On Competing Risk Model Under Random Masking

Analysts are often interested in obtaining component reliabilities by analyzing system life data. Making a series system assumption and applying a competing risk model generally does this. In practice, the data consists of a system life-length and a subset of components that contains the true cause of system failure (the true cause of system failure is masked from our knowledge). We consider a series system composed of independent Weibull components with common shape parameter and different scale parameters. It is shown that the IFRA-ness of the system is measured by the common shape parameter, which is also known as the aging factor. We derive the consistency and asymptotic normality of the MLEs of the scale parameters under random masking.