IQR CUSUM charts: an efficient approach for monitoring variations in aquatic toxicity

Toxicant testing is a major component of the environmental solution testing program. This test system aims to evaluate the sensitivity of the test species, evaluate comparability between laboratory test results, and classify possible variability sources such as healthy organisms, organism batches, laboratory water, and food quality changes. For the continuous assessment of sensitivity and accuracy of laboratory toxicity tests, control charts are often used. The cumulative sum (CUSUM) charting structure is a popular monitoring tool that is often used due to its outstanding ability in recognizing small-to-moderate unusual changes in process parameters. The CUSUM control charts have now been widely accepted/applied for monitoring the process dispersion under the assumption that the process does not have outliers. In practice, most of the processes have outliers. Therefore, the use of the interquartile range (IQR) as a plotting statistic is an attractive choice for dispersion monitoring. Hence, in this study, the CUSUM control chart with auxiliary information-based IQR estimators is proposed and employed to monitor dispersion or variation in the variable LC₅₀ by using quantitative structure–activity relationship (QSAR) aquatic toxicity data set. The proposed IQR-CUSUM charts are compared to its counterparts by using a variety of main output run-length functions, such as average run length (ARL), standard deviation of run length (SDRL), and extra quadratic loss (EQL), derived from the distribution of run-length. Further, results revealed that the proposed CUSUM charts have better detection ability as compared to existing counterpart charts, both in theoretical and practical considerations.