Jorge
Alberto Achcar
University
of São Paulo, Brazil
E-mail: achcar@fmrp.usp.br
Daniel
Marcos de Godoy
Universidade
de Araraquara, UNIARA, Brazil
E-mail: danielmarcosgodoy@hotmail.com
Submission: 5/27/2020 11:33:01 AM
Revision: 7/3/2020 3:57:30 PM
Accept: 7/14/2020 10:14:23 AM
ABSTRACT
The evaluation
of the service quality standard of a telecommunication company using
statistical process control (SPC) methods is the main goal of this paper. The
study used a dataset collected from January 2018 to November 2019 associated
with monthly and weekly customer complaint counts due to the technical services
provided by the company. Multiple linear regression models with the count data
transformed to a logarithmic scale and Poisson regression models with the
original count data detected some significant factors affecting the
weekly/monthly complaint counts. In addition, forecasts of future
complaint counts based on the statistical models could be of interest for the
company to plan the number of technicians in different sectors at different
times of the year leading to improvements in the service provided by the
telephone company.
Keywords: quality of services; complaint counts; multiple linear regression models; Poisson regression models; statistical process control
1.
INTRODUCTION
The great
technological advance, especially in the last decades, allowed
telecommunications companies to expand substantially their markets in economic
terms. Despite this advance, usually there are many everyday problems in a
telecommunication company, especially in customer services with many complaints
about the provided services. The present study has as main goal, the analysis
of service data and complaints from external customers of a telephone company,
investigating service failures, discovering factors that affect the complaint
counts and proposing suggestions for improvements, especially in the technical
service area. Studies on customer complaints are of great interest in companies
in different sectors (Anderson, Fornell & Mazvancheryl, 2004; Claro et al., 2014; Coelho
et al., 2016; Fornell
& Wernerfelt, 1987; Luo, 2007, 2009; Romani, Grappi & Dalli, 2012;
Singh & Wilkes, 1996; Singh, 1988). The research developed in a
telecommunications company, which operates in the central region of the São
Paulo state.
The
main goal of this study is to discover the significant factors affecting the
increase in repair complaints in a medium-sized municipality in the central
region of São Paulo state, Brazil, related to broadband services. The company
in the city has been operating since 2014 with the Optic Fiber product with
VOIP, Broadband and DTH/IPTV TV products. The Broadband product is the most
commercialized due to the high speed of the optical fiber with almost no signal
loss.
However,
the Broadband product, as the most commercialized one, is also the one with the
largest number of customer complaints. Some factors could affect the great
variability in the complaint counts related to the Broadband services. These
factors are into two classes: causes associated with customers (customer
cancels a visit, customer refuses a visit, customer found with different
complaints, customer equipment) and technical causes (Table 1).
Figure 1 shows the plots of the monthly percentages of complaints from the company customers
for the period from January 2018 to November 2019. Table 2 shows the complaint
counts corresponding to that period. Figure 1 and Table 2 show that the monthly percentages of complaints remain
reasonably high associated with different causes of complaints associated with
customers until July 2018 (month 7). From this month, there is a sharp drop.
From month 8 of 2018, there is a tendency for the number of complaints to
increase until the month 9 of 2019 (September 2019), when the number of
complaints associated with the causes due to customers starts to decline.
Regarding technical causes, it is
observed that the number of complaints remains approximately constant with a
decline at the end of the time series (last months of 2019), an indication of
improvement in the technical services provided by the company.
Table1:
Technical causes of customer
complaints
OTB
connection: it is a problem inside the Optical Transmission Box
(OTB). The OTB's are composed of 8 or 16 ports (if they are double counting boxes)
and the connector can present problems. In rare cases, the box own splitter may
be with malfunction. This type of occurrence affects the total functioning of
the customer's products.
Modem
exchange: it is about the equipment itself. The reasons may be
different. However, when the same type of equipment has too many problems,
there is a batch of equipment with problems. For reasons other than this, the
equipment itself for some reason does not synchronize the signal.
Customer
optical cord: a transition fiber comes out of OTP (Optical Transmission
Point) box. It is very thin and by any sharp movement (broom beating, pets or
children), is easily damaged.
Internal
component exchange: it is the coaxial cable or coaxial cable
connector or even the signal splitter that can present problems. Coaxial cable
is the same cable used in antennas. The connector is also the same as that used
for antenna cables. Signal splitter sends signal from the main point to more
rooms in the house / apartment / company.
Unconfigured
TI service: it is a type of error in the firmware update. The
equipment updates itself at systemically determined periods. Sometimes the
download fails and causes an error in the equipment where the synchronism is
lost and the signal does not return, requiring a row back or even changing the
equipment.
Bid customer
OTB: the external fiber that for some reason is broken and needs to be changed.
It may be a breakup due to collision with a high vehicle (cargo truck) or even
theft.
Figure 1: Complaint percentage time series
due to different causes
Table 2: Monthly percentages of
complaints due to various causes in the period from January 2018 to November
2019
Month |
Year |
Complaints |
%customers |
%equipment |
%others |
1 |
2018 |
522 |
0.197318 |
0.544061 |
0.258621 |
2 |
2018 |
440 |
0.172727 |
0.443182 |
0.384091 |
3 |
2018 |
325 |
0.393846 |
0.409231 |
0.196923 |
4 |
2018 |
379 |
0.477573 |
0.430079 |
0.092348 |
5 |
2018 |
468 |
0.423077 |
0.435897 |
0.141026 |
6 |
2018 |
458 |
0.386463 |
0.541485 |
0.072052 |
7 |
2018 |
475 |
0.345263 |
0.549474 |
0.105263 |
8 |
2018 |
529 |
0.043478 |
0.298677 |
0.657845 |
9 |
2018 |
590 |
0.200000 |
0.462712 |
0.337288 |
10 |
2018 |
749 |
0.209613 |
0.435247 |
0.355140 |
11 |
2018 |
531 |
0.209040 |
0.576271 |
0.214689 |
12 |
2018 |
533 |
0.172608 |
0.656660 |
0.170732 |
1 |
2019 |
523 |
0.164436 |
0.611855 |
0.223709 |
2 |
2019 |
544 |
0.191176 |
0.584559 |
0.224265 |
3 |
2019 |
580 |
0.237931 |
0.522414 |
0.239655 |
4 |
2019 |
568 |
0.248239 |
0.577465 |
0.174296 |
5 |
2019 |
833 |
0.301321 |
0.465786 |
0.232893 |
6 |
2019 |
733 |
0.429741 |
0.342428 |
0.227831 |
7 |
2019 |
865 |
0.576879 |
0.230058 |
0.193064 |
8 |
2019 |
738 |
0.588076 |
0.201897 |
0.210027 |
9 |
2019 |
688 |
0.421512 |
0.312500 |
0.265988 |
10 |
2019 |
797 |
0.357591 |
0.321205 |
0.321205 |
11 |
2019 |
764 |
0.357330 |
0.282723 |
0.359948 |
1.1.
Goals of the study
The main goals of this study are:
· To find from different statistical
methods, possible factors of the company's technical services that
significantly affect the complaint counts for the services provided.
· To get appropriate models in the presence
of the covariates mentioned above for the complaint counts to be used by the
company to improve the performance of the
technical services.
·
To get prediction failure counts that can assist the company to make better decisions.
The
article follows: section 2 presents a brief summary of service quality; section
3 presents a review of the literature on customer quality service complaints;
section 4 presents some remarks on statistical process control; section 5
presents the methodology and the data analysis; finally, section 6 presents a
discussion of the obtained results and concluding remarks.
2.
QUALITY OF SERVICES
In
telecommunications company services, customers in general expect good quality
of service and technical assistance. In this sense, Kotler and Armstrong (2003,
p. 475) point out that “Attracting and retaining customers can be a difficult
task. In today's world, even in third world countries, customers have at their
disposal a wide variety of products and brands, prices and suppliers to choose
their products”. In this way, quality of service or customer service is of
great importance for a company, since through good service, companies value
their image, attract and retain customers.
In
another study, Chiavenato (2007, p. 216) establishes that “the customer is
essential for the company to remain in the market and customer service is one
of the most important aspects of the business”. In a telecommunications company,
this relates to a good provision of technical services. It is interesting to
emphasize that a company's foundation relates to the customer. Albrecht and
Bradford (1992, p. 17), states that,
·
The customer is the most important person
in any type of business.
·
The customer does not depend on the
company. The company depends on the customers.
·
The customer does not interrupt our work.
It is the purpose of our work.
·
The customer does us a favor when he
enters in the company. We are not doing any favor waiting for the customer.
·
The customer is an essential part of our
business - not a disposable part.
·
The customer does not just mean cash in
the cash register. He is a human being with feelings, who needs treatments with
all respect.
·
The customer deserves all possible
attention and courtesy.
·
He is anybody's blood. He is the one who
pays our salary.
·
Without the customer, we would close our
doors.
3.
LITERATURE REVIEW ON CUSTOMERS
COMPLAINTS
Claro
et al. (2014) point out that consumer complaints affect the company's market
value and common sense suggests that a negative impact relates to customer
complaints. Low levels of complaints allow companies to increase market value,
while high levels of complaints increase damage to the market value. It is
important to note that consumers today have increasing access to the Internet
where negative or positive information reports at any time.
Usually
customer frustrations or unmet expectation spreads through social media where
complaints about a product or service reach a very large number of consumers,
which can affect a company's reputation (Martins & Julio, 2013; Coelho et
al., 2016; Anderson et al., 2004). It is important to point out that consumers
increasingly use social networks to conduct research on the quality
certification of a service or product, before making the purchase (Pimentel et
al., 2012).
Some
studies show that dissatisfaction can result in very negative images for
companies (Matos & Rossi, 2008; Singh & Wilkes, 1996; Trusov, Bucklin
& Pauwels, 2009), or can lead to complaints in public agencies (Singh,
1988). In many cases, it is possible for regulatory agencies such as ANATEL,
the regulatory agency that deals with all telecommunication problems in Brazil,
to maintain public records of complaints and assess the performance of
companies specially linked to public services based on the levels of consumer
complaints (Luo, 2009; Winchester et al., 2008).
Thus,
a company can become vulnerable to the level of complaints that influence the
market value of the company in a direct linear relationship (Luo, 2007, 2009)
or in a non-linear relationship. Some studies have analyzed the behavior and
background of complaints (Richins, 1983; Singh & Wilkes,
1996) and the direct linear effect on the company's market value (Chevalier
& Mayzlin, 2006; Goldenberg et al., 2007; Mittal et al., 1998; Romani,
Grappi & Dalli, 2012).
Sousa
(2011) emphasizes that competitiveness between companies, based on attracting
and retaining customers, has been increasingly encouraged. Customer
satisfaction levels has become a crucial task for the success and growth of
companies, which must be able to guide their activities towards the market,
thus generating widespread customer satisfaction. The satisfaction survey
conducted in that study allowed the identification of some aspects to improve
the service. In this process also was studied the existence of non-linear
relationships.
Kotler
(1998, p. 59) states that, "to understand the process of relationship with
the consumer, one must first examine the process involved in its attraction and
maintenance". According to this author, the great challenge for companies
is to turn potential consumers into customers. Many consumers can become
inactive or leave the company for some reasons, among them, dissatisfaction,
and the company must somehow reactivate dissatisfied consumers through new
specific strategies and tools to develop greater satisfaction and trust for the
customers. For Mahfood (1994, p.1), “most people who serve the public in some
way, whether they are salespeople, service installers, professionals, or even
public servants, to a certain extent, should try to satisfy the customers they
encounter ”.
Fornell
and Wernerfelt (1987) developed a mathematical model of the effects of
complaints management as a defensive marketing tool. These authors emphasize
that whenever the loss of revenue is greater than the cost, if a sufficiently
large proportion of claimants are convinced to remain customers, complaints
should be encouraged to improve the product or services.
Some
studies related to customer complaints consider questionnaires sent to
customers. In this way, Portaluppi et al. (2006) studied customer service and
satisfaction in an agricultural company based on data obtained by a
questionnaire. From a data analysis (descriptive statistics and graphs), it was
detected that in relation to the service, despite the company serving its
customers well, there are some needs, such as wishes and habits pointed out by
the customers. With the obtained results
from the study, it was possible to establish strategies to win back customers
with a lower degree of satisfaction. Thus, in view of the obtained results,
although the company had many positive responses from the customers, the
authors indicated some suggestions and recommendations to improve the service.
With the obtained results from the study, it was possible for the company to
strengthen its image in the market, because through the obtained results, it
was possible to correct flaws that could harm the business operations.
In
many studies, it is possible to analyze large amounts of complaint data
reported daily and recorded in company databases to discover time trends, discover
possible factors that may imply in large numbers of complaint counts and make
predictions, as is the case of the present study.
4.
STATISTICAL PROCESS CONTROL
Statistical Process
Control (SPC) is a set of procedures adopted to assess, maintain and improve
quality standards at the various stages of manufacture. These process control
procedures guarantee quality in an economical way. The control techniques that
define these procedures help to evaluate process patterns in terms of
dimensions and rework, as well as to study the behavior of the processes, that
is, to help to maintain appropriate quality standards.
If
it is not appropriate, corrective actions return the process to the desired
standard, helping to embed quality in the product and then exercising control
over the process. Gimenes et al. (2013) point out that the use of statistical
methods has shown its efficiency in the control of production processes showing
whether the product is within a degree of compliance or not, based on an
established control parameter.
Melo
et al (2019) report that SPC is a preventive methodology to compare results
with an already established standard and, through additional statistical
techniques, to eliminate or at least control extra variability. In all
production processes, disturbances occur, regardless of the exceptional quality
design and/or maintenance. Melo et al (2019) citing Montgomery (2012), explain
that the variability is:
a)
Random or common causes of variation: they
are intrinsic to the process and arise, in general, from incorrectly adjusted
or controlled machines, operational failures or defective raw material. They
are generally difficult to perceive and are part of a constant system of
variations. However, the process can still work without causing defective
products. A process that has only random causes is under control.
b)
Attributable or special causes of
variation: they have much greater sources of variation than natural
variability, and usually represent an unacceptable level of process
performance. The process that contains them is out of control; we need to
identify and correct the attributable causes.
According
to Carvalho and Paladini (2005), the concept of statistical process control
(SPC) is that processes with less variability enable better levels of quality
in production results, in addition to reducing costs. On the other hand,
Montgomery (2012) states that many organizations believe that it is difficult
and costly to provide products with the same quality characteristics to the
customer.
5.
METHODOLOGY AND DATA ANALYSIS
Weekly
counts of service complaints provided by the company are considered for the
study (Figure 2) consisting of a time series of 119 weeks (between January 1,
2018 and April 30, 2020). Figure 2 shows that there is apparently a temporal
growth in complaint counts and some seasonality.
Associated
with the weekly counts, there are several covariates: customer causes (customer
cancels visit, customer refuses visit, customer found with various complaints,
customer equipment) and technical causes (modem exchange count, customer optic
cord count, internal component exchange count, unconfigured TI service count,
customer OTB bid count), month and year.
Figure 2: Weekly complaint count series
(2018/2019)
In
the statistical data analysis it was considered n = 117 observations, since two observations with missing
covariate information were deleted from the initial sample of size 119. The dispersion diagrams presented in Figure 3 show
that apparently the covariates due to causes associated with customers given by
customer refuses to visit and customer equipment and the covariates associated
with technical factors given by OTB
connection, OTB customer bid, unconfigured
TI service, internal component exchange and modem exchange affect the complaint
counts. The covariate customer optical cord apparently has no effect on the
response, that is, an increase of complaints due to the technical customer
optical cord does not lead to an increase in the
number of weekly complaints.
5.1.
Use of a linear regression model with
normal errors for the weekly complaint counts transformed to the logarithmic
scale
Although the data are weekly counts, a first statistical analysis assumes
the response data transformed to a logarithmic scale, that is log(complaint count),
to verify the possible association between each covariate with the response complaint
count in each week using usual linear regression models for continuous data assuming
a normal distribution for the errors (Montgomery
& Runger, 2011).
(a) Covariates associated with customers
(b) Covariates associated with
technical factors
Figure 3:
Dispersion diagrams
Initially,
simple linear regression models (presence of only one covariate x) in presence
of linear and quadratic effects affecting the response (the choice of this
model was based on the graphs presented in Figure 3, where linear effects and
sometimes curvature effects are observed) are considered in the form,
Yi = log (complaint
count) = β0 + β1 xi + β2 + εi
, (1)
The
errors εi are assumed
to be independent unobserved random variables with normal distribution N (0, σ2),
i =1, …, 117. Associated with each case, we used hypothesis tests to verify
whether the regression coefficients (linear effect and quadratic effect) β1
and β2 are statistically equal to zero. The needed assumptions
(normality and constant variance for the errors) were verified using residual
graphs. Using the Minitab® statistical software, the model fit (1)
is obtained using least squares estimation methods to get the estimators of the
regression parameters β0, β1 and β2
considering the different covariates individually and the p-values for each
case. The significant
covariates affecting the number of complaints are:
· Client covariates: client canceled a visit
(linear and quadratic effects at a significance level of 5%; p-value <
0.05); client refused to visit (linear and quadratic effects at a significance
level of 5%; p-value < 0.05); customer found with complaint (linear effect
at a significance level of 5%; p-value < 0.05); (4) client equipment (linear
and quadratic effects at a significance level of 5%; p-value < 0.05).
· Technical factors covariates: change of
modem (linear and quadratic effects at a significance level of 5%; p-value <
0.05); client optical cord (linear effect at a significance level of 5%;
p-value < 0.05); internal component exchange (linear and quadratic effects
at a significance level of 5%; p-value < 0.05); (4) unconfigured TI service
(linear effect at a significance level of 5%; p-value < 0.05); (5) customer
OTB bid (linear and quadratic effects at a significance level of 5%; p-value
< 0.05); (6) OTB connection (linear and quadratic effects at a significance
level of 5%; p-value < 0.05).
A
second statistical analysis assumed a multiple linear regression model in the
presence of all covariates (covariates associated with customers and technical
covariates) and temporal covariates (months and years). The needed assumptions
(normality and constant variance of the errors) were verified using residual
graphs. Using the Minitab® statistical software, we have the
following fitted model:
log (complaint number)) =
208 + 0.00671 customer.cancels.visit
+ 0.0117 customer.refuses.visit + 0.02642customer.found
+ 0.01233 customer.equipment
+ 0.0105 OTB.connection (2)
+ 0.0054 customer.optical.cord
+ 0.0168 Bid.customer.OTB
+ 0.01405 unconfigured.TI.service
+ 0.0229 internal.component.exchange + 0.01668
modem.exchange
- 0.102 year
- 0.0060 month
From
the obtained results, the covariates that are significatives, that is, the
regression parameters associated with each covariate are statistically
different of zero (p-value < 0.05), are the customer found with complaints,
customer equipment, modem exchange, exchange of internal component and TI
configuration service.
5.2.
Use of a Poisson regression model for
weekly complaint counts
Another possibility in the analysis of the weekly complaint count data
is to assume a Poisson regression model in the original scale (count). Poisson
regression is a form of generalized linear model of regression analysis used to
model count data (Montgomery & Runger, 2011). Poisson regression models
assume that the response variable Y has a Poisson distribution and assumes that
the logarithm of its expected value is modeled by a linear combination of
unknown parameters. Let Yi (complaint count in the i-th week, i = 1,
2, ..., 117) denoting a random variable with a Poisson distribution,
P (Yi=
ni) =
(3)
where ni denotes the observed
number of complaints in the i-th week, ni = 0, 1, 2, .....; i = 1,2,
..., 117. The mean and variance of the Poisson distribution (3) are equal to
μi.
Associated
with each week, it is assumed a regression model for the μi
parameter in the presence of the covariates customer cancels visit, customer
refuses visit, customer found with different complaints, customer equipment,
modem exchange count, client optic cord count, count internal component
exchange, TI service count, customer OTB bid count, month and year, given by,
μi = exp{ β0 + β1customer.cancels.visiti
+ β2customer.refuses.visiti
+ β3customer.foundi
+ β4customer.equipmenti
+ β5OTB.connectioni
+ β6customer.optical.cordi
+ β7Bid.customer.OTBi
+ β8unconfigured.TI.servicei
+ β9internal.component.exchangei
+
+ β10modem.exchangei +
β11yeari + β12 monthi} (4)
We
obtain the estimators of the regression parameters β0, β1,
β2, β3, β4, β5,
β6, β7, β8, β9,
β10 and β11 using the maximum likelihood method
(Montgomery & Runger, 2011). From the obtained results (Table 3) using the
Minitab® statistical software, the significative covariates, that
is, with regression parameters associated with each covariate that are
statistically different from zero (p-value < 0.05) are: client canceled
visit , customer refuses to visit, customer found with complaint, customer
equipment, modem exchange, internal component exchange, defaced TI service,
customer OTB bid and month.
We
observe that the Poisson regression model is more sensitive to detect the
significant covariates affecting the company's weekly complaints counts. With
these results, the company administrator has an excellent diagnosis of the
technical services sectors that increase the complaints counts. Thus, several
improvements and modifications will reduce the complaint counts.
The
fitted regression model for the average number of complaints is given by, exp
(Y') where,
Y' = - 63.1
+ 0.00753 customer cancels a visit
+ 0.00572 customer refuses a visit
+ 0.01936 customer found
+ 0.009055 Customer equipment
+ 0.00481 OTB connection
+ 0.00516 Customer optical cord
+ 0.01413 Bid customer OTB
+ 0.01176 Unconfigured TI service
+ 0.01872 Internal component exchange (5)
+ 0.01299 Modem exchange
+ 0.0331 year + 0.01101 month
We can get predictions from the fitted model (5).
Figure 4 shows the graphs of the observed and predicted counts using model (5),
indicating an excellent fit of the Poisson regression model to the data.
Figure 4: Graphs
of observed counts and predicted by the model (5)
Table 3. Maximum likelihood estimators (MLE), standard errors of the
estimators and p-values (Poisson regression)
Parameter MLE SE p-value |
Constant -63.1
72.8 customer cancels visit 0.00753 0.00147 <
0.001 customer
Refuses Visit 0.00572 0.00263 0.030 customer
found 0.01936 0.00225 <
0.001 customer
equipment 0.00905 0.000481
< 0.001 OTB
conection 0.00481 0.00279 0.085 customer optical
cord 0.00516 0.00343 0.133 customer OTB
bid 0.01413 0.00300 <
0.001 defaced TI servisse 0.01176 0.00147 <
0.001 internal component exchange 0.01872
0.00260 <
0.001 Modem exchange 0.01299 0.00116 <
0.001 Year 0.0331 0.0360 0.359 Month 0.01101 0.00343 0.001 |
6.
DISCUSSION OF THE OBTAINED RESULTS
AND CONCLUDING REMARKS
The
obtained results from the different statistical analyzes associated with the telephone
company's complaint counts can be of great interest to the company.
The
multiple linear regression models with normal errors with the responses
(complaint counts transformed to the logarithmic scale) and the Poisson
regression model can be used in predictions for complaint counts once the
levels of the covariates have been fixed with a slight advantage for the
Poisson regression model for discrete data without the need for transformations
with direct interpretations for company administrators.
From
the regression analysis, we discovered some factors that are affecting the time
counts of complaints: customer canceled visit, customer refuses visit, customer
found, customer equipment, modem exchange, internal component exchange, TI
defaced service, bid customer OTB. These results can be of great interest to
the telephone company.
It
is important to point out that times series models as the moving average time
series (MA) models and ARIMA models (Morettin & Toloi, 1987; Box et al.,
2015; Ho & Xie, 1998; Akgun, 2003; Bell, 1984) are existing alternatives
for the data analysis. These models should be build in each application, which
can be an unfavorable point for the companies, despite
leading to good forecasts.
Figure 5
shows the graphs for the observed and fitted time series by an ARIMA (2,2,2)
model using the Minitab® software. It is observed that there is
similar fit using the ARIMA and the Poisson regression models (see Figure 4). A
great advantage for the use of the regression models (linear multiple
regression model for the number of complaints by week in logarithmic scale and
the Poisson regression model) besides good fit,
is the discovery of important factors that affect the response (number
of complaints per week) that are of great interest for the company to improve
its performance.
Figure 5: Graphs of the observed and fitted counts by the ARIMA (2, 2, 2)
model
Another statistical analysis also was assumed using monthly compositional
models (see Table 1 and Figure 1). Denoting % complaints due to customers,%
complaints due to technical problems and % complaints for other causes
respectively for x1, x2 and x3, we have a
restriction on the data x1 + x2 + x3 = 1,
which makes it impossible to use the usual multivariate analysis techniques
assuming a normal multivariate distribution (Johnson & Wichern, 1998).
Thus, an additive ratio log (LRA) transformation model proposed by Aitchison
and Shen (1985) was considered given the responses given by y1i =
log (x1i / x3i) and y2i = log (x2i
/ x3i), and the following regression models,
Yji = β0j + β1jcustomer.cancels.visiti + β2jcustomer.refuses.visiti + β3jcustomer.foundi
+ β4jcustomer.equipmenti
+ β5jOTB.connectioni
+ β6jcustomer.optical.cordi
+ β7jBid.customer.OTBi
+ β8junconfigured.TI.servicei
+ β9jinternal.component.exchangei
+
+β10jmodem.exchangei+β11jyeari+β12j monthi+εji
(6)
where j = 1, 2; εji are assumed independent errors with normal
distributions N (0, for j = 1, 2.
Associated with model (6),
the following covariates were found (using the Minitab® software) as
significatives (p-value < 0.05) in response y1i: client canceled
visit, client refused visit, found with complaint, client equipment, connection
OTB, customer's optical cord, unconfigured TI service and modem exchange.
Likewise, the following covariates were found to be significatives in the y2i
response (p-value < 0.05): customer canceled visit, found with complaint,
customer's equipment, unconfigured TI service, internal component exchange and
modem exchange. Thus, we have significative covariates similar to those found
in the multiple linear regression analysis assuming transformed responses in
the logarithmic scale.
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