In many manufacturing processes, production takes place in more than one stream, with the objective of increasing the production in order to meet the demands of the consumers for the products. The lots or batches of finished products that can be constructed by grouping the products manufactured from various streams are generally heterogeneous (non-homogeneous) in nature. In such a situation, the lot quality might vary as a result of the machines used, the skill of working personnel, and the raw materials, and existing sampling plans are not suitable or viable for carrying out inspection activity in sentencing such lots. When the inspection lots are non-homogeneous, a finite mixture distribution is an appropriate probability model for determining the quality variation of the product. In this paper, the design of single’ sampling plans by attributes under a mixture of two Poisson distributions is considered under the assumption that the products are manufactured in two independent streams. Tables providing plan parameters protecting the interests of the producer and the consumer for specified strengths are presented. The risk efficiency of Poisson bi-mixture plans relative to Poisson sampling plans is studied. The selection of plan parameters is illustrated.