AbstractApparent water losses can be problematic to water companies’ revenues. This type of loss is very difficult to detect and quantify and is often associated with water meter anomalies. This study was motivated by a water company’s challenge that links a decrease in water consumption to water meters’ malfunction. The aim is to develop a strategy to detect decreasing water usage patterns, contributing to meter performance assessment. The basis of the approach is a combination of statistical methods. First, the time series of billed water consumption is decomposed using Seasonal-Trend decomposition based on Loess. Next, breakpoint analysis is performed on the seasonally adjusted time series. After that, the Mann–Kendall test and Sen’s slope estimator are used to analyze periods of progressive decrease changes in water consumption, defined by breakpoints. A quantitative indicator of this change is proposed. The strategy was successfully applied to eight-time series of water consumption from the Algarve, Portugal.IntroductionA recurring problem that troubles water companies is that of timely detection of malfunctioning water meters. Indeed, defective water meters impair the management of water supply and diminish water companies’ revenues. The management of nonrevenue water (NRW) is one key issue for improving water use efficiency, reducing gaps between water supply and demand (Ncube and Taigbenu 2019). Water losses in the distribution system can be categorized as either real (leakage) or apparent (commercial) losses (Mutikanga et al. 2011). Water meter under-registration resulted in apparent losses and lost revenue (Moahloli et al. 2019; Fourie et al. 2020), being apparent losses one of the components of NRW. As Criminisi et al. (2009) explain, apparent losses are caused by unauthorized consumption and meter inaccuracies, corresponding not to physical but rather to financial losses. Since they are water volumes taken from the network and consumed but not accounted for, as a consequence, the company will be jeopardized by the unaccounted water volume, resulting in an important impact on the utility’s water and economic balances.A long-known fact is that reducing apparent losses caused by meter inaccuracies can result in substantial short-term increases in utility revenue and lead to increasingly equitable service charges for long-term water consumers (Richards et al. 2010; Kadenge et al. 2020). The accurate measurement of the water collected by meters is crucial in reducing any uncertainty affecting the water balance and has significant technical and economic implications (Pacheco et al. 2020). A cubic meter consumed but not measured reduces the company revenue in quantity equal to the selling price of the last cubic meter of water consumed by that consumer (Arregui et al. 2018).The water companies’ awareness for the responsible use of water has gained importance, with climate changes emphasizing this need. In the context of water scarcity, Oviedo-Ocaña et al. (2020) alert to the importance of assessing losses in water distribution systems since the compensation of water losses represents an increase in the source’s water supply. Enhancing that water use efficiency and conservation are priority alternatives to ensure, for example, universal access to drinking water and reducing the number of people suffering from water scarcity. Furthermore, Pacheco et al. (2020) emphasize that water measurement will become an even more critical aspect in the near future because of the increase in the world’s water supplies due to population growth. In this context, one form of water companies to be aware of its important role is to steer the effective water consumption and guarantee an efficient manutention of its equipment, namely the water meters.Current research confirms that several factors affect a water meter’s accuracy, particularly water meterage and total registered volume (Moahloli et al. 2019; Pacheco et al. 2020). Detecting the point in time in which water meters should be replaced implies that they can be substituted proactively to minimize the impact of water consumption nonregistration and under-registration on NRW (Moahloli et al. 2019). There seems to be no specific determination and/or agreement on a water meter lifespan or optimal replacement period. Water meter producers only give a limited warranty against manufacturing defects but do not specify the meters’ lifetime (Moahloli et al. 2019). It is believed that the premature replacement of water meters will result in a higher average life-cycle cost due to the initial fixed costs. However, if a meter is replaced too late, a significant loss of revenue caused by meter nonregistration and under-registration will also increase the average life-cycle cost (Fontanazza et al. 2015). The main studies on this problem have adopted approaches based on laboratory studies, which may implicate two significant issues: (1) the high costs inherent to the laboratory, and (2) the conditions in which the tests are taken upon are far from the real scenario. As Moahloli et al. (2019) recently identified, several methods can be used to determine water meter accuracy, such as laboratory testing or installing a master meter in series to the meter on the ground and the net present value analysis. However, although accurate, the authors also indicate that the first two methods tend to be expensive and time-consuming. Malfunctioning water meters impair water supply management and diminish water companies’ earnings, justifying the need for a detailed data analysis of water consumption.Past research on water consumption in Portugal has shown that the Algarve region has the highest value (Reynaud 2015). The official statistics on water distributed/consumed per inhabitant for 2017 [from FEMS (2021)] reveal higher values for this region. The awareness toward the responsible use of water has increased significantly and, in recent years, periods of drought attributed to climate change emphasized that need. Aware of this problem, water utilities such as Infraquinta and the Loulé Municipality feel the need to improve and develop mechanisms for predictive water planning based on data analysis. In particular, a mechanism able to detect abnormal decreasing trends in water consumption, which they believe is associated with a possible water meter malfunction.This paper aims to develop a procedure capable of detecting decreasing water consumption changes, contributing to meter performance assessment. The decrease in water consumption (progressive or sudden) is, as explained by Monedero et al. (2016), associated with water meter malfunction—one of the possible causes for apparent losses. Thus, it should be investigated by water utilities in order to mitigate this type of loss. The proposed approach intends to contribute and provide a helpful tool for the water utilities within decision analysis on water meter replacement. The strategy developed uses several statistical methods to detect significant decreases (changes) in water consumption after removing the seasonal pattern.In this case study, an empirical analysis of billed water consumption data from seven households and a hotel from the Algarve, Portugal, was performed. Analyzing data on the real conditions on which the water meters operate should provide more precise results than those obtained through laboratory analysis. Time series decomposition is frequently used in many areas, such as in electricity consumption to evaluate electrical meter data [e.g., Miller and Meggers (2017) and Miller (2019)], in hydrological studies to understand groundwater behavior [e.g., Lafare et al. (2016)], and to predict or detect changes in water consumption [e.g., Ohana-Levi et al. (2020), Quesnel and Ajami (2017), Hester and Larson (2016), and Gelažanskas and Gamage (2015)]. Seasonal-Trend Decomposition of time series based on Loess [(Seasonal-Trend decomposition by Loess (STL)] (Cleveland et al. 1990) has been successfully used in studies of water consumption (Hester and Larson 2016). Researchers often use the STL default smoothing parameters because specifying these parameters can be subjective rather than objective. To overcome this issue, the procedure (Cristina et al. 2016) is used to obtain a more accurate decomposition based on the error measure mean absolute error (MAE).In the context of water consumption analysis, some recent studies have adopted the methodology of time series decomposition and breakpoint detection, such as Quesnel and Ajami (2017) and Hester and Larson (2016). The latter points out that decomposition methods have been applied in several hydrological studies, and structural change models have been used in water quality. Also, the opinion of these authors is that the breakpoint analysis appears underutilized in water management. Therefore, the procedure developed in this case study uses breakpoint analysis (Zeileis et al. 2003) to find points in time at which statistical patterns change after the seasonal pattern was removed. These breakpoints are associated with segments where the increases or decreases of the trend are more pronounced. Furthermore, two new formulas estimate the maximum number of breakpoints and the minimum number of observations in a segment.In the analysis of hydrological and meteorological variables, (Gocic and Trajkovic 2013) and (Sharma et al. 2016) conclude that there is an interaction between trends and breakpoints. The significance of the trend and its decreasing rate are analyzed through Mann–Kendall testing [Mann (1945) and Kendall (1975)] and Sen’s Slope (Sen 1968). The negative slope means that there is a decrease in water consumption. The water company must investigate this situation because it could be related to an anomaly in the water meter, and it might be the ideal time to replace it. A water consumption indicator named relative magnitude of the change (RMC) is proposed to provide some guidance in this decision analysis. The idea is to quantify the change of the decrease in water consumption for each consumer and identify which ones the water company should investigate.The paper is organized as follows: the first section presents a brief description of the problem and the dataset analyzed. The next section explains the methodologies applied, followed by a description of the water consumption analysis’s main results on a case study of seven households and one hotel, ending with the discussion and conclusion and future work.MethodologiesIn this section, the methods that constitute the strategy proposed are described in detail.STL DecompositionA time series is a sequence of observations indexed by time t, t=1,…,n, usually ordered in equally spaced intervals. Often, time series exhibit seasonal behavior and adequate control for a seasonal component is essential before using any statistical model. Let consider that a time series is a combination of three components: trend-cycle, which represents an upward or downward movement over the time horizon; seasonality, which is a repetitive pattern over time; and the irregular, which is remaining after the other components have been removed (Hyndman and Athanasopoulos 2018). Both trend and seasonality components are potential confounding features in analysis, so their identification and removal are important. Additionally, this characteristic impacts the computation of the trend-cycle term Tt that bears the time series’s interannual variations but excluding possible variations related to interannual changes in seasonality.Seasonal-Trend Decomposition of time series based on Loess (STL) is used to decompose the time series {Yt,t=1,…,n} into a trend (Tt), seasonal (St), and irregular (It) components using nonparametric regression and is described as (1) STL was chosen over other decomposition methods in the literature because it has attractive modeling features. Such as a nonlinear trend component, the seasonal component is allowed to change over time and is robust in the presence of outliers. Note that these observations are problematic since it influences the estimation of parameters (e.g., in ARIMA models) that will mislead any statistical conclusion. STL is an iterative nonparametric procedure that repeatedly uses a Loess smoother to refine and improve estimates of the trend and seasonal components [see Cleveland et al. (1990) for more details]. In common with all nonparametric regression methods, STL requires the subjective selection of smoothing parameters. The two main parameters are the seasonal (s.window) and trend (t.window) window widths. The Loess smoothing parameters must be defined in advance and set according to the user’s knowledge about the data or as default values. The function stl() (R Core Team 2021) is commonly used setting by default the s.window parameter as periodic. The algorithm proposed in Cristina et al. (2016), (Cordeiro 2016), overcomes this drawback. It performs an automatic selection of the smoothing parameters based on minimizing an error measure, obtained through the function accuracy() in package forecast (Hyndman et al. 2021). The algorithm selects the best STL model, which has the smallest error measure achieved with a specific combination of s.window and t.window.The root mean square error is an error measure widely used to access the model performance and predictability. However, its sensitivity to extreme observations and outliers can mislead data analysis. The MAE is the error measure chosen to be used in this work because it is less sensitive to outliers (Hyndman and Koehler 2006) when compared with the root mean square error, and it presents several advantages as explained in Willmott and Matsuura (2005). In the forthcoming analysis, the seasonally adjusted time series (2) t=1,…,n, is considered.Detect Structural ChangesSome structural disturbances can be observed in the dynamic structure of the time series. Is important to stay alert for breakpoints, points in time at which statistical patterns change, as they represent periods of the time horizon where the increases or decreases of the trend are more pronounced. The R package strucchange (Zeileis et al. 2002) is used to detect structural breaks to test for structural changes in linear regression models, estimating the number of segments (m) and the set of the breakpoints bp={t1*,t2*,…,tm−1*}, minimizing the Bayesian information criterion (BIC) and the residual sum of squares (RSS) (Zeileis et al. 2003). Additionally, this procedure has a bandwidth parameter (h) that determines the minimal segment size (h×n observations). In function breakpoints() (Zeileis et al. 2002) the default bandwidth parameter is h=0.15 but, it is up to the user to change h to a more suitable value based on the knowledge of the data. For example, Verbesselt et al. (2010) use a minimum of 12% of data (23 observations) for a nine-year time horizon; in Awty-Carroll et al. (2019), this minimum was two years (46 observations); and in Hester and Larson (2016), the minimum was three years (36 observations). In line with the previous references, the present study contributes with two new expressions for obtaining the minimum length between consecutive breaks (3) and the maximum number of breaks (4) where n = length of the time series and frequency is the seasonal pattern’s length.Detect Decreasing TrendsResearch on an increasing or decreasing trend in time series is an important issue. It is usually based on the parametric test for the linear model and in the Mann–Kendall (MK) test [Mann (1945) and Kendall (1975)] as a nonparametric counterpart. The test takes Kendall’s Tau coefficient to assess the correlation between the variable of interest and time. Related to MK’s rationale, Sen (1968) developed a nonparametric estimator for the slope of a linear trend in the sample of N pairs of data. The Theil–Sen (TS) slope provides the magnitude of the trend through a robust linear regression. Also, MK and TS are more flexible in the assumptions than parametric t-test, accommodate departures from normality, small sample sizes, and are robust in the presence of outliers [Helsel and Hirsch (2002)]. MK does not depend on the data range and can find a monotonous trend over nonlinear behavior. So, is well-suited for a trend estimated through STL. Also, it is possible to consider the autocorrelation by adjusting the variance of the test statistic when the assumption of independence fails. To investigate a decrease in the segments, MK and TS are applied on Y* and an estimate of the magnitude of the trend (or slope) is obtained. If the result points to a significant and negative trend, the breakpoint is relevant and is included in the new set bp*, where bp*⊆bp. This analysis is performed using the functions mk.test() and sens.slope(), available in the R package trend (Pohlert 2020).Relative Magnitude of the ChangeThe RMC is proposed to assess water consumption behavior change. It is calculated through a ratio that compares the consumption pattern before and after a breakpoint (see Fig. 1). The idea of RMC is in line with the same principle as in Gocic and Trajkovic (2013) and is defined by (5) RMC=slpafter−slpbefore|slpbefore|where slpafter and slpbefore = nonparametric Sen’s Slopes at a breakpoint tk*∈bp*. This unitless indicator measures the relative change, or the relative difference, between the slope after (slpafter) and the slope before (slpbefore) the breakpoint, in reference to the slope before the breakpoint. A negative value of RMC is an alert for a possible meter anomaly. The more negative is RMC, the higher is the reduction of water consumption after the considered breakpoint.Strategy OutlineThe idea behind the approach is the following:Step 1: Estimation of the seasonal component using by minimizing MAE and removing it;Step 2: Breakpoints analysis (bp) on y*;Step 3: Nonparametric trend analysis for analyzing significant decreases on the segments and selecting the “relevant” breakpoints (bp*);Step 4: RMC is calculated [Eq. (5)] for each breakpoint in bp*.The scheme of the strategy is shown in Fig. 1. In Step 1, the was chosen because it showed better performance than the “standard stl” (Cristina et al. 2016). Nevertheless, it is possible to use another decomposition method instead, e.g., classical decomposition. Step 2 uses the function breakpoints() (Zeileis et al. 2002) with h and breaks estimated by Eqs. (3) and (4), respectively. In the case of Step 3, a function that includes mk.test() (Pohlert 2020) was implemented by the authors in R. It considers bp and y* as input and bp* as output. Then, to obtain the RMC values using the TS slopes, another function was build by the authors. The new code was implemented in R version 4.1.0. The data, models, and code are available online (Cordeiro et al. 2020). Moreover, a significance level of α=5% is considered in the statistical analysis performed.Water Consumption AnalysisDatasetTo illustrate the procedure (Fig. 1), eight-time series of billed water consumption from the same region of the Algarve, Portugal, were used [available online (Cordeiro et al. 2020)]. The data were provided by the water company Infraquinta and Loulé Municipality and are described in the following: •Two locations: Quinta do Lago Resort, a well-known tourist destination for holidays; and a small rural village with less than 3,000 inhabitants, mainly retired and older people. Distance between locations is approximately 26 km;•Residential Household (RH): four monthly time series of water consumption, time horizon between January 2011 and December 2016 (nRH=72), from the village;•Nonresidential Household (NRH): three hourly time series of water consumption, time horizon between November 2013 and December 2018, from Quinta do Lago. However, the water companies are only concerned with the monthly levels of water consumption, so the hourly data were aggregated into monthly by taking the average of each month (nNRH=62);•Hotel: monthly time series of water usage with a time horizon from July 2006 until December 2016 (nHotel=120);•Smart meters collected the data of NRH and RH and Hotel by nonsmart meters.Fig. 2 shows water consumption variability in households and hotels. Most of the time series shows a seasonal pattern associated with the year’s season, increasing in the summer and decreasing during the winter.The hotel presents a strong seasonal pattern and a decreasing trend until 2014 that increases after mid-2014 (due to the water meter replacement in July 2014). There is also a clear seasonal effect in RH1, RH2, RH3, and NRH3. Concerning the trend of water consumption, RH2 and RH3 showed a downward. This pattern is also observed in smaller periods in the other time series. Moreover, the magnitude of volumes consumed is significantly different between the households and the hotel. In households (RH and NRH type), the water consumption range from 0 to 120  m3, while at the hotel, the consumption is higher, varying from 0 to 3,000  m3.Time Series DecompositionThe empirical analysis starts by deciding between a robust approach of STL or not. Outliers were detected by inspecting the weights associated with the residuals as in Cleveland et al. (1990). Next, for each time series, the procedure (Cristina et al. 2016; Cordeiro 2016) was applied and an object of class stl with components Tt, St, and It, as in Eq. (1), is returned. Measurements of error is an alternative way of conveying information about the model adjustment, and for that, the MAE was chosen. This accuracy measure has already been used in the context of water planning and management, e.g., Kandiah et al. (2016). The decomposition plots are shown in Fig. 3.Decreasing ChangesIn this subsection, the objective is to detect periods of changes in water usage patterns. The detection of breakpoints, which are points in time k at which statistical patterns change, are estimated on the seasonally adjusted water consumption, as in Eq. (2). The procedure tests for structural changes in linear regression models, considering the maximum number of breaks and the minimum length between breaks estimated using Eqs. (3) and (4), respectively. As a result, breaksRH=3 and hRH=0.17, breaksNRH=3 and hNRH=0.19, and breaksHotel=5 and hHotel=0.1 were obtained. After obtaining the breakpoints (bp, in Table 1), the MK test for analyzing trends was applied to each segment. If a decreasing segment is statistically significant (i.e., pvalue<0.05), the breakpoints are considered “relevant” and included in bp*, and its decreasing rate (Sen’s slope) is obtained (see Table 2). Fig. 4 presents the seasonally adjusted time series, breakpoints (bp), and relevant breakpoints (bp*, blue dashed line). The dashed grey line corresponds to a breakpoint with nonsignificant adjacent segments (slpbefore and slpafter), i.e., pvalue>0.05, or the water consumption is not decreasing. Table 2 contains the information about the date of the water meter replacement, bp*, TS slopes, and RMC [Eq. (5)].Table 1. Breakpoints & decreasing (trend) analysisTable 1. Breakpoints & decreasing (trend) analysisTypeBreakpoints (bp)Segment 1Segment 2Segment 3Segment 4Segment 5RH12012 (June)−0.50 (0.0064)−0.19 (<0.0001)———RH22012 (April), 2015 (December)0.01 (0.8926)−0.02 (0.3947)−0.26 (0.0002)——RH32014 (May)−0.01 (0.0671)−0.06 (0.0011)———RH42015 (November)0.01 (0.4026)−0.19 (<0.0001)———NRH12017 (June)−0.07(0.0099)0.12 (0.2629)———NRH22016 (December), 2017 (November)0.07 (0.0252)−0.11 (0.8370)−0.46 (0.0005)——NRH32016 (December), 2017 (November)0.01 (0.8015)6.58 (0.0075)−0.69 (0.0044)——Hotel2008 (February), 2013 (July)−6.14 (0.381)−2.59 (0.0006)−84.56 (0.0003)5.31 (0.5022)10.88 (0.1501)—2014 (July), 2015 (July)—————Table 2. RMC resultsTypeDate of meter replacementRelevant bp*TSa (slpbefore, slpafter)RMCaRH1b2008 (May)2012 (June)(−0.50, −0.19)0.62RH2b2010 (May)2015 (December)(−0.02, −0.26)−12.00RH3b2003 (November)2014 (May)(−0.01, −0.06)−5.00RH42012 (January)2015 (November)(0.01, −0.19)−20.00NRH12018 (June)2017 (June)(−0.07, 0.12)2.71NRH22018 (April)2017 (November)(−0.11, −0.46)−3.18NRH32018 (November)2017 (November)(6.58, −0.69)−1.10Hotel2014 (July)2008 (February), 2013 (July)(−6.14, −2.59), (−2.59, −84.56)0.58,−31.65——2014 (July)(−84.56, 5.31)1.06The residential household RH1 shows one relevant breakpoint detected in June 2012 (Table 2; Fig. 4). The water meter readings after the break are smaller than the first segment, and the magnitude of the trend (TS slope) is less negative (slpbefore=−0.50 versus slpafter=−0.19), with RMC=0.62, as seen in Table 2. Nonetheless, the trend continues negative after June 2012 with a significant slope, justifying an alert and further investigation by the water utility. Regarding the RH2, the global trend is decreasing (Figs. 2 and 3), and the structural break analysis identifies two breakpoints (Fig. 4). The decrease of the third segment is statistically significant (Table 1) and so the second breakpoint (December 2015) is relevant (Table 2). The RMC=−12 reveals that the downward trend (December 2015–December 2016) is more pronounced in magnitude compared to the previous segment (April 2012–December 2015). Since the consumption is decreasing, the water company should keep RH2 under surveillance. For households RH3 and RH4, only a relevant breakpoint is detected, May 2014 and November 2015, respectively. Moreover, comparing the TS slopes before and after the breakpoint, the magnitude of change is considerably higher in water meter RH4 (RMCRH4=−20 vs RMCRH3=−5). RH4 exhibits an abrupt change at the beginning of 2012 (Figs. 2 and 4), and based on the records from the water company, the meter was replaced in January 2012 (13th month). As already explained in subsection “Detect structural changes,” the breakpoint analysis requires a minimal segment size (h), which in this case is 14 months (corresponding to hRH4×72=0.2×72). So, this breakpoint was out of reach of being detected. However, if data before 2011 were available, this issue would no longer exist.Concerning the nonresidential households from the Quinta do Lago Resort, NRH1 shows one breakpoint in June 2017. According to Table 1, the first segment is statistically significant, so the breakpoint is considered relevant (Table 2). The relative magnitude of change is RMC=2.71, revealing an increase in consumption after the breakpoint, so there is no motive for alarming the water company. Besides, this water meter was replaced in June 2018. However, judging by the graph of the water consumption (Figs. 2 and 4), it seems a hasty decision by the company. In NRH2, two breakpoints were detected (Table 1), but only one is relevant (November 2017) with an estimate RMC=−3.18 (Table 2). According to this table, this meter was already malfunctioning for half a year when the substitution took place. In NRH3, the procedure detected two breakpoints, but only November 2017 is relevant (bp*) with RMC=−1.10. Note that this decline was detected one year before the meter replacement (Table 2). If a surveillance system integrated this approach, the water company would have received an alert one year before.In the case of the hotel, from the five segments (four breakpoints), only two are statistically significant, corresponding to bp*={February 2008, July 2013, July 2014}, as seen in Table 2 and Fig. 4. The estimated RMC are 0.58, −31.65, and 1.06, respectively (Table 2). The negative value of RMC for the second breakpoint and the decrease in consumption shows evidence that the meter should have been replaced sooner, perhaps between July 2013 and July 2014.As observed in Table 2, the results indicate that the company should continue to monitor all households’ meters, except RH1, NRH1, and the hotel since the corresponding RMC values are positive. To sum up, the previous results illustrate the effectiveness of the approach in monitoring water consumption by the consumers, such as sudden changes and continuous decrease. Besides, the approach could detect these changes sooner than the actual replacement time and in instances in time not foreseen by the water utility.DiscussionWater utilities need to be aware of water’s responsible use, a concern emphasized by climate change. One form of the companies to be alert is to steer the effective water consumption and guarantee an efficient manutention of its equipment. However, when it comes to the processing of real metering data, several difficulties arise.It is well known that mechanical water meters metrology becomes more and more inaccurate during their operating lifetime due to the “wear and tear” of the measuring components (Mutikanga et al. 2011). As already mentioned, there are several studies [e.g., Arregui et al. (2006, 2013) and Pacheco et al. (2020)] that analyze the influence of parameters in the water meter metrology such as fatigue tests, depositions, incorrect water meter sizing, water consumption patterns, among others. Apparent losses occur due to inaccuracies in metering, illegal use, meter reading errors, data handling, and billing errors. These type of losses has a significant impact on the revenue of the water companies. The cost for the utility of a cubic meter of real losses is much less than the price of a cubic meter of apparent losses. This issue is of great importance because while real losses are easily recognized, apparent losses are not perceived well likely because apparent losses cannot be directly seen and are mostly related to economic losses. Arregui et al. (2006) present extensive work regarding this issue, and one key observation is that the water company should study the client’s water consumption patterns (private domestic or industrial). Additionally, Oviedo-Ocaña et al. (2020) also suggest that customer meter renovation is an alternative to reduce apparent losses, mitigating inaccuracies associated with the aging of these devices.So far, the usual mechanisms of analyzing the water consumption are performed on a bigger scale, such as considering all the consumers/water meters of cities, as in Monedero et al. (2016) and Hester and Larson (2016). To the best of our knowledge, no similar approach to the one proposed has been developed to examine water consumption trends for a single water meter. Its purpose is to contribute to a better understanding of water consumption by providing useful guidance on the replacement of the meters. It will also provide better analysis and a new perspective on water usage within water management.The case study involved houses with different characteristics (residential and nonresidential, mainly for holidays), and a hotel, from the Algarve. The Algarve is a popular summer holiday destination with a Mediterranean climate, meaning hot summers and mild winters. This seasonal effect is estimated by and removed. The strategy proceeds as follows: breakpoint analysis, nonparametric trend analysis, and its magnitude, and a change of water consumption indicator are calculated. The combination of the methodologies was able to detect statistically significant decreasing trends associated with points in time (i.e., breakpoints) where these changes occur and in some cases even earlier than the company’s decision on the water meter replacement. This is an added value of the strategy. If the water meter is replaced too late, a significant revenue loss (caused by meter under-registration) may occur. On the other hand, if detected after the actual replacement means that it was replaced too soon. Therefore, this approach could become a useful tool to use by the water companies because it provides a better understanding of water consumption patterns and makes a conscious decision regarding the water meter maintenance (to replace or not). The proposal for a unitless indicator of the magnitude of change allows companies to analyze water meters from different infrastructures, with different water volumes such as a household or a hotel. The decision to replace the water meter is of the water company’s responsibility, which must weigh the cost-benefit of changing one or more meters. This decision analysis could gather the results already achieved with an econometric analysis of the optimum level of apparent losses, as described by Arregui et al. (2018), or else a financial analysis as the one performed by Pacheco et al. (2020), to increase the confidence on the timing of the water meter replacement.Conclusion and Future WorkNowadays, water utilities have an essential role in managing water and wastewater services. One of the problems they face is nonrevenue water due to apparent losses. The procedure developed generates an alert based on decreasing water consumption patterns to accomplish the water company’s challenge, contributing to water meter performance assessment. It was developed and implemented using R language and is supported by reliable statistical methods. Besides, a new quantitative measure, designated as RMC, is proposed. The objective is to obtain a magnitude of the water usage change, which can help decide on the meter’s replacement. The water company must also investigate the decline of the consumption (RMC<0) since it might be related to a possible anomaly in the meter. If so, it is the ideal time to replace it. The inclusion of this new approach in a system that automatically analyzes the data and updates the information could be the solution sought by water companies to mitigate the impact of apparent water losses.The proposed approach was successfully applied to eight-time series of billed water consumption from two locations in the Algarve, Portugal, representing three different consumption patterns. The data were collected by meters (Residential Households and the hotel) and smart meters (nonresidential households). A complement is the visual inspection of the results and their interpretation. This is also a valuable tool worth exploring to understand and derive more insights into the consumption pattern. Moreover, the procedure was able to identify points in time that coincide with the date of replacement of the meters. In some cases, they were detected earlier than the company’s decision on the water meter replacement. As so, an alert would have been useful for the company to minimize revenue loss.In future work, it is planned a simulation study on water consumption to evaluate the approach’s performance based on quantitative metrics. Furthermore, an association of the decreasing trend with socio-economic aspects could explain the change in consumers’ behavioral patterns. The latter was not performed because it was out of the paper scope. Future research on this topic should be considered to refine and explain the changes in water usage. This strategy’s extension to identify increasing patterns is straightforward, translating into a viable approach to manage NRW, alert conserving water resources, and encourage responsible water use.Reproducible ResultsSoraia Pereira (Universidade de Lisboa) downloaded all the materials, installed, ran the models using the data and functions in “Workspace_data_functions.RData”, and reproduced the results in Tables 1 and 2.AcknowledgmentsThe authors would like to thank the editors, two referees, and a reproducibility reviewer for their constructive comments and suggestions, which greatly improved this paper and the information available in the GitHub repository. The idea behind this work began at the 140th European Study Group with Industry (ESGI140), held in Portugal in June 2018, and it was motivated by the challenge proposed by Infraquinta ( under the theme “Evaluating Water Meters.” The authors are grateful to the water company Infraquinta and Loulé Municipality ( for providing the water consumption data and inside technical guidance. Clara Cordeiro is partially financed by national funds through FCT—Fundação para a Ciência e Tecnologia under the project UIDB/00006/2020. Ana Borges work has been supported by national funds through FCT—Fundação para a Ciência e Tecnologia through project UIDB/04728/2020. M. Rosário Ramos was partially supported by National Funding from FCT—Fundação para a Ciência e Tecnologia under the project UIDB/04561/2020.References Arregui, F., J. Soriano, J. Garcia-Serra, and R. Cobacho. 2013. “Proposal of a systematic methodology to estimate apparent losses due to water meter inaccuracies.” Water Sci. Technol. 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