A study of EWMA chart with transformed exponential data

Abstract

The exponentially weighted moving average (EWMA) chart has been shown to be effective in detecting small process shifts and predicting the process level at the next time period. In this paper, a new EWMA chart is proposed to monitor exponentially-distributed time-between-events (TBE) data. The proposed EWMA chart is set up after transforming the TBE data to approximate normal using the double square root (SQRT) transformation. The average run length (ARL) properties of an EWMA chart with transformed exponential data are investigated based on which design procedures are developed. Subsequently, the performance of the EWMA chart with transformed exponential data is compared to that of the X-MR chart, the cumulative quantity control (CQC) chart and the exponential EWMA chart. Furthermore, the robustness of the proposed EWMA chart to Weibull-distributed TBE data is examined, followed by an example to illustrate the design and application procedures. The EWMA chart with transformed exponential data performs well in monitoring exponentially-distributed TBE data.

Keywords:

• EWMA
• Time-between-events
• Transformation
• Average Run Length
• Exponential
• Weibull