Generalized Inference for Measuring Process Yield With the Contamination of Measurement Errors—Quality Control for Silicon Wafer Manufacturing Processes in the Semiconductor Industry

The yield index
S
_pk
provides an exact measure of process yield for normally distributed processes, and it has been popularly accepted by many engineers and shop floor controllers as communication tools for evaluating and improving the manufacturing quality. Most research works related to
S
_pk
are carried out under the assumption of no gauge measurement errors. Unfortunately, such an assumption does not accommodate real situations closely even with modern and highly sophisticated measuring instruments. Conclusions drawn from process capability analysis without considering measurement errors are hence unreliable. Recently, Wang studied the impact of the process yield estimation and judgment on the true process yield in the presence of measurement errors and indicated that the presence of measurement errors in the data leads to different behaviors of the estimator according to the entity of the contamination degree. To remedy this, this paper applies the concept of generalized pivotal quantities to construct generalized confidence intervals for
S
_pk
with consideration of measurement errors. A series of simulations was undertaken to evaluate the performance of the proposed generalized inference method. The results reveal that the generalized inference method performs very well for measuring process yield in the presence of measurement errors.