A reliability model with states of partial operation

This article generalizes the classical dichotomic reliability model to include states of partial operation. The generalized model can be considered as a special case of a general jump process. Both continuous and discrete state spaces are included. The relationship to cumulative damage shock models is discussed. Properties of the model are investigated and these are illustrated via examples. The equivalence of three forms of component independence is proved, but this equivalence does not generalize to the property of zero covariance. Alternative forms of series and parallel connections and the effect of component replacement are discussed.