Statistical analysis of total process capability index in two-stage processes with measurement errors

The manufacturing processes often involve multistage processes where the process capability of each stage is affected by the process capability of its previous stages. This property is known as cascade property. Therefore, the measured process capability indices in each stage represent the total capability of that stage. In the multistage processes two kinds of process capability index are defined in each stage of the multistage processes as follows: total process capability index and specific process capability index. The process capability indices are proposed under the assumption that there are no measurement errors. However, sometimes in the real application, this assumption is violated. The measurement errors affect the process capability indices significantly. In this paper, the effect of measurement errors on the total process capability index in the second stage of two-stage processes is statistically analyzed.