Introduction to Reliability in Mechanical Engineering

Project II

송민호Morkache Zinelabidine

Presentation Outline Project 1 Results

Reliability calculation by using graphical method

Reliability calculation by using PDF from project 1 values

Results and Conclusion

Project 1 Results

Zino Data 1 (N= 16)

632457216308196406570397641476599411574491139466

D0.15 0.1880.25 0.172512.4

148.14

Bi-exponential distribu-tionMean rank method

송민호 Data 2 (N=9)Normal distributionMean rank method

42526537638451058

67912588

323.42259.07

D0.25 0.21

80.20 0.22

7

Project 2 Analysis

Determining Strength/Stress for Data 1&2

Data No of Data MeanSet1 16 436Set2 9 323.42

Calculation with only the data sets

CDF value graph of the data

Since the data value does not match one to one, interpolation is done to have CDF values for every natural number data values within the overlapping range

Calculation : Lower limit case

Re = 0.645Pf = 0.329

Calculation : Upper limit case

Re = 0.6706Pf = 0.354

Calculation : Triangle method

Re = 0.6579Pf = 0.342

Reliability calculation from equation

Probality Density Function• Stress : Normal distribution

Fsig(x) = 0.5+0.5*erf((1/2)*sqrt(2)*(x-323.42)/(259.07))

• Strength : Bi-exponential distribution

Fs(x) = 1-exp(-exp((x-512.4)/(148.14)))

Using equation from project 1

CDF value is not 0 when the datavalue is 0 : integrate from -1000 to 1000

Probability distribution function From -1000 to 1000

Graph from Origin by using Derivative() function

f(stress) = Derivative(F(stress))f(strength) = Derivative(F(strength))

Using Origin

Re = 0.64034Pf =0.35966

Results & Conclusion

Lower R Upper R Triangle R Equation R0.645 0.6706 0.6579 0.64034

Upper Pf Lower Pf Triangle Pf Equation Pf0.345 0.329 0.342 0.35966

Sum 0.999 0.9996 0.9999 1.00000

Sum of reliability and probability of failure is almost unity for every calculation method used Calculation is correct

As the reliability is lowest when using the equation from project 1, this method is the most strict method.