Stream-of-Variation (SoV)-Based Measurement Scheme Analysis in Multistation Machining Systems

Today, machining systems are complex multistation manufacturing systems that involve a large number of machining operations and several locating datum changes. Dimensional errors introduced at each machining operation get transformed and cause the occurrence of new errors as the workpiece propagates through the machining system. The appropriate choice of measurements in such a complex system is crucial for the subsequent successful identification of the root causes of machining errors hidden in dimensional measurements of the workpiece. In order to facilitate this measurement selection process, methods for quantitative characterization of measurement schemes must be developed. This problem of quantitative measurement characterization referred to as the measurement scheme analysis problem is dealt with in this paper. The measurement scheme analysis is accomplished through characterization of the maximal achievable accuracy of estimation of process-level parameters based on the measurements in a given measurement scheme. The stream of variation methodology is employed to establish a connection between the process-level parameters and measured product quality. Both the Bayesian and non-Bayesian assumptions in the estimation are considered and several analytical properties are derived. The properties of the newly derived measurement scheme analysis methods are demonstrated in measurement scheme characterization in the multistation machining system used for machining of an automotive cylinder head. Note to Practitioners-Techniques for the measurement scheme analysis presented in this paper enable one to formally and systematically evaluate the amount of information content a given combination of measurements carries about the process-level faults that cause quality problems in machining. Such techniques can be used to optimally select measurements that are the most informative about the machining process before a machining line is even built. Since the basis of the measurement scheme analysis methods presented in this paper is the model of the flow of machining errors referred to as the stream-of-variation (SoV) model, which can currently model only the influence of fixture and tool path parameter errors on the workpiece quality, the results presented in this paper only evaluate the amount of information about those error sources. However, as improvements to the SoV models are made in the future, the measurement scheme analysis methods and their properties demonstrated in this paper will remain valid as long as the newly obtained modes are in the linear state-space form possessed by the existing SoV models