System reliability evaluation for simultaneous production of orders with varying tolerances

Manufacturers may simultaneously receive orders for a product from different customers, each with varying tolerances for key quality characteristics (KQCs) based on cost and quality considerations. However, previous studies on system reliability evaluation typically classify products as conforming and non-conforming based on a fixed tolerance of each quality characteristic. In order to involve the simultaneous production of a product with multiple tolerances for a specific KQC that significantly impacts its subsequent application, products are classified into conforming grades to determine which specifications meet the KQC tolerances required by the orders. The manufacturing system is first modeled as a multistate flow network (MFN), where nodes represent buffers or quality inspection stations, and arcs represent workstations with identical machines. Each workstation has a multistate capacity depending on the number of malfunctioning or under-maintained machines. Then, a novel algorithm is proposed to calculate the system reliability, the probability that the manufacturing system can fulfill the demands for all grades derived from the orders. Results from numerical experiments provide valuable insights for decision-making in order acceptance and offer a comprehensive assessment of the quality improvements needed to achieve the desired system reliability.