An Exponentially Weighted Moving Average Control Chart for Bernoulli Data

摘要

We consider a production process in which units are produced in a sequential manner. The units can,,for example, be manufactured items or services, provided to clients. Each unit produced can be a failure with probability p or a success (non-failure) with probability (1-p). A novel exponentially weighted moving average (EWMA) control chart intended for surveillance of the probability of failure, p, is described. The chart is based on counting the number of non-failures produced between failures in combination with a variance-stabilizing transformation. The distribution function of the transformation is given and its limit for small values of p is derived. Control of high yield processes is discussed and the chart is shown to perform very well in comparison with both the most common alternative EWMA chart and the CUSUM chart. The construction and the use of the proposed EWMA chart are described and a practical example is given. It is demonstrated how the method communicates the current failure probability in a direct and interpretable way, which makes it well suited for surveillance of a great variety of activities in industry or in the service sector such as in hospitals, for example.