Reliability

Reliability of Adhesives used in High Quality Audio

Components

Background

• Adhesives used to bond two metallic components together.

• Adhesive is Key Process Input (KPI) for the construction of speakers.

• Storage conditions (temperature and humidity) are KPI’s to reliability of adhesive.

Background

• Two Conditions:– Factor 1: Length of Storage

• Bond strength was measured for adhesives stored for 3 days to 82 days.

– Factor 2: Storage Temperature and Humidity

• Bond strength measured for adhesives stored at 4 conditions:

Temp (°C) Temp (°F) RH DescriptionTest 1 27 80.6 50% Warm RoomTest 2 27 80.6 70% Warm Room with Elevated RHTest 3 32 89.6 70% Hot, Somewhat humidTest 4 27 80.6 100% Hot, Extremely Humid

Relative Humidity

Analysis

• Steps of Analysis– Excel– Minitab– Maple– Monte Carlo Analysis

Excel Analysis of Storage Conditions

Storage Conditions

202.87

181.91

272.20

25.807 1

126

1

345

325

378

132

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

0 1 2 3 4 5

Test

Bo

nd

Str

eng

th (

psi

)

Average

Min

Max

Storage Time Analysis

200100

99.99

90

50

10

1

0.01

Strength (lbs)

Perc

ent

500200

99.99

99

90

50

10

1

0.01

Strength (lbs)

Perc

ent

1000.00100.0010.001.000.100.01

99.99

90

50

10

1

0.01

Strength (lbs)

Perc

ent

500200100

99.99

99

90

50

10

1

0.01

Strength (lbs)

Perc

ent

Weibull0.980

Lognormal0.960

Exponential*

Loglogistic0.960

Correlation Coefficient

Probability Plot for Strength (lbs)LSXY Estimates-Complete Data

Weibull Lognormal

Exponential Loglogistic

350300250200

0.010

0.005

0.000

Strength (lbs)

PD

F

200

99.9

90

50

10

1

0.1

Strength (lbs)

Perc

ent

350300250200

100

50

0

Strength (lbs)

Perc

ent

350300250200

0.10

0.05

0.00

Strength (lbs)R

ate

Correlation 0.988

Shape 7.64223Scale 296.660Mean 278.750StDev 43.1625Median 282.768IQR 57.5818Failure 85Censor 0AD* 0.380

Table of StatisticsProbability Density Function

Survival Function Hazard Function

Distribution Overview Plot for Strength (lbs)LSXY Estimates-Complete Data

Weibull

82807568524917141312111076543

350

300

250

200

150

100

Days

Str

ength

(lb

s)

Boxplot of Strength (lbs)

150100500-50-100

99.9

99

95

90

80706050403020

10

5

1

0.1

RESI1

Perc

ent

Mean 3.343731E-16StDev 35.99N 85AD 0.470P-Value 0.241

Probability Plot of RESI1Normal - 95% CI

Table of MTTF

Standard 95% Normal CI

Distribution Mean Error Lower Upper

Weibull 266.949 0.908659 265.174 268.736

Storage Conditions Capability

4003002001000

LSL

LSL 25Target *USL *Sample Mean 202.87Sample N 23StDev(Within) 121.172StDev(Overall) 109.545

Process Data

Cp *CPL 0.49CPU *Cpk 0.49

Pp *PPL 0.54PPU *Ppk 0.54Cpm *

Overall Capability

Potential (Within) Capability

PPM < LSL 86956.52PPM > USL *PPM Total 86956.52

Observed PerformancePPM < LSL 71064.08PPM > USL *PPM Total 71064.08

Exp. Within PerformancePPM < LSL 52219.35PPM > USL *PPM Total 52219.35

Exp. Overall Performance

WithinOverall

Process Capability of Test 1

5004003002001000-100

LSL

LSL 25Target *USL *Sample Mean 181.913Sample N 23StDev(Within) 131.568StDev(Overall) 104.718

Process Data

Cp *CPL 0.40CPU *Cpk 0.40

Pp *PPL 0.50PPU *Ppk 0.50Cpm *

Overall Capability

Potential (Within) Capability

PPM < LSL 130434.78PPM > USL *PPM Total 130434.78

Observed PerformancePPM < LSL 116506.13PPM > USL *PPM Total 116506.13

Exp. Within PerformancePPM < LSL 67009.79PPM > USL *PPM Total 67009.79

Exp. Overall Performance

WithinOverall

Process Capability of Test 2

40035030025020015010050

LSL

LSL 25Target *USL *Sample Mean 272.2Sample N 20StDev(Within) 66.2094StDev(Overall) 67.3095

Process Data

Cp *CPL 1.24CPU *Cpk 1.24

Pp *PPL 1.22PPU *Ppk 1.22Cpm *

Overall Capability

Potential (Within) Capability

PPM < LSL 0.00PPM > USL *PPM Total 0.00

Observed PerformancePPM < LSL 94.38PPM > USL *PPM Total 94.38

Exp. Within PerformancePPM < LSL 120.05PPM > USL *PPM Total 120.05

Exp. Overall Performance

WithinOverall

Process Capability of Test 3

12080400-40

LSL

LSL 25Target *USL *Sample Mean 25.8Sample N 10StDev(Within) 40.3861StDev(Overall) 41.215

Process Data

Cp *CPL 0.01CPU *Cpk 0.01

Pp *PPL 0.01PPU *Ppk 0.01Cpm *

Overall Capability

Potential (Within) Capability

PPM < LSL 700000.00PPM > USL *PPM Total 700000.00

Observed PerformancePPM < LSL 492097.96PPM > USL *PPM Total 492097.96

Exp. Within PerformancePPM < LSL 492256.86PPM > USL *PPM Total 492256.86

Exp. Overall Performance

WithinOverall

Process Capability of Test 4

Storage Conditions Minitab Analysis

Distribution ID Plot: Test 1

Goodness-of-Fit

Anderson-Darling CorrelationDistribution (adj) CoefficientWeibull 2.057 0.927

Table of MTTF

Standard 95% Normal CIDistribution Mean Error Lower UpperWeibull 223.489 52.3552 141.205 353.721 Distribution ID Plot: Test 2

Goodness-of-Fit

Anderson-Darling CorrelationDistribution (adj) CoefficientWeibull 2.722 0.911

Table of MTTF

Standard 95% Normal CIDistribution Mean Error Lower UpperWeibull 223.331 81.9036 108.838 458.263

Distribution ID Plot: Test 3

Goodness-of-Fit

Anderson-Darling CorrelationDistribution (adj) CoefficientWeibull 1.187 0.958

Table of MTTF

Standard 95% Normal CIDistribution Mean Error Lower UpperWeibull 271.769 16.1156 241.950 305.264

Distribution ID Plot: Test 4

Goodness-of-Fit

Anderson-Darling CorrelationDistribution (adj) CoefficientWeibull 2.043 0.933

Table of MTTF

Standard 95% Normal CIDistribution Mean Error Lower UpperWeibull 20.2886 7.87081 9.48490 43.3979

400300200150100

95

80

50

20

5

2

1

Test 3

Perc

ent

Weibull0.958

Correlation Coefficient

Probability Plot for Test 3LSXY Estimates-Complete Data

Weibull

400300200100

0.006

0.004

0.002

0.000

Test 3

PD

F

200100

90

50

10

1

Test 3

Perc

ent

400300200100

100

50

0

Test 3

Perc

ent

400300200100

0.045

0.030

0.015

0.000

Test 3

Rate

Correlation 0.958

Shape 4.19920Scale 299.000

Mean 271.769StDev 72.9616Median 274.009IQR 100.949Failure 20

Censor 0AD* 1.187

Table of StatisticsProbability Density Function

Survival Function Hazard Function

Distribution Overview Plot for Test 3LSXY Estimates-Complete Data

Weibull

Conclusions

• Storage Conditions showed significant differences in MTTF.

• Storage Time did not show significant differences in MTTF

• Further Weibull analysis in Maple required.

• Equations from Maple will be used to conduct Monte Carlo Analysis.