Estimation of Nonstationary Process Variance in Multistage Manufacturing Processes Using a Model-Based Observer

In this paper, we propose a recursive algorithm to estimate the process variance in multistage manufacturing or assembly processes. We use a replicated model that includes the process variance to be estimated as a time-varying state that changes slowly. For this model, we develop an estimation strategy including tuning parameters that play a direct role in the tradeoff between the estimation accuracy and the adaptation to changes. We also develop a statistical confidence interval for the estimations which enhances the decision of whether the process variances have changed. Unlike other batch methods in the literature, our proposal is computed recursively, and it allows us to tune the tradeoff between the convergence speed and the accuracy without modifying the sample size, which only contains the data of the last manufactured piece.
Note to Practitioners
—Variation reduction appears as the key to succeed in improving product quality, which is a major asset in manufacturing. To achieve variation reduction, it is necessary to quickly identify the root causes, which are responsible for these variations. The state of the art in root cause analysis is based on a stationary point of view, where the estimations regarding the mean and variance of the variation sources are based on the sample provided by a batch of multiple manufactured pieces. This paper focuses on the development of an online estimation strategy, which recursively updates the estimation of the variance of the variation sources with the data provided by the last manufactured piece in order to enhance a rapid decision of whether any fault has occurred in the process at the same time of reducing the computational cost and the data storage needs. We present a design strategy of the estimation algorithm, which sets the tradeoff between the accuracy of the estimations and their capability of tracking changes through two well-known physically meaningful engineering parameters: the cumulative squared error under abrupt changes and the variance of the estimations. Two detailed cases of study illustrate the effectiveness of this method. The strategy presented in this paper represents a novel approach for dealing with quality-control online algorithms and it can be used for the quality improvement of multistage manufacturing processes.