Thinking Abnormally: A New Way to Look at RO Data

1. APPLICABILITY
Potable reuse requires pathogens removal by many orders of magnitude (log reduction values or LRVs). Intact reverse osmosis (RO) removes pathogens by over 99.999% (5 LRVs). However, this removal is challenging to verify in real-time. Total organic carbon (TOC) or electrical conductivity (EC) are measured with sensors in the RO feed and permeate. Pathogen LRVs are assumed to be equal to or greater than these surrogates because of their larger size compared to the molecules that constitute TOC and EC. However, even a slight error in the permeate sensor results in a low outlier in the calculated LRV.

Giving treatment processes the pathogen LRV credit they merit is becoming increasingly important for reuse. In December 2023, California finalized direct potable reuse (DPR) rules requiring 20 LRVs of virus, 14 LRVs of Giardia, and 15 LRVs of Cryptosporidium. These LRVs are much higher than the 12/10/10 rule for indirect potable reuse. The California DPR Rules require monitoring continuous surrogate(s) that would have alarms when the RO integrity is compromised. However, the statistical trigger for these alarms is not specified.

Nonetheless, both conventional (e.g., TOC) and innovative (e.g., strontium) surrogates have intermittent erroneous outliers. This raises the question of how to best set alarms that balance the need for prompt response while avoiding false alarms that lead to unnecessary downtime. Common approaches for setting alarms assume the data are normally distributed (i.e., a symmetrical bell curve). However, for even moderately skewed data, this assumption results in more false alarms than expected.

The objective of this study was to evaluate a new statistical method for monitoring RO LRV surrogates that would (1) be valid for non-normal data, (2) result in at least 50% faster event detection than methods like daily direct integrity testing, and (3) cause at least 50% fewer false alarms than triggering based on single points. The technique assessed was a Shewhart sign chart. While analyzed in the context of RO, this mathematical approach would also be valid and promising for monitoring other non-normal variables in wastewater and reuse.

2. DEMONSTRATED RESULTS AND OUTCOMES
2.1 Methodology
The Shewhart sign chart is an advanced statistical monitoring technique that tests whether the median has likely dropped below a target value. Unlike the conventional Shewhart control chart, the Shewhart sign chart does not assume normality. Rather, it treats each datapoint like a 'coin flip' that is either above or below a hypothesized level. This approach treats large outliers no differently than a slight exceedance, but nonetheless triggers if exceedances repeat.

We first investigated the statistical distribution of RO LRV surrogate variables at two reuse systems: the Orange County Water District (OCWD) Groundwater Replenishment System (GWRS) and the Las Virgenes Municipal Water District (LVMWD) Pure Water Demo. Variables included the conventional RO monitoring surrogates TOC and EC, as well as promising emerging surrogates free ATP, Peak C fluorescence, and various elements including calcium, strontium, and sulfur. For non-normally distributed surrogates, we next investigated what averaging window might result in a normal distribution of means considering the Central Limit Theorem. Finally, we applied a Shewhart sign chart as a method for monitoring LRV surrogates for meaningful changes without assuming normality. Analyses were conducted in R using open-source packages.

2.2 Result
Preliminary analysis confirmed that RO LRV surrogate data was rarely normally distributed, with a possible exception of ATP. Variables such as calcium, strontium, TOC, and EC were highly skewed, and sulfur was bimodal (Figure 1). These variables remained skewed even when averaged over 12 hours.

Set to a window of the past 12 measurements, the Shewhart sign chart would detect true RO events in three measurements (i.e., in three hours with hourly data). At the same time, for all surrogates evaluated except for Peak C, the Shewhart sign chart resulted in half or less as many alarms compared to alarms on single points (Table 1). Figure 2 illustrates how this alarm approach did not trigger for single, non-consecutive outliers, but did trigger when LRV surrogates remained below their target value.

2.3 Conclusions/Outcomes
Overall, this study demonstrated that most RO LRV monitoring data is not normally distributed, thus the commonly applied statistical assumption of normality inherent to certain statistical approaches should not be assumed without thorough justification. Non-parametric statistics such as the sign test are applicable to non-normal data. Real-time data from conventional or novel sensors paired with Shewhart sign charts can strike the balance of detecting events more promptly than daily testing while avoiding excessive false alarms or invalid statistical assumptions. Based on the promising desktop results, OCWD has been implementing this control chart on full-scale RO in real-time with a cloud-based dashboard since July 2024.

3. RELEVANCE TO AUDIENCE This presentation will show how the Shewhart sign chart was applied and how this approach could be used by utilities implementing RO for reuse or monitoring other non-normal data. The presentation will also show has this approach can be implemented at scale in real-time using low-cost equipment and opensource software.