System-level fault diagnosis is an important means to ensure the reliability of a complex multiprocessor system.The PMC model is regarded as an important system-level diagnosis model.By analyzing and demonstrating the properties of

t

-conditional diagnosable system under the PMC model

this paper first introduces a necessary and sufficient condition of

t

-conditional diagnosable system under the PMC model

constructs conditional fault model equations

and then solves the conditional fault model equations by using relational algebra such as natural join and cartesian product

so that a fast and convenient conditional fault model algorithm is proposed.Finally

according to the necessary and sufficient condition of

t

-conditional diagnosable system under the PMC model

this paper proposes a new

t

-conditional diagnosable decision algorithm which is simple and effective.