The success of a business do not depends only on a quality product but also on the continuous increase in productivity to remain competitive, since by improving productivity an organization can benefit from cost and quality advantages compared to its competitors ( Snyman, & Smallwood, 2017). Productivity is considered a key factor in measuring the performance of a company's manufacturing system ( Rawat et al., 2018). According to Martins & Laugeni (2005), the term productivity was first used officially in an article by the French economist Quesnay in 1766. In 1883, another French economist, Littre, used the term with sense of "capacity to produce". At the beginning of the twentieth century, the term assumed the meaning of the relation between what was produced (output) and the resources used to produce it (input).

In 1950, the European Economic Community presented a formal definition of productivity as "the quotient obtained by the division of production by one of the factors of production", thus allowing to speak in productivity of capital, raw materials, labor, among others ( Martins & Laugeni, 2005).

For Rodrigues (2004), the productivity is related to the production of goods or services, and is represented by the ratio of what is necessary to accomplish the production by the final result. Gronroos and Ojasalo (2004) complement the aforementioned author by defining productivity as a measure of how input resources are used and transformed into value for customers. While Chen & Liaw (2001) and Huang et al. (2003) treat productivity as an indicator of efficiency.

Generally, the productivity of a productive system can be defined as the relation between what is generated by the system (its products or outputs) and what enters that system (its incomings or inputs) in a certain period of time. It implies in the establishment of two basic categories of measures: static productivity, originating from the division of the measures of the outputs by the measures of the inputs, in a given period of time; and dynamic productivity, defined as the relationship between static productivity measures at different periods, reflecting productivity variation from one period to another ( Torres Júnior & Lopes, 2013).

The definition that will guide this study is the one most used today in the specialized literature, that is, productivity is a quotient obtained in the division of a product by one of its elements of production, namely: raw material, workmanship, machinery and equipment, electricity, water, time spent, idle time, rework, etc.

Given the current competition in the market, companies need to monitor their practices and results to ensure competitiveness. To survive these challenges and compete successfully, organizations need to monitor processes through Performance Indicators ( Silva & Borsato, 2017). Performance Indicators are key managerial tools for decision making in organizations ( Gunasekaran et al., 2015) and important for monitoring the performance of a productive sector ( Lindberg et al., 2015). They allow to gather knowledge and explore the best way to achieve the objectives of an organization ( Badawy et al., 2016).

According to Martins & Laugeni (2005), performance indicators are indexes to measure a certain quantity of a manufacturing or administrative process, to determine if the process is within the acceptable parameters. If not, management and operational actions are determined that will lead the process to performance. For the authors, the main indicators are Productivity and Quality of Service. Soares (2006) says that a performance indicator is a measure such as percentage, index, quotient, rate or other comparison, which is monitored at intervals and compared to one or more criteria. According to Tadachi & Flores (2005), indicators are quantifiable forms of representation of the characteristics of products and processes. They are used by the organization to control and improve the quality and performance of its products and processes over time.

Nova (2002) comments that performance indicators are used to quantitatively measure performance in a company and uses as benchmarks numerical indices such as percentages, quotients, amounts, multipliers. The author lists characteristics of the performance indicators that should be observed:

• Objectivity: subjective indicators make it difficult to measure, which justifies the preference for quantitative data;

• Measurability: Indicators should be measurable, in the sense that their quantification is possible on a given scale of values;

• Comprehensibility: indicators are used to inform performance, therefore, measures that have meaning for managers should be used;

• Comparability: indicators should be comparable between periods for the same entity and between entities or other companies within the same evaluation sector;

• Cost: the evaluation should always consider a cost/benefit analysis, the information generated must have its utility at the cost of obtaining it.

Batista (1999) typifies the indicators as follows:

• Strategic indicators: inform how the organization is in the direction of achieving its vision, reflecting performance in relation to critical success factors;

• Indicators of productivity (efficiency): measure the proportion of resources consumed in relation to the outputs of the processes;

• Quality indicators (effectiveness): focus on measures of customer satisfaction and the characteristics of products or services;

• Indicators of effectiveness (impact): focus on the consequences of products or services;

• Capacity indicators: measure the responsiveness of a process through the relationship between the outputs produced per unit of time.

For Rodrigues (2004), the most frequently used performance indicators are productivity, capacity, flexibility, speed and reliability. Given the focus of this study, the subsequent topic will discuss productivity indicators.

Factorial Analysis (FA) is a generic name given to a class of multivariate statistical methods whose main purpose is to define the underlying structure in a data matrix. It addresses the problem of analyzing the structure of interrelationships (correlations) between a large number of variables, defining a set of latent dimensions, called factors ( Hair et al., 2009). Its purpose is to unveil existing structures, but they are not directly observable, so Furtado and Furtado (2017) comment that FA has as one of its objectives to intend to describe a set of original variables, by creating a smaller number of dimensions or factors.

Tian et al. (2018) define factorial analysis as a multivariate statistical analysis method that studies the relationship between the correlation matrix of the sample and the number of variables or samples that have a certain relation to the number of unobservable factors (also known as factor main).

FA assumes that high correlations between variables generate clusters that configure the factors, in other words, the existence of the factor explains the correlation in a certain group of variables. Thus, after creating factors, FA ends up simplifying complex relationship structures, allowing a better understanding of the data structure.

According to Hair et al. (2009), with FA, the researcher can first identify the separate dimensions of the structure and then determine the degree to which each variable is explained by each dimension; the dimensions and the explanation of each variable, the summary and the reduction of the data can be obtained. For the authors, in summarizing the data, the Factor Analysis obtains latent dimensions that, when interpreted and understood, describe the data in a much smaller number than the original individual variables. Figure 1 graphically illustrates the simplification of the phenomenon by the use of FA.

Figure 1
Latent variables and factor formation.
Adapted from Bezerra (2009)

FA assumes that the correlation between variables arises because these variables share or are related by the same factor ( Bezerra, 2009). In this sense, the author comments that the main objective of FA is to identify factors not directly observable, based on the correlation between a set of variables, which are observable and measurable.

The most commonly used method of FA is the Exploratory Factor Analysis (EFA), which is characterized by the fact that it does not require the researcher to know the relationship between the variables prior to their use ( Bezerra, 2009). In this type of FA, the researcher is not sure that the variables have a relationship structure. He/she analyzes, understands and identifies a relationship structure between the variables from the FA result. In the present study, we chose to use this modality of multivariate analysis.

Hair et al. (2009) states that under the exploratory perspective, factorial analytical techniques consider what the data offer and do not establish restrictions on the estimation of components or on the number of components to be extracted.

According to Bezerra (2009), prior to performing FA, the researcher must make some choices that will be influenced by the type of research to be performed, namely: the method of extracting the factors to be used, the type of analysis to be carried out; how the choice of factors will be made; and how to increase the explanatory power of FA. Table 1 summarizes these choices, listing and describing possible alternatives.

Chart 1
Previous FA choices

Prepared by the authors (2018)

As to the percentage of variance explained, Hair et al. (2009) defines that in the natural sciences, the procedure of obtaining factors should not be stopped until the factors extracted explain at least 95% of the variance or until the last factor explains only a small portion, less than 5%. However, the authors comment that in social sciences, where information is not as accurate as in the natural sciences, at least 60% of the total variance can already be considered satisfactory.

According to Bezerra(2009) and Sun et al. (2017), the steps to be followed in developing a FA are:

• Calculation of the correlation matrix: the degree of relationship between the variables and the convenience of the application of FA is evaluated;

• Extraction of the factors: determination of the method for calculating the factors and definition of the number of factors to be extracted; trying to find out how much the model is appropriate;

• Rotation of factors: we seek greater capacity to interpret the factors;

• Calculation of scores: results in scores that can be used in other analyzes.

In addition to these points, care should be taken regarding the sample size. Pestana & Gageiro (2014) indicate 5 observations per variable. Stevens (2009) recommends 5 to 20 observations per variable. Hair et al. (2009) argues that it is necessary 20 cases per variable. Regarding the correlation matrix, the authors emphasize that if a visual inspection does not reveal a substantial number of correlations greater than 0.30, then Factorial Analysis is probably inappropriate. In the correlation matrix, the values of the test of significance (p-test) should be close to zero to obtain a good FA. Table 2 describes, according to Bezerra (2009) and Hair et al. (2009), the tests used to evaluate if the original data of the research make FA satisfactory:

Chart 2
FA?s Viability tests

Adapted from Hair et al. (2009) and Bezerra (2009)

Table 2 presented the tests used to evaluate the feasibility of a Factor Analysis satisfactorily. However, once FA is performed, the reliability of its factorial structure should be ascertained.

According to Sijtsma (2009), one of the main criteria of consistency presented in the literature is the calculation of the internal consistency index, through Cronbach's Alpha, criterion presented by Lee Cronbach, in 1951. Pereira et al. (2018) consider the Cronbach's alpha coefficient to be one of the main questionnaire reliability estimators. Taber (2017) commented that this alpha is commonly reported for the development of scales designed to measure attitudes and other affective constructs. Hora et al. (2010) define the Conbach Alfa as a way of estimating the reliability of a questionnaire applied in a research; the alpha presents the function of measuring the correlation between the answers of a questionnaire by analyzing the profile of the answers given by the respondents, treating it as a mean correlation between questions.

According to Vaske et al.(2017), the Conbach's alpha measures the extent to which item responses (responses to survey questions) are correlated with each other, so it can be said that ? estimates the proportion of variance that is systematic or consistent in a set of research responses. Maroco & Garcia-Marques (2006) comments that Cronbach's alpha index varies on a scale of 0 to 1, where the closer to one, the greater the reliability of the analysis. For the interpretation of the alpha, there is no consensus among the authors about the reliability of a questionnaire obtained from the value of this coefficient. Works as with Urdan?s (2001), Oviedo & Campo-Arias? (2005) and Milan & Trez?s (2005) recommend at least 0.70 Cronbach's alpha index. George & Mallery (2003) suggest more detailed values ??for interpretation, such as: excellent (Alpha above 0.90); good (0.80 <Alpha ? 0.90); acceptable (0.70 <Alpha ? 0.80), questionable when it is below 0.6 and unacceptable when below 0.50. Simões & Pellegrinotti (2017) and Passos et al. (2017) indicate an alpha from 0.70 as satisfactory. Moreover, Azevedo-Santos et al. (2017) define an alpha between 0.70 and 0.80 as acceptable and above 0.80 as good.

According to Table 2, the Kaiser-Meyer-Olkin test (Measurement of Sampling Adequacy - MSA) resulted in 0.655, which is an acceptable value for the analysis, according to Hair et al. (2009). Thus, there are indications that the factors can reasonably describe the variations of the original data, that is, the performance of the factor analysis is satisfactory due to the correlation between the variables. The Barlett's sphericity test presented significance at 5% (p-value = 0.000), that is, there is an indication of the possibility of application of FA in the variables analyzed.

Table 2
KMO and Bartlett Test (1st attempt)

Prepared by the authors (2018)

The anti-image correlation matrix ( Table 3) presents the explanatory power of the factors in each variable. The main diagonal indicates the MSA (Measure of Sampling Adequacy). It is observed that with a single exception, all variables are above 0.50, which is a desirable result for the model, since these values ??validate the use of all the remaining indicators in the FA. The only exception was the case of the variable Yield Time (X09), because its MSA is below 0.5; there are indications that it may be withdrawn from the analysis.

Table 3
Anti-image correlation matrix (1st attempt)

Prepared by the authors (2018)Note: MSA represented on the main diagonal (a).

Table 3 shows a low MSA for the variable Yield Time (X09). However, even though it shows little relation with the factors, according to Table 4, this presented commonality of 0.771, that is, this value represents the power of explanation considering all the factors obtained.

Table 4
Communality (1st attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method

Figure 2 graphically represents the percentage of variation explained by the component in the ordinates and the eigenvalues, in descending order. In this way, it is possible to graphically analyze the dispersion of the number of factors until the individual variance curve of each factor becomes horizontal or abruptly falls. A fall from the fourth factor is observed, and there are indications of using three factors in the model.

Figure 2
Scree plot (first try)

Table 5 illustrates that, through three factors, the model explains almost 84% of the variance of the original data (83.799%), thus corroborating the indications in Figure 2.

Table 5
Total Variance Explained (1st attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method

After analyzing the degree of explanation of the productivity indicators model, Table 6 identifies which indicators are part of each of the factors. The Component Matrix allows you to check which factor best explains the indicators. However, this matrix causes doubts about the composition of each factor in relation to the data, since there are very close explanatory values ??in some cases (note that factor loads below 0.30 were excluded); in these cases, Tian et al. (2018) and Rocha et al. (2018) recommend the verification of the values ??after the application of factor rotation by the Varimax criterion.

Table 6
Component Matrix (1st attempt)

Prepared by the authors (2018)Note 1: Extracted by the Principal Component Analysis method.

Table 7 shows the matrix after factor rotation, in which there are still doubts regarding the selection of the indicators. Since, according to Hair et al. (2009), after identifying variables with high factor loads above 0.40 in both components, the authors argue that the same variable can not contribute to the construction of different factors. Thus, Andersen et al. (2017) suggest to adopt 0.40 as the acceptable limit of the contribution of the variable in the creation of the factor, in order to avoid the problem of indetermination, the relation between variables and factors. However, even when rotating, four variables violated this assumption (X03, X04, X05 and X07). Thus, we opted for the exclusion of the smallest number of variables, selecting Table 6, indicating X01, X04 and X05 for FA removal.

Table 7
Component Matrix and Rotated (1st attempt)

Prepared by the authors (2018)Note 1: Extracted by the Principal Component Analysis methodNote 2: Rotation performed by the varimax criterion with the Kaiser normalization (converged with 5 interactions).

After extracting the three indicators (X01, X04 and X05), according to Table 8, an improvement in the explanatory power of the model was detected. The KMO test was 0.677 (higher than the previous 0.655 trial of Table 2). The sphericity test remained significant at 5%. The Anti-Image Matrix that displays the individual MSA values ??( Table 8) detected an indicator less than 0.50 (X09).

Table 8
Anti-image correlation matrix (2nd attempt)

Prepared by the authors (2018)Note: MSA represented on the main diagonal (a).

Table 9 presented the same indicator with commonality 0.250. For these reasons, this variable was excluded from the study and a new factorial analysis will be performed with 6 indicators.

Table 9
Communality (2nd attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method.

The new FA, now with 6 indicators, showed the KMO test equal to 0.724 (higher than the analysis of topic 4.2). The sphericity test remained significant at 5%. The Anti-Image Matrix ( Table 10) presented all the indicators with MSA values ??above 0.50. Table 11 presents the commonalities. It is observed in this case that all are above 0.77.

Table 10
Anti-image correlation matrix (3rd attempt)

Prepared by the authors (2018)Note: MSA represented on the main diagonal (a)

Table 11
Communality (3rd attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method.

Table 12 illustrates, by means of two factors, an explanation of 83.71% of total variability, a result similar to Table 5, but with four variables less. It is observed the possibility of representing the same percentage with fewer variables.

Table 12
Total Variance Explained (3rd attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method

The Component Matrix is ??presented in Part I of Table 13. Note that an indicator (Processed Meters - X03) has factorial loads close to both factors. In this way, Part II illustrates the rotated components. Again X03 presented high load, for this reason, it was chosen for its withdrawal and realized again an FA, now with 5 indicators.

Table 13
Component Matrix and Rotated (3rd attempt)

Prepared by the authors (2018)Note 1: Extracted by the Principal Component Analysis methodNote 2: Rotation performed by the varimax criterion with the Kaiser normalization (converged with 3 interactions).

With a new FA performed, now with 5 indicators, the KMO test resulted in 0.655 (lower than the attempt of topic 4.3). The sphericity test remained significant at 5%. Table 14 shows the Anti-Image Correlation Matrix with all individual MSAs greater than 0.50. The commonalities are illustrated in Table 15. It is observed that all are above 0.79. This is a very satisfactory result.

Table 14
Anti-image correlation matrix (4th attempt)

Prepared by the authors (2018)Note: MSA represented on the main diagonal (a).

Table 15
Communality (4th attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method.

Table 16 presents, through two factors, a total explanation of the original data variability of 85.328% (above that obtained in the model of topic 4.3 with 6 indicators). Thus, with 5 variables, we obtained the highest percentage of explanation of the total variance of the model. Although the second factor of FA is extremely relevant for the analysis, Szabó & Dobróka (2018) consider the first most important factor to present a higher percentage of explanation of the total variance.

Table 16
Total Variance Explained (4th attempt)

Prepared by the authors (2018)Note: Extracted by Principal Component Analysis method

Based on the Scree Plot of Figure 3, a fall from the 3rd factor is observed, corroborating the use of only two factors, a fact already seen in Table 16.

Figure 3
Scree plot (fourth attempt)

The Component Matrix is ??presented in Part I of Table 17. Note two indicators (Processed Kilos/Useful Time - X10 and Yield Parts - X06) with factorial loads on both factors. By analyzing the rotated factors, Part II detects all the indicators with factorial loads in only one factor.

Table 17
Component Matrix and Rotated (4th attempt)

Prepared by the authors (2018)Note 1: Extracted by the Principal Component Analysis method.Note 2: Rotation performed by the varimax criterion with the Kaiser normalization (converged with 3 interactions).

The matrix, after factor rotation (Part II of Table 17), allows a more accurate classification of the indicators in each of the two factors. Therefore, it can be concluded that FACTOR 1 is composed of Kilos Produced (X02); Useful time (X07) and Time worked (X08). FACTOR 2 is composed of Processed Kilos/Useful Time (X10) and Yield Parts (X06).

From this selection of factors, it was possible to name the first factor as the yield of production (F1), the second factor interpreted as the yield of processing (F2). In order to verify the internal consistency of the factors, Cronbach's alpha was used. Factor 1 had an Alpha of 0.935 and Factor 2 had an Alpha of 0.752. This means that the factors presented good internal consistency, since they were higher than 0.7.

The study began with 10 indicators of productivity, however, in the end represented by two factors, culminated in only 5. However, it is possible to observe that all the indicators that were excluded from the analysis, they underwent several tests to verify the possibility of creating clusters between these variables that could result in other factors that, isolated from the three factors initially identified, would represent the evaluation model of productivity indicators.

However, the results of these tests were not sufficient to maintain these indicators in the factor analysis. In all attempts to work with the eliminated factors, in none of the analyzes, the KMO value exceeded 0.56. Moreover, in most attempts, the model did not fit the data; and even rotating the component matrix, there was still a variable with a high factor load in more than one factor.

Another criterion also used, besides the percentage of total variance explained by the minimum model of 70%, was the calculation of Cronbach's alpha, which in all the attempts, it was inferior to 0.5. Therefore, due to these reasons and those presented previously, the excluded variables did not become part of the model for evaluating productivity indicators.