Statistical Quality Control in Uniformity of Drip Irrigation With Different Slopes

Allan Remor Lopes, Marcio Antonio Vilas Boas, Felix Augusto Pazuch, Luciano Dalla Corte, Diane Aparecida Ostroski, Marcelo Bevilacqua Remor, Fabíola Bogoni Mundstock Mohr, Marcelo Dotto, Alessandro Paggiarin Zanella, Acir Felipe Grolli Carvalho, Alvaro Rodrigo Freddo, Ivan Carlos Bertoldo, Kelli Pirola & Camila Moreno Giarola 1 Program in Agricultural Engineering, State University of Western Paraná, Cascavel, Brazil 2 Education Union of South-West Paraná, Dois Vizinhos, Brazil 3 Federal University of Technology Paraná, Pato Branco, Brazil 4 Paranaense University, Umuarama, Brazil


Introduction
Drip irrigation is characterized by the application of water in the form of drops, allowing water to be supplied in small quantities (Resende et al., 2004). The benefits of this method are: Water economy, favors the development of plants, reduction of salinity, possibility of chemigation, limits the development of weeds, reduces labor and energy consumption (Frizzone et al., 2012).
The evaluation of the irrigation system in operation is determined by performance parameters that must be defined based on field determinations, such as flow and application uniformity (Souza et al., 2006).
The performance of an irrigation system is directly proportional to the improvement of crop production variables (Geisenhoff et al., 2015) and minimization of water and energy expenditures (Gris et al., 2015). Distribution uniformity is the main way to determine whether an irrigation system is acceptable or not (Brennan, 2008).
The evaluation of drip irrigation systems in areas with slopes and aclives is necessary due to the variation of pressure in the system, resulting in different flow rates that interfere with distribution uniformity (Lima et al., 2003). The percentage of a localized irrigation system due to declivity can lead to an increase of up to 8.86% per hectare (Cunha et al., 2014). Souza et al. (2018) concluded that the slope influences the dimensions and geometry of the wet bulb.
Statistical quality control is a tool composed of control charts and statistical process control, which seeks to maintain variables within limits or standards pre-established by technical norms, seeking to ensure that a given process behaves appropriately. For Justi et al. (2010), irrigation systems are perfectly adequate to apply statistical quality control.
Control charts are used to monitor the process and signal to analysts the need to investigate and adjust it according to the size of the deviations found (Walter et al., 2013).
(2) jas.ccsenet.org Journal of Agricultural Science Vol. 11, No. 16;2019 Where, Q = Arithmetic mean of flows (L h -1 ); Qi = flow in the dripper of order i, (L h -1 ); n = Number of drippers evaluated in the irrigation system; Q25 = Average of ¼ of the flows with lower values, (L h -1 ).
To classify the UC and UD data, the following classifications were used, which are described in Table 1. In the quality control process, the Shewhart, Zones and CUSUM charts were used.
The Shewhart control chart consists of a center line representing the mean of the desired quality characteristic, an upper control limit line (UCL) and another lower control limit line (LCL) (Frigo et al., 2016 ).
The Zones graph consists of eight zones (four on each side of the center line) (Zhang et al., 2018), bounded by a central line, the limits: 1-sigma, 2-sigma and 3-sigma. Its use is recommended for practical use because of its performance, simplicity, efficiency, ease of use and understanding (Ho & Case, 1994). For the interpretation of the Zones graphs, the scoring rules (Davis et al., 1990), described in Table 2, were used, and a graph is considered out of statistical control when it reaches 8 points. Table 2. Scores for each sigma of the zones graph Zone Score Between Central Line and 1-sigma 1 Between 1 and 2-sigma 2 Between 2 and 3-sigma 4 In addition to 3-sigma 8 Source: Davis et al. (1990).
For the construction of the Shewhart and Zones control charts it was necessary to calculate the upper and lower specification limits obtained by Equations 3 and 4, respectively.
Where, UCL = Upper control limit; LCL = lower control limit; x = Average of the data; MR = Average of the mobile range of data; d 2 = Constant when used a moving amplitude of n = 2 observations (d 2 = 1.128) (Montgomery, 2016).
In the CUSUM control chart, the deviations from the mean are accumulated over time, generating a cumulative sum obtained according to Equation 5. The CUSUM graph accumulates deviations that are below or above the target value, with statistics (CUSUM lower) and (upper CUSUM), which are expressed by Equations 5, 6 and 7.
Where, x j = Average of the jth sample size n ≥ 1; C i = cumulative sum up to the i th sample; u 0 = sample mean; K = compensation value or gap. To measure how much the process is able to meet specifications, we use what are called capacity indices. The centered (Cp), lower limit (Cpl) and non centered (Cpk) process indices described in Equations 8, 9 and 10 were used.
Where, USL = Upper specification limit; LLS = Lower limit of specification; σ = Standard deviation of the data; X = Average of the data.
All statistical and graphical analyzes were performed in MINITAB 18 software.
Source: Nakayama and Bucks (1980); Capra and Scicolone (1998).   The CUSUM control charts for the UC and UD are shown in Figures 7 and 8 Table 6 contains the process capability indices for UC and UD, at different slopes.

Discussion
The physical-chemical analysis of the water (Table 4) didn't present any parameters with a severe risk of clogging according to the Nakayama and Bucks indexes (1980), and Capra and Scicolone (1998). Only the concentrations of total iron and pH had a moderate risk of clogging and the other parameters having a low risk of clogging.
According to the contour map ( Figure 2), a similar behavior is observed in the system in level and aclivity, with the larger flows at the beginning of the lines and decrease until the end of them. Alves et al. (2015) report that the flow decreases due to the pressure drop during the stretch. For the sloping system, a concentration of the largest flows at the end of the last line was explained by the gradual increase of the pressure that occurs until the end of the pipe (Marcuzzo & Wendland, 2011).
The average uniformity (Table 5) was excellent for all situations (> 90%). The declivity system showed higher excellence in relation to the others, with a higher average uniformity for CUC (99.03%) and for UD (98.45%). Ella et al. (2009), when studying the uniformity of water distribution in a low-cost drip irrigation system with different slopes and hydraulic loads, verified that uniformity decreased as the slopes increased.
In the Shewhart chart for the UC (Figure 3), it is observed that the level and declivity system were outside the control limits. The level system showed a point outside the control limits. The declivity system presented two points outside the control limits, however, the aclivity system was under statistical control. Pressure destabilization can lead to a point outside the control limits (Silva et al., 2015).
The comparison of UC and UD in the Shewhart chart ( Figure 4) shows a different behavior, and the level system was under statistical control. The Shewhart control chart proved to be a good statistical tool in the study of conventional sprinkler irrigation, demonstrating very well the process variability (Frigo et al., 2016).
The control chart of Zones presents high sensitivity, as shown in figure 5. The UC presents all slopes (0%, 2% and -2%) outside the statistical control. The level and aclivity system obtained a point out of control, while the declivity system obtained 3 points out of statistical control. Davis and Krehbiel (2002), when comparing the performance of the Shewhart and Zonas control charts, concluded that the zone chart is slightly better at detecting processes that take linear changes over time.
Exploring the UD data in the Zones control chart (Figure 6), it was verified that the level system remained under statistical control by the Zones control chart, while the slopes in aclivity and declivity were out of statistical control. Thus, aclivity, got 3 points and declivity 2 points out of control. Isolated points may be the result of fluctuations in pressure, operator fatigue, some equipment variable or climatic variations (Justi & Saizaki, 2015).
The CUSUM graph with the UC data (Figure 7) at the level was presented under statistical control, differing from the Shewhart and Zone graphs, which were out of statistical control. Table 6 shows that the process capacity indices for UC and UD coefficients in all slopes were higher than the established limits (> 1.33), that is, they were statistically capable. Silva et al. (2015) also obtained capacity indices above the required limit in drip irrigation. Thus, statistical process control is an excellent tool for the quality of the drip irrigation system.
All coefficients and slopes have Cpk > Cp, this implies that the processes are within specification point and the distribution is centered. Silva et al. (2015) by studying the process capability index in saline water self-compensating emitters and also obtained Cpk > Cp. The results also corroborate with Andrade et al. (2017) who observed an increase in the process capacity index directly proportional to the mean values of UC and UD.