Water Quality Analysis of Drinking Water by Identification of Their Distribution and Process Capability

The present study deals with the water quality management using Water Quality Index (WQI) and Distribution Identification model. The drinking water quality in Jaipur city has been used for the various physio-chemical parameters such as temperature, pH, turbidity, conductance, total hardness, alkalinity, magnesium, calcium, nitrate, chloride, fluoride, sodium, potassium. Drinking water suitability for domestic purposes was examined by WHO and BIS standards, which indicate the drinking water in almost all the areas, were not much suitable for drinking purpose. It is observed that Water Quality Index (WQI) is very high in Sanganer and VKI areas and Gamma distribution model fits on all the parameters for different sites of water data. Thus it was observed that potable water quality has degraded with respect to all the parameters and almost in all the Sites parameters.


Introduction
Potable water or drinking water has always been an important and life sustaining drinks to humans and is essential to the survival of all living organisms. The potable water should be free from pathogenic agents and chemical constituents, pleasant to taste and usable for domestic purposes. Parameters for drinking water quality typically fall under two categories -Chemical and Physical. Chemical parameters causes' chronic health risks through built up of heavy metals whereas physical parameters affect the aesthetics and taste of drinking water [10]. Water supply in Jaipur comes either from surface water or ground water sources. The ground water is characterized by multiple quality problems. Many hazardous pollutants viz., colored dyes, heavy metals, nitrates and fluoride, agriculture runoffs, waste water treatment plants, combined sewage overflows, storm water discharges, failed septic tanks, prescription drugs etc. Pollute it.
Water Quality Index may be defined as a rating, reflecting the composite influence on overall quality characteristics of water of individual quality parameters, which is being regarded as one of the most effective way to communicate water quality.
This will give us only certain numerical value but for estimating exact quality of water an indexing system has been developed known as Water Quality Index, which gives us the idea of water of whole system [2].
Quality rating equal to zero means a complete absence of pollutants. While 0 to 100 implies that the pollutants are under consideration means within the prescribed standards. When quality rating is more than 100 it implies that the pollutants are above the standards. Similarly when WQI is 0 to 100 indicate that the water is under consideration and is safe for use.
Distribution Identification Model is used to evaluate the optimal distribution based on the probability plots and goodness-of-fit tests prior to conducting a capability analysis study [2].
Capability analysis study is used to produce a process capability report when data do not follow a normal distribution. The report includes a capability histogram overlaid with a distribution curve, and a table of overall capability statistics [7]. The report also includes statistics of the process data, such as the mean, distribution parameter estimates and process specifications; the actual overall capability (Pp, Ppk, PPU, and PPL), and the observed and expected overall performance. The report can be used to visually assess the distribution of the process relative to the target, whether the data follow a specified distribution, and whether the process is capable of meeting the specifications consistently.
Study Area: The present study was carried out in Jaipur city which in situated in eastern part of Rajasthan surrounded on three sides by the rugged of Aravali hills. The city has total geographical area of 14,068 sq. km. (4.11 percent of the state). It is located at 26.92°N 75.82°E. It has an average elevation of 431 meters.
The climate of the city is hot semiarid with extremes of temperature (15-45°C) and rainfall 650 mm (26 inch.). In this city water samples of selected for 10 different areas such as VKI, Jhothwara, Chitrkoot, Vaishali Nagar, Transport Nagar, Kanota, Bari Chopar, Subhash Chowk, Gopalpura and Sanganer were used with the view to understand the quality of potable water.

Analysis for Water Quality Index
The basic equation for Water Quality Index is W. Q. I. = Σ qi wi Where qi = quality ratings of parameters wi = unit weight of different parameters qi wi = parameters sub-index

Quality Ratings of the Parameters
Quality ratings qi = [ ] * 100 Where VO = observed value of the parameter VS = standard value of the parameter VI = ideal value of the parameter VI for pH = 7 and for dissolved oxygen = 14.6 mg/l While VI is zero for other parameters.

Distribution Identification Model
By the help of Mini Tab (Software) Distribution Identification Model is used to evaluate the optimal distribution based on the probability plots and goodness-offit tests prior to conducting a capability analysis study.

MLE
Maximum likelihood estimates of the parameters are calculated by maximizing the likelihood function with respect to the parameters. The likelihood function describes, for each set of distribution parameters, the chance that the true distribution has the parameters based on the sample [5].
The Newton-Raphson algorithm is used to calculate maximum likelihood estimates of the parameters which define the distribution. The Newton-Raphson algorithm is a recursive method for computing the maximum of a function. The percentiles are calculated from that distribution.

Pp
Pp is calculated using the parameter values estimated using maximum likelihood method for a distribution used in the analysis.

PPL
PPL is calculated using the parameter values estimated using maximum likelihood method for a distribution used in the analysis.

PPL =
−F (p ) 3 where: F -1 (p) = p * 100th percentile of a standard normal distribution p 1 = Prob (X < LSL) X follows the distribution used in the analysis

PPU
PPU is calculated using the parameter values estimated using maximum likelihood method for a distribution used in the analysis.

PPU = F (p ) 3
Where: F -1 (p) = p * 100th percentile of a standard normal distribution p 2 = Prob (X < USL) X follows the distribution used in the analysis

Ppk
The minimum of PPU and PPL Table 1 and Table 2 give the detail of Quality Ratings, unit Weight and Water Quality Index of different areas for all quality parameters. It is observed that WQI is not in the prescribed limit for all the areas and for Sanganer and VKI, WQI is so high. Identification of distribution and process capability for different parameters:

Result and Discussion
Ph Descriptive statistics The table of descriptive statistics provides the summary information for the whole column of data. All the statistics are based on the non-missing (N = 10) values. For these data, µ = 8.16 and σ = 0.483506.
Goodness-of-fit test The table includes Anderson-Darling (AD) statistics and the corresponding p-value for a distribution. For a critical value α a p-value greater than α suggests that the data follow that distribution. The p-value 0.259, 0.003, 0.250, and 0.238 indicate that the gamma distributions fit the data well because this has the largest p value which is greater than α Probability plot: The probability plot includes percentile points for corresponding probabilities of an ordered data set. The middle line is the expected percentile from the distribution based on maximum likelihood parameter estimates. The left and right line represents the lower and upper bounds for the confidence intervals of each percentile.
The probability plots shows that the data points fall approximately on a straight line and within the confidence intervals for Normal, Weibul and gamma distribution.   The histogram shows the evidence of serious discrepancies between the assumed model and the data.
WE can see that the right tail of the distribution falls outside the upper specification limit. This means at all the areas the parameter Ph shows the values higher than the upper specification.
The Ppk and PPU indices tell us whether the process within the tolerance limits. Both indices are -0.79, below the guideline. Thus this process of Ph cannot be considerable. Likewise, the observed PPM > UCL is 1000000. This value means that 1000,000 out of 1,000,000 points more than the upper specification limit that is in all areas Ph has more than the upper specification limit of 7.

Turbidity
Descriptive statistics The table of descriptive statistics provides the summary information for the whole column of data. All the statistics are based on the non-missing (N = 10) values. For these data, µ = 9.36 and σ = 0.839577.
Goodness-of-fit test: The table includes Anderson-Darling (AD) statistics and the corresponding p-value for a distribution. For a critical value α a p-value greater than α suggests that the data follow that distribution. The p-value 0.68, 0.003, 0.250, and 0.250 indicate that the Normal, Weibull and gamma distributions fit the data well because this has the largest p value which is greater than α Probability plot: The probability plot includes percentile points for corresponding probabilities of an ordered data set. The middle line is the expected percentile from the distribution based on maximum likelihood parameter estimates. The left and right line represents the lower and upper bounds for the confidence intervals of each percentile.
The probability plots shows that the data points fall approximately on a straight line and within the confidence intervals for Normal, Weibull and gamma distribution.  The histogram show the evidence of serious discrepancies between the assumed model and the data.
WE can see that the right tail of the distribution falls outside the upper specification limit. This means at all the areas the parameter Turbidity shows the values higher than the upper specification.
The Ppk and PPU indices tell us whether the process within the tolerance limits. Both indices are -1.66, below the

Probability Plot for Turbidity
N ormal -95% C I E xponential -95% C I Weibull -95% C I Gamma -95% C I guideline. Thus this process cannot be considerable. Likewise, the observed PPM > UCL is 1000000. This value means that 1000,000 out of 1,000,000 points more than the upper specification limit that is in all areas Turbidity has more than the upper specification limit of 5.00. Goodness-of-fit test. The table includes Anderson-Darling (AD) statistics and the corresponding p-value for a distribution. For a critical value α a p-value greater than α suggests that the data follow that distribution. The p-value 0.054, 0.003, 0.045, and 0.071 indicate that the gamma distributions fit the data well because this has the largest p value which is greater than α Probability plot The probability plot includes percentile points for corresponding probabilities of an ordered data set. The middle line is the expected percentile from the distribution based on maximum likelihood parameter estimates. The left and right line represents the lower and upper bounds for the confidence intervals of each percentile.
The probability plots shows that the data points fall approximately on a straight line and within the confidence intervals for Normal, Weibull and gamma distribution.

Process Capability of Turbidity
Calculations Based on Gamma Distribution Model The histogram show the evidence of serious discrepancies between the assumed model and the data.
WE can see that the right tail of the distribution falls outside the upper specification limit. This means at all the areas the parameter TDS shows the values higher than the upper specification.
The Ppk and PPU indices tell us whether the process within the tolerance limits. Both indices are -1.10, below the guideline. Thus this process cannot be considerable. Likewise, the observed PPM > UCL is 1000000. This value means that 1000,000 out of 1,000,000 points more than the upper specification limit that is in all areas Turbidity has more than the upper specification limit of 500.

Probability Plot for TDS
N ormal -95% C I E xponential -95% C I O v erall C apability P p 0.15 P P L 1.88 P P U -1.10 P pk -1.10 O bserv ed P erformance P P M < LS L 0 P P M > U S L 1000000 P P M Total 1000000 Exp. O v erall P erformance P P M < LS L 0 P P M > U S L 1000000 P P M Total 1000000

Calculations Based on Gamma Distribution Model
(AD) statistics and the corresponding p-value for a distribution. For a critical value α a p-value greater than α suggests that the data follow that distribution. The p-value 0.016, 0.003, 0.138, and 0.017 indicate that the Weibull distributions fit the data well because this has the largest p value which is greater than α Probability plot The probability plot includes percentile points for corresponding probabilities of an ordered data set.
The middle line is the expected percentile from the distribution based on maximum likelihood parameter estimates. The left and right line represents the lower and upper bounds for the confidence intervals of each percentile.
The probability plots shows that the data points fall approximately on a straight line and within the confidence intervals for Normal, Weibull and gamma distribution.  The histogram shows the evidence of serious discrepancies between the assumed model and the data.
WE can see that the right tail of the distribution falls within the upper specification limit. This means at all the areas the parameter DO shows the values lower than the upper specification.
Likewise, the observed PPM > UCL is 0 and PPM < LCL is 600000. This value means that 6000,00 out of 1,000,000 points less than the lower specification limit that is in almost all areas DO has less than the lower specification limit of 6. The probability plots shows that the data points fall approximately on a straight line and within the confidence intervals for Normal, Weibull and gamma distribution.  The histogram shows the evidence of serious discrepancies between the assumed model and the data.
WE can see that the right tail of the distribution falls outside the upper specification limit. This means at all the areas the parameter Nitrate shows the values higher than the upper specification.
The Ppk and PPU indices tell us whether the process within the tolerance limits. Both indices are -0.84, below the guideline. Thus this process cannot be considerable. Likewise, the observed PPM > UCL is 1000000. This value means that 1000,000 out of 1,000,000 points more than the upper specification limit that is in all areas Turbidity has more than the upper specification limit of 50.

Conclusion
Statistical analysis of water quality parameters has been studied by using MINI TAB. It is observed that WQI is so high in all the areas of Jaipur under study and for Sanganer it is highest.
The textile industry is one of the oldest and largest organized sectors in Sanganer area with geographical coordination 26° 49' 0" North, 75° 47' 0" East. Which houses almost 400 small-scale textile printing units, a large volume

Process Capability of Nitrate
Calculations Based on Gamma Distribution Model of textile wastewater (>10 000 KL/day) is discharged. Further, untreated and sometimes even treated effluents from these industries are released into surface waters of Amanishah drainage or through the drainage systems, seep into the ground water and adjoining water bodies. Since many textile dyes are known carcinogens and mutagens12. These disposal practices have contaminated the environment and caused adverse effects on the flora, crops and fauna in Sanganer town13 and had higher fluoride (2.8 mg/L) compared to other areas.
We study that all the parameters are responsible for this increased WQI in the city. Since all the parameters show the higher values then UCL in Process Capability.
DO is essential for living organism and we has been observed that in all the areas DO has near to its minimum value. Now we have to think that what we are getting by this urbanization, industries, textile mills etc.