Problem 2. A reliability test of a product produced the foll…
Problem 2. A reliability test of a product produced the following 10 observations: five exact failure times t1, t2, t3, t4, t5, one additional test unit failed but its failure time was not recorded, and four more test units did not fail at the end of the testing period, tc. Use the following Weibull reliability function, R(t) = e-(t/θ)^β. a. Derive the likelihood function for this dataset. Please express it as a function of times and Weibull parameters. (10 points) b. If it was later found out that the test unit that was previously recorded as a failure without exact failure time was actually misdiagnosed due to an inspection instrument error, do you need to adjust the likelihood function? Explain. You don’t need to write down the equation. (10 points) c. If it was later found out that all of these test units had been burn-in tested by the part supplier before, do you need to adjust the likelihood function? Explain. You don’t need to write down the equation. (10 points)