Reliability Engineering in Mechanical Engi-

neeringProject II

Group #1: 천문일 , 최호열

Conclusion from Project #1: Data set 1

• Linearity test (eye test):Weibull distribution seems most suitable

• value comparison:Weibull distribution has the highest value

• K-S test:Weibull distribution and Lognormal distribution passes test

• Rank conclusion: values are highest under Mean rank

• Overall: Weibull distribution and Mean rank best satisfies

373 283

207 176

373 98

49 509

205 92

104 230

149 170

550 187

599 191

327 585

234 414

448 100

592 249

n=26

ξ 327.01

m 1.67694

Conclusion from Project #1: Data set 2

• Linearity test (eye test):Normal distribution seems most suitable

• value comparison:Normal distribution has the highest value

• K-S test:Weibull distribution and Normal distribution passes test

• Rank conclusion: values are highest under Mean rank

• Overall: Normal distribution and Mean rank best satisfies

365 433555 504214 531227 244306 472517 133636 7331 444

687 2925 137

256 236560 126226 16116 21

n=28

μ 298.4

σ 227.3

Determining Strength/StressData set # Data MeanData set #1 26 288.23Data set #2 28 298.68

2 > 1Data 1 : StressData 2 : Strength

Reliability Calculation Methods

Calculations using equations from project I• Data #1: mean rank, Weibull distribution:

Fsigma(x)=1-(exp(-(x/327.01)^1.64694))

• Data #2: mean rank, normal distribution:

Fstrength(x)=0.5*(1+erf((x-298.4)/(227.3*sqrt(2))))

Probability Distribution Function

f(stress)

x

Range: -1000 to 1000

Calculations through Origin program• Using Integrate() function on origin, we determined our

values to be:R=0.52328 Pf=0.47672

Using Data Sets

CDF Value Graph of Data

• Values don’t match one to one

• Interpolation needed

Lower Limit (Reliability)R=0.50692 Pf(upper)=0.49308

Upper Limit (Reliability)R=0.51575 Pf(lower)=0.48425

Triangle method (Reliability)R=0.51134 Pf=0.48866

Verifying Lower and Upper Limit Reliability Values

• R(lower)=0.50692• R(upper)=0.51575• R(average)=0.51134=R(triangle)

• Pf(upper)=0.49308• Pf(lower)=0.48425• Pf(average)=0.48866=Pf(triangle)

SummaryValue Lower Upper Triangle PDFR 0.50692 0.51575 0.51134 0.52328Value Upper Lower Triangle PDFPf 0.49308 0.48425 0.48866 0.47672Sum 1 1 1 1

Conclusion:

The most strict method is the Lower method (lowest R value)

The method with the closest value to PDF method is the Upper Method.