Uncertain Random Alternating Renewal Process With Application to Interval Availability

As a mixture of a random variable and an uncertain variable, an uncertain random variable is a tool to deal with the indeterminacy quantities involving randomness and human uncertainty. This paper aims at proposing a concept of an uncertain random alternating renewal process to model a repairable system with random on-times and uncertain off-times. An alternating renewal theorem is proved, which gives the limit chance distribution of the interval availability of the uncertain random alternating renewal system.