Homework answers / question archive / Simulate Weibull distribution

Simulate Weibull distribution

Statistics

Share With

---

Simulate Weibull distribution.

a)Simulate data from a stress test on 100 units (i.e., generate 100 random failure times) assuming the failure times follow a Weibull distribution with c=10,000 hrs and m=0.75. Run 100 iterations of the simulation (i.e., repeat the simulation 100 times, generating 100 random unit failure times in each iteration, and keep track of all (100×100) failure times).

b)     For each iteration, rank the failure times and estimate the characteristic life c by using the time to the 63^rd failure (why 63^rd?).

c)     Estimate the MTTF (average of the sample), median, and standard deviation of each sample (i.e. iteration).

d)     Using the estimated characteristic life and the median, estimate the shape parameter via the expression

.

e)     Generate a histogram of the 100 estimates of c and a histogram of the 100 estimates of m. Comment on the results. (Are they normally distributed? How are the means of the 100 estimates for c and m compared to the true values of c=10,000 and m=0.75?).

 

(Hint for simulating by Excel: sort the failure time and pick up the 63rd for each iteration may be time consuming. Alternatively, you can use command 'percentile' in Excel. e.g, for simulation in column A, use formula "percentile(A1:A100,0.63)" to get the 63% percentile.)