Construction of Capacity Indices for the Analysis and Evaluation of Processes with Multiple Responses
Abstract
Currently manufactured products have several quality characteristics, all of which are important to the customer, and controlling and evaluating them has become an activity of prime interest. The automotive industry establishes capacity indices to evaluate the capacity of processes where there is only one response variable, and when these are stable, it recommends using Cp and Cpk as measures of the capacity of the manufacturing process to manufacture products that comply with specifications and are cataloged as quality products. To evaluate the complete quality of a product, which depends on meeting several quality characteristics simultaneously, there are proposals in the literature on how to measure the capability of multivariate processes; most of these agree that a specification region should be clearly established to represent the customer's requirements and another region to show the variation as a measure of process performance. In the definition of both regions there is a great controversy among the authors, which leads to present this new proposal, by which these two regions are defined in a reliable way, and by making a comparison between them, the multivariate capacity indexes Cpm and Cpkm can be obtained as an extension of the univariate indexes Cp and Cpk. The document includes the data analysis of a process where the product to be of good quality must meet two quality characteristics simultaneously. The measurements obtained from the process can be represented by a multivariate normal distribution, which allows measuring the process capability using the proposed indexes and interpreting them in relation to the process performance.
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