GLOBAL PERFORMANCE EVALUATION BASED ON MULTIVARIABLE STATISTICAL CONTROL OF A PUBLIC UTILITY COMPANY

ABSTRACT In this research article, the service provision in a public company was evaluated through multivariate statistical control to determine the performance of its dimensions. For this purpose, the methodology used was: 1) characterization of the information associated with the quality dimensions provided, through consolidated databases recognized for their high level of quality, such as: Elsevier, Inderscience, among others; 2) calculation of Six Sigma metrics (DPMO, Z-level and performance), which will allow from a monthly average, to evaluate the quality of the service provided by the company in a timely and periodic manner in the 12 periods of 2019; 3) Evaluation of the performance of the service dimensions in a global and comprehensive manner, through multivariate analysis. Finally, the quality of the company’s service is presented. Thus, allowing the control and continuous improvement of the processes, through its prompt replanting.


INTRODUCTION
The implementation and control of quality in processes have become one of the indispensable practices in the private business environment (Bloj, Moica & Veres, 2020); as these reflect the level of commitment of companies to quality and good customer service (Kubińska, et al., 2022).Likewise, performance measurement and management control in public companies are perceived as the key to increase the quality of life in the public sector (Avelé, 2021).That is why many companies, independent of their nature, have decided to rely on various techniques and procedures dedicated to statistical quality control, to assess the capacity and performance of the dimensions of their processes (Deeb, et al., 2018), in relation to a series of requirements of interest to customers.Such requirements, called specifications, which are frequently given in objective and limiting value for each of the analyzed characteristics (Costa, Lopes, & Brito, 2019).
Within the techniques, there is the analysis of multivariate capability indicators, which has been used in production and similar environments, since they provide quantitative measurements of the potential and performance of processes characterized by several evaluable and related quality dimensions simultaneously (Fontalvo, Herrera, & De la hoz, 2020).Thus, allowing the control and continuous improvement of processes for their prompt replanning, being clear about the actions that lead to the optimization of jobs, and thus generate competitive advantages for the company, and at the same time, added value for customers to whom the service is provided (San-jose, Retolaza & Bernal, 2021) The added value is born from the cautious study of the reactions of customers to the services provided and the requirements not yet satisfied, hence it is evident the characteristics to be improved and/or implemented in an action plan by the company (Sakyi, 2020).This is why companies must have clearly and concisely defined the market segment to be addressed with their services (Costa, et al., 2021), as well as knowing the needs of their customers to create strategic plans that meet them and manage to turn it into a competitive advantage over its competition (Mancosu, et al., 2018).
The previously studied perspective led to the generation of the following problem questions for this research: How to characterize the information associated with the quality dimensions of the service provided?How to articulate the six sigma metrics with the multivariable statistical control techniques to evaluate the performance of the service provided by the company in a timely and periodic manner in the 12 periods of 2019?What multivariable statistical control techniques allow to reliably assess the performance of the service provided by the company in a global and comprehensive manner?
Considering the above, the following objectives emerged for the study: 1) to characterize the information associated with the quality dimensions of the service provided; 2) to evaluate the performance of the service provided by the company in a timely and periodic manner in the 12 periods of 2019; 3) to assess the performance of the service provided by the company in a global and comprehensive manner, through a multivariate capacity indicator.

Multivariate capability indicators
The analysis of the multivariate capacity of processes is an essential methodology in the study of service quality, with respect to the tolerance that customers have for the objective requirements that they themselves impose, based on their tastes and expectations (Fontalvo, Herrera, & De la hoz, 2020).This process capability allows estimating the level of quality and performance that the company presents, historically monitoring its performance to identify whether the characteristics of the good or service comply with its specification limits.

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K. S. Chen, et al. (2003), presented by Fontalvo, Herrera & De la hoz (2020), proposes the monitoring of v characteristics, taking for normality and independence, as well as applying the multivariate capability index, CMT, the following formulation: This methodology evidences a geometric average of the conforming units in the v dimensions studied in the quality monitoring, and also allows to evaluate the nonconformities of the customers through the six sigma metrics.
Where, Pj is the average percentage of nonconformities in the dimension; jth and pk are the probability measures of each of the categories or modalities of the dimension evaluated, in other words This proposal assumes an optimal process in its performance, when the values present values greater than unity.For the use of the proposed metrics, the operating conditions of the service or the evaluated process must have a sigma level higher than 3, which is evidence of a stable process.

Six sigma in service companies
With globalization and the high competitiveness it has brought with it; the ability to meet customer expectations, as well as the improvement of quality in service processes, has become an issue of great relevance for companies in this sector (Lizotte-Latendresse & Beauregard, 2018).That is why, companies have decided to adopt new business practices, which lead them to achieve efficiency and excellence in their processes (Ali, et al., 2019).
It is there, where the six sigma methodology becomes known as a tool of great importance for service companies, since it allows them to optimize their resources (De la hoz, Fontalvo, & Fontalvo, 2020), as well as to achieve more efficient processes capable of meeting the customer's requirements; the latter being very relevant when it comes to giving the acceptance of the service and its recommendation.This allows improving the profitability of the company by obtaining greater customer satisfaction (Abbes, et al., 2022), which may possibly lead to customer loyalty with its services, thus increasing its income.
Knowing that six sigma is a customer-oriented strategy (Perramon, et al., 2022), which seeks to reduce the variability that exists in the various processes that occur in companies and that can damage the services and lose the reliability of the company.Within its applicability, it could be said that the model is based on the number of standard deviations or six sigma (process variability) that can correspond to the assumed process quality characteristics (Antosz, et al., 2022).The quality characteristics are determined by the maximum permissible error within the production process, thus determining whether it is capable of meeting customer requirements (Vincent, et al., 2021).The key to implementing a sigma index is not sigma results, but identifying the root cause of the errors and developing an improvement plan aimed at reducing or eliminating them and thus improving the process (Bennion, et al., 2018).

Public service
Public services can be considered as the response to the needs of society to have a decent life, regardless of their economic and physical condition.Likewise, all those activities carried out by the government with the purpose of satisfying the needs of the citizens.Hence, providing drinking water, electricity, security, subsidized health, among other services, are part of the primary functions of government, seeking to promote the welfare and human dignity of citizens, taking into consideration the human rights established in the Constitution of Colombia.
It should be emphasized that it is not enough to simply provide the service, but also to comply with the quality standards necessary to provide a good service to society (Longo, Zappatore & Bochicchio, 2019), and thus achieve social and economic development, in addition to effectively reducing the level of poverty by increasing the quality of life (Mamani & Vilca, 2022).
According to, Avelé (2021), Gaie (2021), Nguyen, et al. (2019) and Malpartida, et al. (2022), the quality of public service, is seen as an opportunity for companies to obtain competitive and sustainable advantages in a globalized and changing economic environment.All of the above, generates the need to study and promote quality in the dimensions of public services, and even more so in Colombia that, despite statistically managing the overall satisfaction of citizens with public services, through the National Administrative Department of Statistics (DANE), there are few individual researchers who have decided to conduct studies focused on making a comprehensive assessment of the quality of the Colombian system.
The new demands of society for administration, combined with the development of industries and achievements in economic and social practice, demonstrate the deficiency of current quality (Gaie & Mueck, 2021), which leads to the redefinition of public organizations, especially organizations that provide services.
The current situation regarding the quality of services is quite worrying (Avelé, 2022), which requires a general transformation of organizations (Laitinen, Kinder & Stenvall, 2018), starting from the study and control of errors, enabled by different statistical control methods that involve reliable and feasible systematic procedures for such studies.

METHODOLOGY
The method proposed for the study allowed the characterization of the information associated with the dimensions of quality provided in the public service, through the review of primary information of the company and the conceptual review associated with the object of study of this research.
In order to measure the metrics, primary information provided by the public entity was used to calculate the six sigma metrics (DPMO, Z level and performance), presented in section 3.1.1,was carried out, which allowed, based on a monthly average, to evaluate the quality of the service provided by the company in a timely and periodic manner in the 12 periods of 2019, followed by the use of a multivariate capacity indicator (see section 2.1.),with which the performance of the service dimensions was evaluated in a global and comprehensive manner, through multivariate analysis.Finally, the company's service quality is presented below.In the proposed method, 12 periods were established as criteria to be able to perform an evaluation per year, which will allow longitudinally analyzing the punctual performance through the metrics, and globally and integrally through the Multivariable quality capacity indicator.This can be compared year after year for analysis and decision making.
In order to proceed with the evaluation of the dimensions of quality provided, a series of criteria, formulas and a scheme are presented below:

Definition of quality dimensions
Considering the nature of the service provided, it was established that the objective of this research would be to evaluate the overall performance from the multivariable statistical control of a public service company, through its dependencies, which are: availability of the reconnection service, bill collection, escalation of attention, call reception, service stability and operation of the attention page.
In order to evaluate the performance of the different departments, a review of the historical PQRS of the year 2019 was carried out, generated in monthly periods, which contain the amount of services rendered (U), number of conformities and non-conformities (n), and an opportunity for error (O) was contemplated, in order to be able to make a study with the six sigma metrics and finally an analysis of the results.In the six sigma methodology, the defects per million opportunities (DPMO) are related to the actual number of defects observed, equation 3, and the sigma level Z, through equation 4.
The following is the type of service to be evaluated with its respective quality dimensions and the metrics to be used for the study:

Service
Complaints and/or claims system for billing terms, collections, reconnection and customer service.Process performance is calculated by Y in equation 5.
In the evaluation carried out by means of the six sigma metrics, it is expected that the performance (Y) is equal to or greater than 95% and the sigma level (Z) achieved is equal to or greater than 3, for a good performance.And Excellent if the Z sigma level performance is greater than 4.5.This is to prove that the evaluated processes achieved a good performance in the evaluated dimensions.

RESULTS
To evaluate the performance associated with the dimensions of public service quality, the primary information provided by the entity under investigation was tabulated, associated with the performance of the entity's departments, in relation to citizen service, which contained the highest number of complaints and/or claims, in the months from January to December 2019, as can be seen in Table 1.As previously observed, the number of non-conformities is quite low for the level of service provided, which indicates that the process is efficient.
The quantitative estimation of the quality of the service provided to the customer by the departments is achieved through the appropriation of the six sigma metrics.As can be seen in Table 2.In order to evaluate the performance of the dimensions of public service quality, the sigma level and the performance of the units were used, and the average of these variables per month of 2019 was calculated, in order to perform an analysis as a whole, as shown in Table 3. From Table 2 and Table 3 it can be observed that the sigma Z levels, both point and average all range between 3 > Z< 5, which shows an acceptable performance, and is consistent with what is expected in a process where six sigma metrics are used, where the ideal performance should range between 3 > Z< 6.
From the results obtained, it could be said that there is a good monthly performance, which was above 95% in the units as a whole, despite the fact that their sigma level is not very high (3.7; 4).
Continuing with the study of the dimensions of public service quality, we proceed with the presentation of the result obtained from the multivariate indicator, based on the formula below: (0, 9913 * 0, 9887 * 0, 9892 * 0, 9925 * 0, 9879 * 0, 9853 * 0, 9894 * 0, 9901 * 0, 9898 * 0, 9921 * 0, 9938 * 0, 9918) Even without comparing the results achieved by the company with the criteria established in the study, the good performance of the quality provided by the public servant is remarkable.
The criteria to be taken into consideration when evaluating the multivariable indicator of the study will also be presented (Table 4).

Criterion
Service performance Taking by consideration the performance criteria, expressed in Table 4, it can be found that the global, periodic and multidimensional performance of the quality dimensions of the public service provided is excellent, due to the fact that the multidimensional geometric quality capacity indicator exceeds CM T k ≥0, 75 (0,778044847).

DISCUSSION
From the results found, it can be noted that as a finding of this research, Table 2 and Table 3 show that the months in which there was the highest performance by the dimensions of quality of public service were November and April consecutively and it is also notorious its relationship with the sigma level, which are the highest in the whole year 2019.
In relation to this research, other authors such as Attia, et al (2021), as well as, Fontalvo, De La Hoz, and Fontalvo, (2022b), assure that the six sigma methodology is a powerful tool in the measurement of services, which guarantee the quality with a high level of statistical confidence and specific performance, in addition to a high level of accuracy and precision, which serves to perform an analysis of capacity and performance, so it is considered valid in several quality control laboratories.Likewise, Costa, A., Et al. (2019), Hariyani, et al., (2022), Canc ¸ado, et al., (2019) and Zhu, et al., (2019), consider six sigma as a very complete study methodology and that includes multiple tools and quality techniques for handling real or simulated data analysis projects, which allows researchers to quickly analyze any process.
Similarly, the authors Fontalvo, Herrera and Zambrano (2022c), as well as Kam, A., Et al. (2021), state that the six sigma methodology recognizes that there is a direct correlation between the number of defects and customer satisfaction, so its focus is on finding the most efficient combination Pesquisa Operacional, Vol.43, 2023: e270103 between both aspects, which implies that the process must be between 3>Z< 6, as can be effectively observed in the analyzed performances of Z in Table 2 and Table 3.For their part, Madhani (2022), Lamine (2022), as well as Fontalvo, Herrera and Zambrano (2022a), add that the sigma value indicates how often defects or malfunctions occur in the process.The higher the sigma level, the fewer defects or errors occur in the process.Thus, increasing sigma reduces the need for testing and inspection, increases process reliability, reduces quality costs and significantly reduces rework.
Meanwhile, authors Swain, et al (2018), Gupta, et al (2021), Steere, et al (2018), Johnson, et al (2019) andRandell, et al (2018), argue that six sigma is a tool that provides competitive opportunities, in today's dynamic, competitive and uncertain business environment, where continuous improvement of process and service quality can create sustainable competitive advantages.
From a multivariate approach to statistical quality control, other authors such as Casacci and Pareto (2022), Fontalvo, et al (2021a), andKhadse, et al (2021), in their studies have used multivariate capability indicators as an integral part in the evaluation of the quality dimensions of goods and services.Thus, showing the relationship between the actual performance of the process and the tolerance limits of customer specifications.In this sense, the author Morelos (2021) shows that the advantage of this multivariate method over the classical methods is that in many cases it reduces the complexity of the problem.Therefore, these latter investigations allow to evaluate the punctual, longitudinal and multidimensional performance of the object of study.This provides an additional measure of application similar to the one used in this research.

CONCLUSION
As a scientific contribution, this research work articulates the conception of the theoretical elements associated with the provision of service, as well as the conceptualization of the dimensions of quality and of the different departments of the public sector company, integrated with the six sigma metrics and the capacity indicators of multivariable statistical control.
Similarly, this research presents a structured and reliable methodology in the study of the quality of a public service company, through the analysis of the multivariate capacity indicators, supported by the six sigma metrics that allow evaluating the quality dimensions of the services in a more efficient way; these contributions will be useful to the business and academic environment in their future research.This is a topic that has not been worked on very much, even though it is of great relevance for the competitiveness and efficiency of the processes of the companies.
As a differentiating point, this research provides a novel and little worked method by the scientific community, which is indispensable in the creation of new ideas and the acquisition of new knowledge in the business, scientific and social fields.
On the other hand, the theoretical formulation of the six sigma metrics and the multivariate statistical control capacity indicators provide practical tools for evaluation, analysis and decisionmaking in-service companies, thus making it possible to meet the requirements of customers, while ensuring a better quality of life.The above is replicable at local, regional, national or international level in any public or private company.
As future research, the scientific community is invited to replicate the proposed method, considering other departments and other dimensions of quality, associated to a service provision, to measure performance in a periodic, punctual, global, longitudinal and integral way in the processes of public and private companies.
Finally, the use of the six sigma metrics, as well as the analysis of the multivariate capacity indicators, were a key point for the achievement of the objectives set out in the research, since they effectively allowed the evaluation of the stipulated quality dimensions.

Figure 1 -
Figure1-Operational units to be evaluated in the home Internet server company and their study metrics.

Table 1 -
Consolidated data related to the provision of services to citizens by the ministry's departments.

Table 2 -
Six Sigma metrics for the citizen service provided by the areas of the Ministry of Housing.

Table 3 -
Sigma level assessment and average performance by quality dimension.

Table 4 -
Multivariate Analysis Performance Criteria.