Process capability analysis for multivariate simple linear profiles in a multistage process

Process capability indices (PCIs) are developed to assess process performance based on the specification limits (SLs) provided by customer. Sometimes the quality of a process or product is characterized by a regression relationship between a response variable and one or more independent variables referred to as "profile". On the other hand, modern production systems often involve multistage manufacturing processes, in which the output of one stage is the input of the next stage. This property is known as the cascade property. Due to this property, the capability in each stage is dependent on the capability of the preceding stages. This study provides an approach to assess PCIs in a multistage process when the quality characteristics of interest are represented by multivariate linear profiles. Process performance is specified based on profile intercept and slope parameters. In other word, in addition to PCIs of the response variable in each stage, the PCIs of profile parameters are also investigated. By using the SLs of the response variable and considering in-control profile, the SLs for intercept and slope can be obtained. Therefore, PCIs for profile parameters can be computed. The results indicate that the proposed method eliminates the effect of the cascade property for different autocorrelation values. Simulation results reveal satisfactory performance of the proposed method for a two-stage process.