Combined Shewhart-EWMA and Shewhart-CUSUM schemes for monitoring the ratio of two normal variables

Abstract

As a measure of quality characteristics, the ratio of two normal random variables (RZ) has been adopted to be monitored by different schemes. As has been shown in some existing works, the CUSUM-RZ and EWMA-RZ schemes operate well in detecting small and medium changes. On the other hand, the Shewhart-RZ scheme performs well in detecting large changes. However, practically, a variety of changes may occur in processes. To improve the sensitivity of these existing RZ schemes to different sizes of change, the combined RZ monitoring schemes are proposed. Using the Monte Carlo simulation, the statistical property of the constructed schemes is simulated. A detailed comparison is made between the existing Shewhart-RZ, CUSUM-RZ, EWMA-RZ and the developed combined RZ schemes. The results reveal the excellent performance of combined RZ schemes. For practical implementation, the benefits of the proposed charts applied to the food industry are shown in an example.

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