Quality evaluation plan using adaptive Kalman filtering

An important function of the Bell Laboratories Quality Assurance Center and the Western Electric Quality Assurance Directorate is to audit the quality of the products manufactured and the services provided by the Western Electric Company to determine if the intended quality standards are met. Until the sixth period of 1980, the t-rate system was used to make inference on the product quality. Starting the seventh period of 1980, the Quality Measurement Plan (QMP) has been implemented. The QMP is based on an empirical Bayes model of the audit-sampling process using the current and the preceding five periods of data. Because it ignores the time order of the data, it is slow in responding to drifts in the process mean. The Quality Evaluation Plan (QEP) has been designed to take into account the time order of the data and to be more sensitive to drifts in the process mean. In this paper we present the Quality Evaluation Plan, which uses the entire time series of data on a given product to determine if that product meets the quality standard. The time series is modeled by a stochastic process, which allows for the possibility that the process mean may drift or fluctuate around a fixed value. An adaptive Kalman filtering theory is developed for filtering out the sampling variance and obtaining the best estimate of the true defect index and its confidence interval. Thus, in QEP the best estimate of the true defect index is obtained by a combination of adaptive exponential smoothing and shrinkage to the mean. The QEP computations are recursive, and the total computing efforts of QEP and QMP are roughly equal. The paper contains several examples to illustrate the QEP.