Module 5 - E-Courses
Module 5 - E-Courses
Module 5 - E-Courses
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Reliability Engineering Prof. G. L. Sivakumar Babu<br />
Step1.Partial differentiation of performance functions with respect to each random<br />
variable.<br />
⎜<br />
⎛ ∂ g<br />
7 . 5 * 2 * 1<br />
1<br />
⎟<br />
⎞ f = x σ<br />
⎝ ∂ x ⎠<br />
⎜<br />
⎛ ∂ g<br />
= 7 . 5 * 1 * σ 2<br />
2<br />
⎟<br />
⎞ f x<br />
⎝ ∂ x ⎠<br />
⎜<br />
⎛ ∂ g<br />
= −σ<br />
3<br />
3<br />
⎟<br />
⎞ f<br />
⎝ ∂ x ⎠<br />
Indian Institute of Science Bangalore<br />
Step2.computation of direction cosines,α .<br />
α =<br />
⎜<br />
⎛∂g<br />
⎟<br />
⎞ f<br />
⎝ ∂Xi⎠<br />
⎛ 2 *<br />
⎞<br />
⎜∑<br />
⎜<br />
⎛∂<br />
⎜<br />
⎛∂g<br />
⎟<br />
⎞ g<br />
⎟<br />
⎞<br />
⎟<br />
⎝ ⎝ ∂Xi⎠<br />
⎝ ∂Xi⎠<br />
⎠<br />
Step3.calcualtion of new Xif<br />
Xif = α β<br />
Step4.using estimated values of mean and standard deviation, calculate Xif new<br />
Xifnew = µ i + σ Xif<br />
Step5.repeat the iteration until reliability index value converge to single value.<br />
Evaluation of reliability<br />
Limiting state of interest g(X1, X2, X3) = 7.5*X1*X2 – X3 = 0. Iteration process is<br />
illustrated in the following sections.<br />
MEAN COEFFICINET<br />
OF<br />
VARIATION<br />
INITIAL x1f 22.0 17.8 17.7 17.7<br />
INITIAL x2f 5.2 4.6 4.7 4.7<br />
INITIAL X3f 600 620 623 623<br />
g<br />
⎜<br />
⎛∂<br />
f<br />
X<br />
⎟<br />
⎞<br />
⎝ ∂ 1⎠<br />
171.6 153.2 154.6 154.8<br />
STANDARD<br />
DEVIATION
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