonzalezluna.wordpress.com/

https://ricardogonzalezluna.wordpress.com/