Case of Preferential Selection of Attribute over Variable Control Charts in Trend Analysis of Microbiological Count in Water

transformation using Microsoft Excel. Then, control charts were constructed using Statistical Process Control (SPC) software. The results showed that transformation improved data normalization for the Individual-Moving Range (I-MR) chart while the original pattern of the dataset was lost distorted. On the other hand, other advantages could be retained when using the Laney chart where no transformation was implemented on original raw data. The selection should be based on the nature of the process aim and condition.


INTRODUCTION
Consistency in the quality of the materials used in healthcare industry is crucial for delivering products with safe, predictable and effective properties to the final consumers (Mosadeghrad, 2014). These customers are usually health-defective and ill populations with a high risk of vulnerability to microbial infections. Water is one of the vital components in the industry that is involved in many activities (Eissa, 2016). Purified water is used in many non-sterile processes including pharmaceutical and biopharmaceutical manufacturing.
Water is highly dynamic in its inspection characteristics that may change and fluctuate rapidly under various conditions (Sardella et al., 2021). Thus, careful monitoring of its properties is of paramount importance. One of the critical quality items to be examined is the microbiological bioburden level (Eissa et al., 2022). Under these circumstances, the incorporation of the trending concept would be of great value over the reliance on the daily results only.
The use of the process behavior charts is an advantage in this situation as could be proved from earlier works that have involved quality management https://prensip.gen.tr/ and improvement strategies following Six Sigma principles and rules (Drinking Water and Health, 1982).
However, the appropriate selection of the trending chart is the dilemma that faces the interpreter, especially, if the primary database might be subjected to modifications, essentially the transformation due to a significant deviation in data distribution from the perquisite distribution (Eissa, 2015).
The crux of the present case is the presentation of two different point of view for analysis of dataset trends from non-normally distributed water samples results with pros and cons that could be drawn from the outcome of this investigation.

CASE STUDY
A small water plant for preparation of Purified Water (PW) from a municipal city source was monitored for quality characteristics, including total viable aerobic microbial count (TVAC) over about 16 months (70 weeks) on an average weekly basis. The number of accessible sampling ports was two: one after processing of water (denoted by PW) and the other at the Sanitization Port (denoted by SP) or specifically the Ultraviolet (UV) compartment. The sampling procedure, transfer and storage were conducted according to earlier research (Essam Eissa, 2018). Handling of samples, analysis, incubation and interpretation were performed using conventional microbiological techniques (Eissa, 2018a). Data were gathered and processed in Microsoft Excel then subjected to further processing using Statistical Process Control (SPC) software (Newton, 2014;Triola, 2014;Held, 2018;Levine et al., 2021).

Count in Water
Monitoring the mesophilic aerobic microbial count in water throughout the study period is illustrated in

Examination of Dataset Distribution
The distribution and comparison of data before and after the logarithmic transformation study are demonstrated numerically in Table 1 and illustrated visually in Figures 3 and 4. The core finding from this section is that logarithmic transformation (to base ten) has significantly improved data normalization by reducing data scatter and spreading which is indicated by the absence of outliers after transformations. Accordingly, the use points' results had passed the Kolmogorov-Smirnov (KS) normality test, in addition to the noticeable improvement of skewness and kurtosis of the distribution curve. Also, the spreading between data points was appreciably reduced when variation parameters were reviewed.

Control Charts: Two Approaches Investigation
Two types of trending charts were used herein as an approach to monitor the process pattern and behavior. Figures 5 and 6 show attribute (For counting data, attribute control charts (most often integers, e.g., 4, 5, 6) and variable charts using variable controls for measurable data (most often decimals, e.g., 2.43) types of control charts, respectively. Red dots represent the alarming sample points that embrace assignable causes of variation which could be isolated from the common sources of natural variabilities in the inspection characteristics. The assignable differ from common causes variabilities in that they show special patterns between successive points rather than random variations that occur naturally in stable processes or inspection properties. These variations in turn embrace hidden factors that could lead to out-ofcontrol situations with undesirable outcomes (Hubbard, 2003). Point     Normality assumption for the use of variable control charts has been stated by various statisticians and experts (Khakifirooz et al., 2021). Despite the robustness of the I-MR chart has been demonstrated previously by some researchers, the Normalization procedure has been adopted in the present study to evaluate the pros and cons against the counterpart attribute chart through one of the well-known transformation paths (Keller, 2011;Elisson, 2017). This transformation tactic -for the original data -has been proved formerly to minimize data scattering and reduce outliers. Thus, Log10 [(CFU/100 mL) + 1] formula was used in the construction of data points in I-MR charts (Eissa, 2015;Smarter Solutions Inc., 2022).
Number "1" in the equation is necessary to correct for zeros in the data record without distorting the data significantly.
On the same line, Laney's correction of the attribute chart was used for datasets that failed to show Poisson distribution assumptions of u or c charts. In this case, Laney modification was used to mitigate the risk of possible elevated alarm rates (Laney, 2002). This correction would be important to keep an eye on a process' defect rate and make any necessary adjustments for over-or under-dispersion in the present data. A conventional chart (for multiple defects per unit (D/U)) may display more points outside the control limits due to over-dispersion (Jones & Govindaraju, 2001 investigation to prevent the occurrence of this incidence in the future. Water of poor quality will be produced if the process is under control, but the control limits are outside of the specification limits.
The control limits will, in the ideal case, if centered inside of the specification limits with space to spare.
The microbiological quality of water is stable and within the required process capacity if the CLs are within the SLs. It produces the best quality and has few inspection problems. The process also complies with consumer requirements. However, if one or more of the water samples showed results above CLs even if within SLs, then the process is unstable with out-ofcontrol points detected then fast corrective and preventive actions (CAPA) are required to bring the process again within the stability window.
Laney charts could be easily correlated and interpreted along with time series plots and Pareto diagrams as could be seen from Figures 1 and 2