Abstract
It is an important problem to estimate component parameters. We sometimes cannot investigate the cause of failure immediately, we say that the cause of failure is masked. We consider k-component series system, whose component lifetime follows the exponential distribution. When the couse of failure is randomly masked, we show the maximum likelihood estimator and the unbiased one under not only the case that every failure is observed but also type II censoring or two kinds of negative binomial sampling Under the negative binomial sampling for 2-component series system, we illustrated the numerical examples about the variation of the expected total number of systems and that of the relative errors of the unbiased estimators as the masking probability varies. We decide the number of successes (failure systems) in a sequence of Bernoulli trials, then we have the required precision of the estimator and show its precision of the estimator is smaller than that without masking. Under one of the negative binomial sampling which we propose, we show that the precision of the unbiased estimator of failure rate need not depend on the other failure rate.
