MODELING MICROBIOLOGICAL COUNTS IN PURIFIED WATER AT A HEALTHCARE FACILITY USING ARIMA

The microbiological quality of purified water is a crucial aspect in the healthcare industry to ensure safety for different applications and uses. Understanding the trend and forecasting would be of prime importance to take proactive control and protective measures before catastrophic excursions might occur leading financial and health casualties. This study analyzes microbial density, a key metric for monitoring water purification system efficacy in healthcare facilities. The objective was to transform irregular, cumulative data into a regular time series and identify the optimal ARIMA model for forecasting to support predictive maintenance and regulatory compliance. Preliminary modeling attempts were conducted using simpler approaches such as linear, exponential and Holt-Winters methods without showing promising outcomes. Descriptive statistics and distribution analysis, including the Johnson Transformation for normality, were performed. ARIMA models with differencing orders d=0, d=1, and d=2 were fitted to the Aggregated cumulative logarithmically transformed data series, with the best model at each order selected based on minimum AICc. Model adequacy was assessed through parameter significance and residual diagnostics (Ljung-Box test). Descriptive statistics showed the aggregated series non-normal (p<0.005). ARIMA(5, 0, 4) (d=0) performed poorly (AICc=319.39) with residual autocorrelation. ARIMA(0, 2, 1) (d=2) showed improved fit (AICc=258.98) and white noise residuals (p>0.5). The ARIMA(2, 1, 2) model (d=1) was optimal (AICc=256.91), with all significant parameters and white noise residuals (p>0.3), effectively addressing non-stationarity. Forecasts from ARIMA(2, 1, 2) predict stable future growth. The ARIMA(2, 1, 2) model with first-order differencing is the most appropriate and robust model for forecasting data trends. Its strong statistical fit and reliable residual properties make it a valuable tool for predictive maintenance, optimizing resources, and enhancing patient safety in healthcare water systems, provided model performance is continuously monitored. Addressing data limitations and processing requires monitoring and exploring alternative models for future improvement.