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International Journal for Quality Research 15(3) 1007–1022

ISSN 1800-6450

1 Corresponding author: Nayara Nicole de Sene Pereira

Email: [email protected]

1007

Nayara Nicole de Sene

Pereira1

Evandro Eduardo

Broday

Article info:

Received 24.03.2020.

Accepted 15.07.2020.

UDC – 005.6

DOI – 10.24874/IJQR15.03-20

APPLICATION OF CONTROL CHARTS

FOR MONITORING THE WAIT ING TIME

IN A BASIC HEALTHCARE UNIT IN

BRAZIL

Abstract: Brazilian public healthcare service is highly

demanded. However, the system has been through a restrained

scenario, with a long waiting time to have a doctor’s

appointment and scans. This research aims to analyze the

waiting time in the services of a Basic Healthcare Unit (BHU)

in a small city in the state of Sao Paulo, Brazil, by using

statistical control charts. The field research relays on

Taguchi’s loss function smaller-the-better, in other words, the

shorter the waiting time for patients, better is the perception of

quality. A direct observation was carried out in order to

acquire the patients’ waiting time for a medical appointment

and to evaluate the quality of the service. The patient waiting

time was monitored with Control Chart for Individual

Measurements and Moving Range and then it was determined

the capability of the service by using the 𝐶𝑝𝑘 index. It was

concluded that the service is inefficient based on Process

Capability Index (𝐶𝑝𝑘=-0.15), being the average waiting time

for a doctor’s appointment around 121.88 minutes

(approximately 2 hours).

Keywords: Quality Management; Control Charts; Public

Health Service; Waiting Time.

1. Introduction

The Brazilian Constitution (1988) says that

access to healthcare is a right of all Brazilian

citizens, either through the National Health

Service, which is the public service offered by

the government, or through private

agreements with private companies.

According to Tieghi (2013), the National

Health Service serves 200 million people, of

which 152 million are exclusive users of this

system. Brazil has more than 6000 hospitals,

45000 Basic Healthcare Units (BHU) and

30300 family health teams.

It is evident, then, that public health services

are the most demanded by the population.

However, the system has flaws in its main

programs and, as a consequence, there are

crowded hospitals, lack of manpower, lack of

training for professionals and problems

related to National Health Service financing

(Rossi, 2015). Thus, preserving a free

universal health system is an obstacle for

Brazil, mainly due to its territorial extension

(Tieghi, 2013).

These flaws can also be evidenced through

research carried out by the Brazilian Institute

of Geography and Statistics (IBGE) (2015),

which points out that 40.4% of the population

cannot get care due to the absence of doctors

and dentists, 32.7% do not have access to a

BHU, 6.4% do not find specialized

professionals to attend, 5.9% waited a long

time and gave up, 2.3% due to unavailability

1008 N.N.S. Pereira, E.E. Broday

of equipment, 2.1% due to the health service

not working, 0.5% for not being able to pay

for the consultation and 9.7% for other

reasons.

Al-Shdaifat (2015) conducted a survey where

TQM (Total Quality Management) was

implemented in hospitals in Jordan. Results

showed that less than 60% of hospitals

implemented, being the main principle to be

implemented costumer focus. Kalaja et al.

(2016) conducted a study at the regional

public hospital in Durrës, Albania, and

reported that healthcare is on the rise in the

country, receiving the attention of researchers

and doctors, due to deficiencies that the sector

faces and the challenges to be overcome. This

situation is very similar to that faced by

Brazil, which also faces deficiencies in the

sector.

In this way, quality tools can help the

limitations of the health sector. Control charts

are an example of a quality tool used in this

sector. According to Fry et al. (2012), even

though these graphs have been developed to

assist manufacturing quality control, control

charts have been suggested for assessing

clinical outcomes. It can be shown that

Statistical Process Control (SPC) can bring

many benefits to the health sector, reducing

waste, reducing costs and making better use

of resources, in order to prioritize patient

satisfaction. In order to bring benefits to the

services, the use of quality methods is

increasing, concerned with the quality of

service and improvements, with the consumer

satisfaction as the main goal (Rosa and

Broday, 2018).

The present research sought to evaluate the

capability of the Health System, based on the

Cpk index, in a small city in the state of Sao

Paulo, Brazil. The patients’ waiting time was

monitored with Control Charts for Individual

Measurements and Moving Range using data

from the waiting time of patients collected in

a Basic Healthcare Unit.

2. Literature Review

2.1. Statistical Process Control (SPC)

Statistical Process Control (SPC) is focused

on quality improvement processes. This

refers to the use of statistical methods, in

order to monitor and supervise a process so

that it can produce a product according to

predetermined specifications (Madanhire and

Mbohwa, 2016).

According to Costa, Epprecht and Carpinetti

(2005) the intermittent control of the

processes is the minimum condition to

maintain the quality of the goods and services

offered. Therefore, quality is paramount in

processes and services. Montgomery (2009)

states that the process of awareness of the

need and the insertion of formal methods and

tools to obtain control aimed at improving

quality are progressive procedures.

SPC brings several benefits to organizations

that use it. Nordström et al. (2012) point out

that one of the benefits is that it allows a

quantitative analysis of the variability of the

process, with emphasis on the early

verification and prevention of possible

problems. According to Ho and Aparisi

(2016), intervening in the production process

seeks to minimize the production of

nonconforming items.

For Montgomery (2009), the evolutionary

process of this tool had its origin with

Frederick W. Taylor with his first studies of

division of tasks, which led to improvements

in productivity and work patterns. These

studies, however, sometimes took the focus

away from the characteristics of the quality of

work, thus opening gaps in aspects of quality,

product and the work developed. Thus, it was

only in 1924 that SPC started with the

development of control charts by Walter

Shewhart at Bell Telephones Laboratories.

According to Fry et al. (2012), Shewhart

noted the existing variability in the processes

and developed the charts in order to

understand and improve the production

processes.

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According to Ahmad et al. (2014), the control

charts assist in the investigation of the process

and in the differentiation of control and out-

of-control situations for different parameters

of interest. From this tool, it is possible to

state whether or not a process is under

statistical control. Dupont et al. (2014) claims

that a process will be in statistical control

when the value of its indicator varies between

the lower and upper control limits. If it

crosses one of the limits it will express the

presence of a cause to be investigated,

corrected and used for future improvements.

Fry et al. (2012) state that Shewhart divided

this variation in two ways: variations of

common causes and variations of special

causes.

Common causes are an intrinsic part of the

process, that is, a process that operates with

these causes will be under statistical control.

Special causes are when internal or external

failures occur in the processes. Montgomery

(2009) complements stating that these causes

can come from machines adjusted or

mistakenly controlled, errors by the operators

or even defects found in the raw material,

being this out of statistical control.

Nordström et al. (2012) state that there are

several types of control charts and the

selection of the most suitable becomes a

difficult task. This scope made it possible to

reach new areas: the control charts at the

beginning were exclusive to industrial

processes, currently they are not limited to

this sector, they are also used in the service

sector (Nascimento and Broday, 2018).

Control charts can be divided into attributes

(quality characteristic that cannot be

measured on a continuous scale) or variables

(everything that can be measured on a

continuous scale).

Shewhart Control Charts for Individual

Measurements and Moving Range were used

in this study, since the goal is to monitor one

variable (waiting time). This chart is used

when the sample size is equal to 1. For the I-

MR graph the moving range is given by

Equation 1 (Montgomery, 2009):

𝑀𝑅𝑖 = |𝑥𝑖 − 𝑥𝑖−1 | (1)

Equations 2, 3 and 4 present the control limits

for the individual measurements chart:

𝑈𝐶𝐿 = �̅� + 3 𝑀𝑅̅̅ ̅̅̅

𝑑2

(2)

𝐶𝑒𝑛𝑡𝑒𝑟 𝑙𝑖𝑛𝑒 = �̅� (3)

𝐿𝐶𝐿 = �̅� − 3 𝑀𝑅̅̅ ̅̅̅

𝑑2

(4)

where:

UCL = upper control limit;

LCL = lower control limit;

MR = moving range;

d2 = constant value.

The moving range chart has center line 𝑀𝑅̅̅̅̅̅

and the Upper Control Limit as UCL =

D4𝑀𝑅̅̅̅̅̅. In this graph, normally, LCL = 0.

When using control charts for individual

measurements, Montgomery (2009) claims

the importance of performing a Normality

Test, since this chart is sensitive to lack of

normality. In order to obtain the potential

capability, Cp index is used as shown in

Equation 5:

𝐶𝑝 =

𝑈𝑆𝐿 − 𝐿𝑆𝐿

6𝜎

(5)

where:

USL = upper specification limit;

LSL = lower specification limit;

𝜎 = standard deviation.

As can be seen in equation 5, Cp does not take

into consideration where the process mean is

located relative to the specifications.

Equations 6, 6.1 and 6.2 present the index Cpk

(minimum value between Cpu and Cpi) that

takes process centering into account:

𝐶𝑝𝑘 = min (𝐶𝑝𝑢, 𝐶𝑝𝑙) (6)

𝐶𝑝𝑢 = USL − 𝜇

3𝜎

(6.1)

𝐶𝑝𝑖 = 𝜇 − 𝐿𝑆𝐿

3𝜎

(6.2)

1010 N.N.S. Pereira, E.E. Broday

By using the Cp index, it is possible to obtain

the potential capability, that is, how much the

process uses its capacity according to

specification limits. While the Cpk index

measures the effective (real) capability of the

process, it then checks whether the activity is

centered or not. Thus, the degree of similarity

between Cp and Cpk has direct relation and

indicates the magnitude of the centrality of

the process (Montgomery, 2009).

2.2 Service Sector

Service sector has been gaining a large space

within today's society. Borges (2007) states

that it is possible to visualize the growth of

this sector in recent years, as well as its

contribution to the growth of the economy. In

this way, it is possible to define the

importance of services since it has a major

contribution to the Gross Domestic Product

and in the generation of jobs in developed and

developing countries, including Brazil.

For Kotler, Hayes and Bloom (2002), services

originated in the Middle Ages with

professions focused on the law, since these

together with the armed forces and the church

were an acceptable social way of earn a

living. The growth took place in the 16th

century, with new professions originating

from capitalism and the increase in industrial

technology. Over time these activities have

been improving and diversifying to escape

from the market competition.

Meesala and Paul (2018) state that the

concession of high-quality services is the

basis for success in the service sector.

Services can range from renting hotel rooms,

making deposits at banks, consulting doctors,

getting a haircut, traveling by plane, renting

movies, etc. They may include physical

components such as meals or not include

physical components, such as consultancy

services (Kotler, Hayes and Bloom, 2002).

In this way, it is possible to perceive the

intangibility, simultaneity and the

participation of the customer throughout the

process in the service sector. For Grönroos

(1990), the service refers to the activity or set

of activities with a usual relationship between

customers, employees, physical resources or

goods and service providers, and may be

intangible in nature with the aim of solving

customer problems. Services are intangible

because they are experienced by customers,

while products can be purchased. As a result,

the evaluation of quality becomes more

complex for the customer, as it is based on the

opinion of third parties and the image of the

company, which is responsible for the service

provided (Carpinetti, 2012).

Customer has a role in the service process,

since the consumer is present in the front

office of the companies, thus the quality of the

service provided is influenced according to

the environment where it is offered. The

services are simultaneous due to the lack of

an intermediate stage between production and

delivery. Thus, services cannot be stored, that

is, when the productive capacity of the system

is not used, it will be wasted and lost forever

(Fitzsimmons and Fitzsimmons, 2014).

The service sector also has a service package

that must be offered to the customer, and this

refers to a set of products and services, which

are offered in a given environment and have

five aspects, as shown in Table 1.

Hora, Moura and Vieira (2009) emphasize

that organizations and companies must aim

for the excellence of the services provided,

aiming at satisfaction and even exceeding

customer expectations. The service provider

system should be able to meet these

expectations in a short time, since it is in

relation to them that the service will be

judged. Minimizing customer waiting time

makes it possible to improve the quality of

service and increase satisfaction with the

service (Nascimento and Broday, 2018).

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Table 1. Service Package (Adapted from Fitzsimmons and Fitzsimmons, 2014)

Aspect Characteristic Example

Support

Facilities

Physical resource needed to offer the

service Hospital, Airplane, Mall

Facilitating

Goods

Items to be offered or purchased by

customer Snacks during the flights, meals

Informations

Offered to the customer or supplier, in

order to obtain an effective and

customized service

Information on hotels in the region, medical

records, seat availability, GPS location

Explicit

Services

Inherent and essential characteristic

perceived by the customer

Car runs smoothly, no pain after medical

procedure, waiting time for firefighters after

an emergency call

Implicit

Services

Features beyond the service, that is,

psychological advantages perceived by

the customer

Status obtained after obtaining a degree,

privacy obtained by a credit company

2.3 Healthcare Services

Despite the fact that healthcare services may

be private or public origin, Kalaja et al.

(2016) claim that is important measuring,

evaluating and monitoring the quality of

health services. Mohebifar et al. (2016) state

that since the 90s one of the methods to

measure patients' perception of the quality of

the health service provided takes into account

satisfaction.

Thus, Kalaja et al. (2016) state that the sector

that targets health care is a growing sector

receiving attention from doctors and

researchers. Caldwell (2008) reports that one

of the goals of improving quality in relation

to healthcare is through the increase in human

factors engineering and systems engineering

principles in the predominance of adverse

events.

Meesala and Paul (2018) claim that hospitals

seek to identify the most critical factors and

that solving and managing these problems

will guarantee survival and success in the

future, and that it is necessary to identify

strategic factors. But, in addition, it is

necessary to have the satisfaction of your

patients in order to ensure the quality of the

service. It is important than to identify the

specific characteristics of a service so that

they contribute especially to patient

satisfaction, with which the hospital can focus

on these characteristics.

Mohebifar et al. (2016) add that customers

(patients) assess quality by comparing their

expectations with understandings of actual

performance. If the patient's understanding

exceeds their expectations, then the services

provided are of a high quality. However,

Senot et al. (2016) state that patients have

different needs in a hospital environment,

varying in relation to severity, such as a

simple cold, heart attack, fracture, among

others. Thus, quality is a multidimensional

concept, but it has customer satisfaction as

one of the essential aspects that reflects the

quality of service in a hospital environment.

Greer et al. (2014) claim that the perceptions

of service quality of customers and service

providers may not be aligned, as in the

perception of employees they may judge that

there was no failure, that is, that the service

was delivered with quality.

Many companies in the manufacturing or

service sector use quality management and

quality assurance as a way to achieve the

desired quality of their product or service and

meet customer needs and expectations. Rath

(2008) reports that in order to have a

successful management and quality

assurance, it is necessary to focus on the

processes and empower the people involved

in it with the necessary tools and give them

the responsibility to improve the quality of

the service. However, this approach is not

adopted due to the non-use or misuse of the

1012 N.N.S. Pereira, E.E. Broday

proposed tools; most organizations adopt

only the removal of the defective product or

rework or hope that there will be a failure so

that they can subsequently search for its

causes so that they do not occur again.

Thus, service companies in the health sector

seek tools with the objective of improving the

quality of the services provided, thus

obtaining greater satisfaction from their

customers. As reported by Plantier et al.

(2017), the processes of using quality

indicators in hospitals are being encouraged

as a way to assess quality in these

environments in order to improve the quality

care and patient safety.

3. Methods

3.1 Data Collection

Waiting time data were collected in a BHU in

a small city located in the state of Sao Paulo,

Brazil. This city is located in the

administrative region of Bauru, as shown in

Figure 1.

Figure 1. BHU’s Location (Adapted from

Portalpower, 2016)

The city has five HBUs strategically

distributed to serve the residents and anyone

in the city can have access to these units. They

operate from Monday to Friday from 7am to

5pm. The HBU has a team of six nursing

technicians, one nurse, three janitors, one

pharmacy technician, five community agents,

one dentist, one speech therapist, one

psychologist and eight doctors, being: an

otorhinolaryngologist, an orthopaedist, a

cardiologist, a gynecologist, two

pediatricians, a gastroenterologist and a

general practitioner.

Among the services offered in the HBU, there

are consultations and scans such as

electrocardiogram, rapid tests, PAP test and

vaccination, which are performed weekly.

Medical, dental, psychologist and speech

therapist consultations work with

appointments. In this case, the system is

computerized, when the patient arrives, a

number is generated in order of arrival, then

it goes through a pre-consultation, only to

perform the scheduled consultation

afterwards. Vaccination works under the

condition of scheduling or spontaneous

demand, whereas rapid tests and PAP tests are

performed by means of scheduling with a

password.

Regarding the population, patients can come

from all regions of the city, however due to

the presence of more units in the city, the

majority of them serve an audience from the

nearest neighborhoods. Only people who had

preferential care were not counted for the

study, since their time at the UBS is reduced.

Regarding sex, both genders will be included

in the research, since there is no distinction in

treatment in relation to waiting time.

3.2 Data Analysis Procedures

After obtaining the waiting time of patients at

the HBU, two types of analysis were

performed: a qualitative analysis and a

quantitative analysis. The qualitative analysis

was made using the Ishikawa Diagram, in

order to verify the reasons for the waiting

time in the analyzed HBU being so high. The

Kolmogorov-Smirnov normality test was

performed, with 95% confidence, using the

SPSS 23 software. After verifying the

normality of the data, the control charts of the

individual measurements and moving range

were then constructed, in order to perform a

quantitative analysis.

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For the control chart for individual

measurements, the parameters were

calculated using equations 1-4, as described

in section 2.1. Calculations can be performed

using �̅� which is the mean, MR which is the

moving range and d2 which is a constant value

according to the number of observations in

the sample. Since the sample size is one, d2

always takes the value of 1.128. In order to

perform the moving range calculation, sample

must take two by two.

It is noteworthy that for this research,

Taguchi’s loss function smaller-the-better is

used, because smaller the time the patient

waits to be seen, the better it will be for the

quality perception. For the preparation of the

control charts, Action Stat 3.2 was used.

Subsequently, from the waiting times, the

UCL (Upper Control Limit), CL (Center

Line) and LCL (Lower Control Limit) were

calculated. In this way, it was possible to

carry out a more detailed analysis

.

Finally, the effective process capability index

(Cpk) was calculated. In this situation, it has

only the upper specification limit (USL),

since there is no minimum value for the

patient to wait for a medical consultation. So,

there isn’t a lower specification limit. As an

upper limit of specification, the waiting time

was considered, since in Brazil there is no

legislation determining the maximum waiting

time for patients in the HBU.

4 Data Analysis and Discussion

4.1 General Data

Sixty patients who would have medical

appointments in the three days of field study

were analyzed (otorhinolaryngology (A),

pediatrics (B), orthopedics (C), dentistry (D)

and general practitioner (E)). Through the

waiting times obtained, it was possible to

perform a statistical analysis by medical

specialty and a general value for the HBU, as

shown in Table 2.

Table 2. Mean Waiting time (The Authors, 2020)

Statistical Analysis by medical specialty

A B C D E HBU

Sample (n) 12 12 11 7 18 60

Minimum waiting

time (min) 50 125 33 101 40 33

Maximum waiting

time (min) 200 255 275 260 194 275

Mean waiting time

(min) 114 187 110 159 100 134

Standard

Deviation (min) 42.91 42.72 78.22 59.82 40.09 60.78

When observing data in Table 2, it is possible

to conclude that the specialty that obtained the

longest average waiting time was Pediatrics.

It is also noted that pediatrics and dentistry

have an average waiting time greater than the

average waiting time at the BHU in general.

It was also concluded through Table 2 that

orthopedics is the specialty that has the

shortest minimum waiting time; however, it is

also the one that has the longest maximum

waiting time. Consequently, it is the specialty

that has the highest standard deviation.

1014 N.N.S. Pereira, E.E. Broday

Figure 2. The Ishikawa Diagram (The Authors, 2020)

4.2 Ishikawa Diagram

To better understand the reasons that

generates a long waiting time, the Ishikawa

Diagram was used, with the main objective of

listing the root causes of this problem. The

Ishikawa Diagram is illustrated in Figure 2.

Possible main causes for the problem were

divided in the following categories:

measurement, method, manpower,

machinery, mother nature and materials.

From these causes and the conversations with

patients at the HBU, it was possible to obtain

the secondary causes that originated the main

problem. In relation to the mother nature

(environment), it was possible to list the lack

of structure as secondary causes, since there

is no infrastructure for the queues before and

when opening the HBU. Lack of material and

financial resources, because if there was a

password system when the patient arrives at

the HBU it could be easier to organize the

screening and with that the service would be

faster. The screening time increases the

patient's waiting time and occurs on the same

day as the consultation. As, for example, in

the case of pediatric consultations, children

must be weighed beforehand, so this

weighing could occur on the previous day in

order to optimize services on the day of the

consultation.

Regarding to the manpower, the secondary

causes related are the lack of professionals,

their delay and even the lack of specialties. In

view of the high demand for people, it appears

that there is a lack of professionals to serve

everyone, as well as specialties. The HBU in

question has only an otorhinolaryngologist,

gastroenterologist, orthopedist, pediatrician

and gynecologist, when interviewing the

patients, they reported the need for more

specialties such as dermatologists, urologists,

neurologists, among others, as well as more

doctors of the specialties already offered.

The method, that is, the way services are

offered at the HBU stands out as secondary

causes for political changes, which refer to

the strategy that will be adopted by the health

department. In addition to problems already

addressed, such as lack of organization, since

patients line up outside the HBU, however

when it opens the first in line, it is not always

the first to be attended. As well as, the lack of

passwords and inadequate scheduling, since

more appointments are often scheduled than

the medical service hours tolerate.

In relation to the measurement, the

complementary causes are attributed to the

lack of prioritization, that is, in addition to

scheduling, a new prioritization scale could

1015

be created according to the urgency of the

service according to the patients' symptoms

and with that the assistance would be more

agile. As well as, the operation above

capacity, that is, due to the high demand,

doctors are few for the number of patients to

be treated.

In addition, old equipments to perform the

exams and the lack of some basic materials,

such as gloves and masks, complete the

problems that make the waiting time so long.

In this way, it is possible to attribute the long

waiting time to the most varied causes and

with this setting priorities in order to

eliminate root causes.

4.3 Normality Test

In order to be able to use the Control Charts

for Individual Measurements and Moving

Range, data must be normal. Therefore, the

Kolmogorov-Smirnov normality test, with

95% confidence, was performed. The results

obtained are shown in Table 3.

Thus, it is observed through the software

result table that the data have a normal

distribution, since the significance is greater

than 0.05 (0.089 > 0.05). Therefore, data can

be used to build the control charts for

individual measurements and moving range.

Table 3. Kolmogorov-Smirnov test for data

Waiting

Time

N 60

Normal

Parameters

Mean 127.95

Std. Deviation 59.825

Most

Extreme

Differences

Absolute 0.106

Positive 0.106

Negative -0.067

Test Estatistic 0.106

Asymp. Sig. (2-tailed) 0.089

4.4 Control Charts

For the construction of the charts, the Action

Stat 3.2 software was used. Initially, a table

was built with the waiting time data obtained

through observations to patients in the three

days analyzed. The data obtained are shown

in Table 4.

Table 4. Waiting Time data (The Authors, 2020)

Sample Waiting time

(min) Sample

Waiting time

(min) Sample

Waiting time

(min)

1 65 21 135 41 33

2 45 22 165 42 168

3 115 23 220 43 135

4 90 24 165 44 260

5 120 25 177 45 218

6 109 26 240 46 101

7 65 27 152 47 110

8 50 28 215 48 122

9 120 29 225 49 182

10 137 30 255 50 95

11 200 31 275 51 139

12 137 32 227 52 93

13 155 33 103 53 40

14 55 34 55 54 94

15 110 35 88 55 70

16 115 36 55 56 85

17 117 37 90 57 194

18 105 38 58 58 92

19 165 39 163 59 88

20 125 40 67 60 88

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The Action Stat generated for the sample of

the values of the time that the users waited for

the attendance in the Health Care Unit the

following parameters: UCL = 255.80, center

line = 128.95 and the LCL = 2.10 for the

Chart of Individual Values. Using the same

data, but for the Moving Range chart, the

UCL values = 155.87, the center line = 47.74,

the LCL = 0 and the σ = 42.28. Figure 3

illustrates both charts:

Figure 3. Control Charts

When analyzing the control charts

constructed from the waiting time of patients

at the BHU, it is possible to verify that for the

moving range graph all values were within

the determined control limits and show a

behavior random. However, for the graph of

individual measurements it is possible to

check two points outside the control limits,

which refer to samples 31 (275min) and 44

(260 min) indicating special causes.

When investigating the special cause found in

sample 31, it was found that it refers to a

patient who was waiting for a withdrawal to

undergo a medical consultation with the

orthopaedist. So, he arrived at HBU earlier in

order to ensure that he would be attended to

that day. However, as this is a case of

withdrawal, this is the last patient to go

through the consultation, so it is the one that

presented a long waiting time. When

investigating the special cause identified in

the sample 44, it was found that it also refers

to a patient who was waiting for withdrawal,

however to undergo a dental consultation.

Like the other patients who are waiting to

give up, he arrived early to guarantee the

appointment that day. In addition to the

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longer waiting time, it was found that the

times for dental consultations are also long.

As a result, samples 31 and 44 were

eliminated and the control limits for the

control charts of individual measurements

and moving range were recalculated.The new

values obtained were: UCL = 249.69, center

line = 124.17 and the LCL = 0 for the Chart

of Individual Values. Using the same data,

but for the Moving Range chart, the UCL

values = 154.24, the center line = 47.21, the

LCL = 0 and the σ = 41.84. Figure 4 illustrates

both charts:

Figure 4. Control charts without samples 31 and 44

When analyzing the control graphs of

individual measurements and moving range

without the samples 31 and 44 presented in

Figure 4, it is possible to verify that their

control limits were shifted downwards, that

is, the values of upper control limit and

average limit decreased. Thus, it is possible to

identify that for the moving range control

graph all points are within the established

control limits and that they behave in a

random manner. However, for the control

chart of individual measurements, it is

possible to check a point outside the limits,

which refers to the sample 30 (255 min).

When investigating the special cause found in

sample 30, it was found that it refers to the

last child who went to the pediatric

consultation on the first day of research, who

was also awaiting withdrawal. The mother

arrived very early with the child to guarantee

the withdrawal and waited until everyone was

attended to. When eliminating sample 30, the

control limits were recalculated again.

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The following parameters were obtained:

UCL = 246.98, center line = 121.88 and the

LCL = 0 for the Chart of Individual Values.

Using the same data, but for the Moving

Range chart, the UCL values = 153.75, the

center line = 47.05, the LCL = 0 and the σ =

41.70. Figure 5 illustrates both charts:

Figure 5. Control charts without samples 30, 31 and 44 (The Authors, 2020)

When analyzing the control charts illustrated

by Figure 5, it is possible to verify that both

are in control, since all waiting times are

within the control limits and these are

randomly arranged. Thus, it is possible to

conclude that the waiting times are between 0

to 246.98 minutes (4.12 hours) and that the

difference between the current patient's time

and the one previously analyzed varies from

0 to 153.72 minutes (2,56 hours).

Thus, it is possible to conclude that by

eliminating patients waiting for withdrawal, it

can be said that the waiting time for patients

is in statistical control. Thus, we classify

dropouts as special causes of this process and

should be eliminated. As a way of eliminating

these causes, patients should be shown that

there is no need to arrive at HBU 4 or 5 am

for care. To do this, it should have an order

for the waiting list too, so that the patient

already has a password among the patients

who are waiting to give up for their care, that

is, a queue must be created between the

patients who are waiting withdrawal.

4.5 Capability of the HBU Service

To calculate the process capability, the pre-

determined specification limits are necessary.

In the case of waiting time, there is no lower

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specification limit, since the ideal is that the

patient did not wait to be seen. With this, there

is a unilateral specification presenting only

the upper specification limit.

The upper specification limit will be the

maximum time the patient must wait for a

medical appointment. This limit is related to

the function smaller-the-better, meaning, the

shorter the waiting time for patients, better is

the perception of quality. In Brazil, there is

currently no law that limits the maximum

waiting time for a patient for a medical

consultation in HBU, hospitals or even in

private offices. In this sector, there is only the

resolution of the Federal Council of

Medicine, CFM 2.077/14. This resolution

states that the maximum waiting time for

patients with less urgency should be around

120 minutes.

Therefore, considering that the patient is

waiting for a screening and a medical

evaluation to classify his degree of urgency,

the waiting time of 120 min was considered

as the upper specification limit for the

calculation of the effective process index

(Cpk). The mean and standard deviation of the

process are described in Figure 5, with the

mean being the center line of the control chart

of individual measurements (121.88 minutes)

and the standard deviation (41.70 minutes).

By using equation (6) it is possible to obtain

the effective capability index of the HBU:

𝐶𝑝𝑘 = min (𝐶𝑝𝑢, 𝐶𝑝𝑙)

𝐶𝑝𝑢 = USL − 𝜇

3𝜎

Cpk = 120 − 121,88

3 x 41,70 = −0,015

The Cpk index demonstrates that the service in

the HBU is not capable to attend patients in

120 minutes, since its value is less than one

(Cpk < 1). Changes in the way of attendance

are required in order to improve the service.

This result goes against the resolution of the

Federal Council of Medicine.

4. Final Considerations

According to the established objectives, it is

verified that the present research made it

possible to analyze the waiting time by means

of statistical control charts and how they

influence the capability of the service offered.

Through the research, the functioning of the

HBU was better understood through the direct

observation, since it was possible to

experience the unit's routine.

It was found that the health service has been

going through some changes in order to

improve the services offered and increase the

satisfaction of its patients. The introduction of

the time clocking system, for example, is an

improvement to be made in the unit, since it

will be possible to avoid delaying

professionals and thereby reduce the waiting

time for patients. Another improvement that

has been observed is the reduction in the daily

workload of doctors, as this way they will be

available on more days of the weeks and will

be less idle, in order to provide care more

quickly.

With that, it is possible to observe that

changes in the sector are appearing in order to

reduce the waiting time of patients for

medical care. However, there is also a cultural

change in patients that needs to occur. Many

of them arrive at the HBU before it even

opens. Currently, as consultations are

scheduled there is no longer a need for

patients to arrive at the unit so early, however

it is still a common habit among them,

especially when it comes to dropouts.

Therefore, through the research it was

possible to verify that the HBU still has

restrictions and improvements to be carried

out in order to improve and optimize the

services offered. However, it was found that

there are already some actions being taken to

reduce this waiting time and improve the

quality of the service. In general, it was found

that patients evaluate the service offered as

good.

1020 N.N.S. Pereira, E.E. Broday

Thus, it was proved that in times of crisis or

difficulties, quality engineering becomes

more important, because through tools it

seeks to bring solutions in order to improve

the services offered, bringing a new view of

the system. It was found that the health sector

has space for future projects involving

engineering tools and that through them it is

possible to improve the quality of services

offered and optimize material and financial

resources. In this way, in future research it is

possible to go deeper into the waiting time by

making a comparison between units or

applying in new locations, but different

studies involving forecasts and demand

monitoring, materials, exams and other

resources can be carried out. make analyzes

necessary.

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Nayara Nicole de Sene

Pereira Federal University of

Technology - Paraná

(UTFPR),

Ponta Grossa,

Brazil

[email protected]

Evandro Eduaardo

Broday Federal University of

Technology - Paraná

(UTFPR),

Ponta Grossa,

Brazil

[email protected]