Unidentified competing causes. Consider a series system with two independent competing failure causes. Suppose that cause k has a Weibull distribution with parameters αk and ßλ, k = 1, 2. Also, suppose that the cause of any failure is not identified.
(a) Give the log likelihood for a sample multiply censored on the right.
(b) Comment on the theoretical and numerical labor to obtain the ML estimates and asymptotic covariance matrix.
(c) Under the assumption ß =ß = 1 (exponential distributions), can αI and α2 be estimated separately? Explain.
(d) Under the assumption ßI =& ß, can αI and az be estimated separately? Explain.