ISO/DIS 7870 has presented the cumulative sum chart, the moving average chart, and the exponentially weighted moving average chart as control charts using accumulated data. In this paper, we compare the three control charts in terms of change‐point estimation. We show the probability distribution, the bias and the mean square error of the change‐point estimators using a Markov process and Monte Carlo simulation. These control charts have almost equivalent performances based on average run length considerations when parameters of each control chart are set appropriately. However, from the viewpoint of change‐point estimation we recommend the CUSUM chart.
In this article, we explain how to obtain data by sampling and implement statistical process control (SPC) over its life cycle. The SPC life cycle consists of three steps: mass production preparation, early‐stage mass production, and routine mass production. In mass production preparation, machine performance is ensured by sampling according to an experimental design. In mass production stage, by sampling in control charts, process variation is reduced and process capability is ensured. Sampling to prevent the escape of a nonconforming product in routine mass production is also explained. In addition, considering semiconductor wafer process, the inherent process variation related to sampling is introduced.
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