Error equivalence concerns the mechanism whereby different error sources result in identical deviation and variation patterns on part features. This could have dual effects on process variation reduction: it significantly increases the complexity of root cause diagnosis in process control, and provides an opportunity to use one error source as based error to compensate the others. There are fruitful research accomplishments on establishing error equivalence methodology, such as error equivalence modeling, and an error compensating error strategy. However, no work has been done on developing an efficient process design approach by investigating error equivalence. Furthermore, besides the process mean shift, process fault also manifests itself as variation increase. In this regard, studying variation equivalence may help to improve the root cause identification approach. This thesis presents engineering driven approaches for process design and control via embedding error equivalence mechanisms to achieve a better, insightful understanding and control of manufacturing processes. The first issue to be studied is manufacturing process design and optimization based on the error equivalence. Using the error prediction model that transforms different types of errors to the equivalent amount of one base error, the research derives a novel process tolerance stackup model allowing tolerance synthesis to be conducted. Design of computer experiments is introduced to assist the process design optimization. Secondly, diagnosis of multiple variation sources under error equivalence is conducted. This allows for exploration and study of the possible equivalent variation patterns among multiple error sources and the construction of the library of equivalent covariance matrices. Based on the equivalent variation patterns library, this thesis presents an excitation-response path orientation approach to improve the process variation sources identification under variation equivalence. The results show that error equivalence mechanism can significantly reduce design space and release us from considerable symbol computation load, thus improve process design. Moreover, by studying the variation equivalence mechanism, we can improve the process diagnosis and root cause identification.