Parameter and Tolerance Economic Design for Multivariate Quality Characteristics Based on the Modified Process Capability Index with Individual Observations

The process capability index (PCI) is widely used in an on-line quality control stage for measuring and controlling the quality level of a production process. The calculation of PCI requires a large number of samples, but in the off-line quality control stage, a certain production process in off-line quality control stage only has a few individual observations. From the perspective of quality loss and tolerance cost, this paper proposes a parameter and tolerance economic design approach for multivariate quality characteristics based on the modified PCI with individual observations. The response surface models of mean and variance are constructed using individual observations, and exponential models are fitted according to the tolerance cost data of design variables. A modified PCI is proposed with the consideration of three types of quality characteristics. The optimal design variables and tolerances are obtained by a comprehensive optimization model that is constructed based on the proposed PCI. An example of an isobutylene-isoprene rubber (IIR) inner tube is used to (i) demonstrate the implementation of our proposed approach, (ii) improve the PCI value and reflect the sensitivity of the deviation between process mean and specification, and (iii) reduce the risk of increasing cost of quality caused by replicated experimental design and some other unknown reasons.