Summary: This paper is concerned with the analysis of periodic-review order-up-to inventory systems with backorders in which stochastic replenishment order crossovers may be observed, i.e., where it is possible that orders arrive in a different sequence to that in which they were issued due to high stochastic lead time fluctuations. This may be the case whenever sequentially placed orders are processed on parallel replenishment systems with independent stochastic processing times, and multiple orders may be open at the same time. Following the widespread tendency in the manufacturing industry to reduce order sizes and thus increase order frequency while parts and materials are replenished from distant sources, these conditions are nowadays met in many real-world processes. Such systems typically use regular order intervals, e.g. to enable joint replenishment of various item positions. In this paper, the concept of effective lead times is elaborated as a methodological basis for analyzing periodic replenishment processes that may exhibit order crossover. It is compared with the existing concept of outstanding orders. Based on this, formulae are developed to give an exact analysis of three essential performance indicators of a periodic-review order-up-to inventory system with independent stochastic lead times.