Park (2002) proposed a TPM analysis model including three stages. The first stage represents the effect of TPM factors on TPM performance. The second stage represents how TPM performance factors influence productivity. The third stage also represents the testing of the TPM analysis model with univariate and multivariate regression and correlation analyses and the results show that TPM performance factors improve productivity through TPM activity’s characteristics. Wang (2006) suggested a simple methodology for efficiency evaluation in TPM. In this study, DEA was used to evaluate the efficiency score when the utility function considers its many attributes. A prediction model by the multiple regression method was performed to obtain the expected efficiency score for checking the performance of implementing TPM. Wang (2006) measured TPM efficiency at the factory level using the DEA method, which has some limitations. Therefore, Jeon et al. (2011) measured three types of TPM efficiency by self-directed work teams (SDWTs) using DEA. Firstly, DEA efficiency scores of SDWTs were measured for three stages (stage 1: from TPM input to TPM intermediate output; stage 2: from TPM intermediate output to TPM final output, and stage 3: from TPM input to TPM final output). Then, the relationships between the three types of efficiency scores were analyzed by Spearman correlation analysis (Gibbons and Chakraborti, 1971). SDWTs were also clustered by the three types of TPM efficiency. Based on the results of the literature review, there are a few studies related to efficiency measurement in TPM implementation. In summary, while there are a few studies in the literature on TPM performance measurement, there are still gaps in the research that need to be addressed in order to develop best practices for TPM implementation (e.g., lack of standardization and lack of research on human factors of TPM). For instance, lack of standardization means that there is currently no widely accepted standard for TPM performance measurement, and many companies measure different metrics or use different approaches. This makes it difficult to compare results across companies and industries. Additionally, while TPM is often viewed as a technical or engineering-focused approach, there is a need for research that examines the human factors involved in TPM implementation. This includes factors such as employee engagement, training, and development as this study examines in the designing of novel performance indicators.

The aim of this study is to develop a new framework for the measurement of TPM performance based on novel performance indicators which include uncertain information or imprecise data. Fuzzy set theory, introduced by Zadeh (1965), provides a new mathematical tool to deal with the uncertainty of information (Zadeh, 2008). In the proposed TPM PMS, after the design of novel TPM performance indicators, these indicators are evaluated and measured using some methods under a fuzzy environment. For example, in the evaluation phase, since the evaluation involves multiple attributes, it can be thought of as multi-attribute decision-making (MADM) problem, and thus a method called COmplex PRoportional ASsessment of alternatives with Grey relations (COPRAS-G), which is one of the most popular MADM methods, is modified with fuzzy numbers, and thus fuzzy COmplex PRoportional ASsessment of alternatives (FCOPRAS) proposed by Turanoglu Bekar and Kahraman, (2016) is used for evaluation of novel TPM performance indicators. Then, in the implementation phase, a fuzzy data envelopment analysis (FDEA), which is a mathematical programming approach for the evaluation of performance with uncertainty pertinent to the existence of qualitative data set, is utilized to evaluate TPM performance based on these indicators. The fuzzy utility degrees obtained by the FCOPRAS method are integrated into the Generalized Fuzzy Data Envelopment Analysis with Assurance Region (GFDEA/AR) models in order to find efficient and inefficient TPM performance. In these models, desirable and undesirable performance indicators (inputs and outputs) are also considered which are explained in Section 3. The positioning and contributions of the proposed TPM PMS are summarized in Table 1.

DEA can be described as a series of models, whereas the type of returns to scale is what characterizes the two main ones: a) CRS (constant returns to scale), or CCR which is an acronym for Charnes, Cooper, and Rhodes (Charnes et al., 1978); and b) VRS (variable returns to scale) or BCC which is an acronym for Banker, Charnes, and Cooper (Banker et al., 1984) which is one of the broadenings of the CCR model where the efficient frontiers set is characterized by a convex curve passing through all efficient decision-making units (DMUs) and structured by both constant and -decreasing returns to scale (Faizrahnemoona et al., 2012). In brief, while the CCR model assumes that outputs always grow proportionally to inputs, in the BCC model this proportionality is not required, as a DMU may display returns to scale: a) increasing: where outputs grow proportionally more than inputs; b) constant: where there is proportionality; or c) decreasing: where outputs grow proportionately less than inputs (Mariano et al., 2015).

The traditional DEA models require accurate and precise performance data since it is a methodology focused on frontiers or boundaries (Gua and Tanaka, 2001). However, in real-world applications such as in a manufacturing system, a production process, or a service system, the observed data are volatile and complex and generally include uncertainty (Emrouznejad and Mustafa, 2012). In this context, the data with crisp numbers will not satisfy the real requirements and this restriction will diminish the practical flexibility of DEA in an application (Agarwal, 2014). Thus, imprecise or vague data can be represented with bounded intervals, ordinal (rank order) data or fuzzy numbers (Hatami-Marbini et al., 2011). Fuzzy set theory, established by Zadeh (1965), has been proven to be useful as a way to quantify imprecise and vague (expressed by linguistic variables) data in DEA models. Therefore, the DEA models with fuzzy data can more realistically represent real-world applications than the conventional DEA models (Lertworasirikul et al., 2003), which is also preferred to be used as a basis in this study. The applications of fuzzy set theory in DEA are generally classified into four groups (Lertworasirikul et al., 2003; Karsak, 2008) such as the tolerance approach, the α-level based approach, the fuzzy ranking approach, and the possibility approach. Emrouznejad et al. (2014) extended this classification and attached two new groups: the fuzzy arithmetic and the fuzzy random variables and other extensions of fuzzy sets. In this study, an integrated FCOPRAS-FDEA method is conducted. Therefore, this paper examines some articles that combine different MADM methods with FDEA; and then develops hybrid methods. According to the literature, AHP and FAHP are the most widely used MADM methods with FDEA, specifically for the application areas, which are facility layout design and supplier evaluation and selection, as summarized in Table 2. There has not been any study in the literature about the application and theory of combined FCOPRAS-FDEA methodology. Additionally, to the best knowledge of the author, this can be the first study that integrates the FCOPRAS-FDEA method to evaluate the performance of TPM with novel performance measures, which can be considered a significant contribution to the TPM literature.

The GFDEA/AR model proposed by Zhou et al. (2012) is one of the adapted models within the scope of this study. For a comprehensive overview of the GFDEA with AR, the reader is referred to Zhou et al. (2012). The fuzzy Q ∼ i values, i.e., lower and upper bounds of the utility degrees of inputs and outputs obtained from FCOPRAS are incorporated into the models which are explained in the following equations: E j 0 α L = max ∑ r = 1 s u r Y r j 0 α L − δ 1 u 0 (1)

Subject to; ∑ r = 1 s u r Y r j 0 α L − ∑ i = 1 m v i X i j 0 α U −   δ 1 u 0 ≤ 0 , (2) ∑ r = 1 s u r Y r j 0 α U − ∑ i = 1 m v i X i j 0 α L −   δ 1 u 0 ≤ 0 , j = 1 , … , n .   j ≠ j 0 (3) ∑ i = 1 m v i X i j 0 α U = 1 , (4) Q I p q L ≤ v p v q ≤ Q I p q U , 1 ≤ p < q = 2 , … , m (5) Q O p q L ≤ u p u q ≤ Q O p q U , 1 ≤ p < q = 2 , … , s (6) v i ≥ ε , i = 1 , … , m ;   u r ≥ ε , r = 1 , … , s (7) δ 1 δ 2 − 1 δ 3 u 0 ≥ 0 . (8) where v i is the weight for the ith input, u r is the weight for the rth output for i = 1 , … , m , r = 1 , … , s , and ε is a positive number less than any positive real number. Q I p q L , Q I p q U , Q O p q L , and Q O p q U are the lower and upper bounds of the fuzzy relative significance of inputs and outputs respectively obtained from the FCOPRAS method. The parameters δ 1 , δ 2 , and δ 3 are binary ones assuming only values zero and one. In the above model, the values of these parameters are taken as zero.

In Model 1), the objective function in Eq. 1 calculates the lower bound of efficiency at any given α-cut level for the D M U p . The constraint in Eq. 2 is shown as ∑ r = 1 s u r Y ∼ r p α L ∑ r = 1 m v i X ∼ i p α U ≤ 1 meaning that the ratio of the maximum value of the output data to the minimum value of the input data is less and equal than one for the D M U p at the given α-cut level. The constraint in Eq. 3 is also shown as ∑ r = 1 s u r Y ∼ r j α U ∑ r = 1 m v i X ∼ i j α L ≤ 1 meaning that the ratio of the maximum value of the output data to the minimum value of the input data is less and equal than one for the other DMUs at the given α-cut level. The constraint in Eq. 4 demonstrates that the sum of the maximum value of the weighted input data for the D M U p is equal to one at the given α-cut level. This constraint also provides converting the fractional linear programming model to a conventional linear programming model. The constraints in Eqs 5, 6 give the assurance regions for the inputs and outputs data, respectively. Additionally, Eq. 7 provides the sign constraints for the decision variables. Finally, Eq. 8 gives the binary constraint for the parameters δ 1 , δ 2 and δ 3 .

In Model 2), the objective function in Eq. 9 calculates the upper bound of the efficiency at any given α-cut level for the D M U p . The constraint in Eq. 10 gives that the ratio of the maximum value of the output data to the minimum value of the input data is less and equal than one for the D M U p at the given α-cut level. The constraint in Eq. 11 also presents that the ratio of the minimum value of the output data to the maximum value of the input data is less and equal than one for the other DMUs at the given α-cut level. The constraint in Eq. 12 provides that the sum of the minimum value of the weighted input data for the D M U p is equal to one at the given α-cut level. The constraints in Eqs 13 and 14 give the assurance regions for the inputs and outputs data, respectively. Additionally, Eq. 15 provides the sign constraints for the decision variables. Finally, Eq. 16 gives the binary constraint for the parameters δ 1 , δ 2 and δ 3 . E j 0 α U = max ∑ r = 1 s u r Y r j 0 α U − δ 1 u 0 (9)

Subject to; ∑ r = 1 s u r Y r j 0 α U − ∑ i = 1 m v i X i j 0 α L −   δ 1 u 0 ≤ 0 , (10) ∑ r = 1 s u r Y r j 0 α L − ∑ i = 1 m v i X i j 0 α U −   δ 1 u 0 ≤ 0 , j = 1 , … , n .   j ≠ j 0 (11) ∑ i = 1 m v i X i j 0 α L = 1 , (12) Q I p q L ≤ v p v q ≤ Q I p q U , 1 ≤ p < q = 2 , … , m (13) Q O p q L ≤ u p u q ≤ Q O p q U , 1 ≤ p < q = 2 , … , s (14) v i ≥ ε , i = 1 , … , m ;   u r ≥ ε , r = 1 , … , s (15) δ 1 δ 2 − 1 δ 3 u 0 ≥ 0 (16)

Secondly, Models 1) and 2) are extended by adding three different undesirability approaches. The first approach is the ignorance of undesirable outputs and desirable inputs. Thus, Models 1) and 2) are solved without any modifications. The second approach is to treat the undesirable outputs as inputs and the desirable inputs as outputs. In this way, Models 1) and 2) are solved without any modifications. Therefore, in these models, the number of inputs and outputs is only changed. Therefore, these models are called “Models 3) and 4)”. The third approach is to apply the FDEA model proposed by Puri and Yadav (2014) with ignorance of the desirable inputs. In this context, Models 1) and 2) are integrated with the FDEA model, and then Models 5) and 6) are obtained as demonstrated in Eqs 17–34. Here it should be also noted that Puri and Yadav (2014) used a method developed by Saati et al. (2002) to solve the FDEA model. However, Models 5) and 6) are proposed based on the approach developed by Kao and Liu (2000). In the Models 5) and 6), it is assumed that the performance of a homogeneous set of n DMUs ( D M U j ; j = 1 , … , n ) is to be measured. The performance of a DMU is characterized by a production process of m fuzzy inputs to yield s fuzzy outputs in which s 1 fuzzy outputs are desirable (good) and s 2 fuzzy outputs are undesirable (bad) such that s = s 1 + s 2 . Let Y ∼ be the fuzzy output matrix consisting of positive fuzzy elements. Then the fuzzy output matrix Y ∼ can be decomposed as Y ∼ = Y ∼ g Y ∼ b T , where Y ∼ g and Y ∼ b are the matrices for desirable fuzzy outputs and undesirable fuzzy outputs respectively. Let X ∼ be the fuzzy input matrix consisting of positive fuzzy elements. Further, let X ∼ i j 0 = X ∼ i j 0 α L , X ∼ i j 0 α U ( i = 1 , … , m ) be the m fuzzy inputs used by the j 0 th DMU, Y ∼ r j 0 g = Y ∼ r j 0 g α L , Y ∼ r j 0 g α U ( r = 1 , … , s 1 ) be the α-level form of the s 1 desirable fuzzy outputs, and Y ∼ p j 0 b = Y ∼ p j 0 b α L , Y ∼ p j 0 b α U   p = 1 , … , s 2 be the α-level form of the s 2 desirable fuzzy outputs produced by the j 0 th DMU respectively. The lower bound E j 0 α L and the upper bound E j 0 α U of the fuzzy efficiency score of the j 0 th DMU with the undesirable fuzzy outputs can be evaluated from the Models 5) and 6). E j 0 α L = max ∑ r = 1 s 1 u r g Y r j 0 g α L − ∑ p = 1 s 2 u p b Y r j 0 b α L (17)

Subject to; ∑ r = 1 s 1 u r g Y r j 0 g α L − ∑ p = 1 s 2 u p b Y r j 0 b α L − ∑ i = 1 m v i X i j 0 α U ≤ 0 , (18) ∑ r = 1 s 1 u r g Y r j 0 g α U − ∑ p = 1 s 2 u p b Y r j 0 b α U − ∑ i = 1 m v i X i j 0 α L ≤ 0 , j = 1 , … , n , j ≠ j 0 (19) ∑ r = 1 s 1 u r g Y r j 0 g α L − ∑ p = 1 s 2 u p b Y r j 0 b α L ≥ 0 , (20) ∑ i = 1 m v i X i j 0 α U = 1 , (21) Q I p q L ≤ v p v q ≤ Q I p q U , 1 ≤ p < q = 2 , … , m (22) Q O p q L ≤ u p g u q g ≤ Q O p q U , 1 ≤ p < q = 2 , … , s 1 (23) Q O p q L ≤ u p b u q b ≤ Q O p q U , 1 ≤ p < q = 2 , … , s 2 (24) v i ≥ ε , i = 1 , … , m ;   u r g ≥ ε , r = 1 , … , s 1 ;   u p b ≥ ε , p = 1 , … , s 2 , (25) where u r g , u p b , and v i are the weights for the rth desirable fuzzy output, pth undesirable fuzzy output, and ith fuzzy input of the j 0 th DMU respectively, and ε is the non-Archimedean infinitesimal.

In Model 5), the objective function in Eq. 17 calculates the lower bound of the efficiency at any given α-cut level for the D M U j 0 . The constraint in Eq. 18 gives that the ratio of the lower bound of the desirable output data to the lower bound of the undesirable output data and the upper bound of the input data is less and equal than 1 for the D M U j 0 at the given α-cut level. The constraint in Eq. 19 also presents that the ratio of the upper bound of the desirable output data to the upper bound of the undesirable output data and the lower bound of the input data is less and equal than 1 for the other DMUs at the given α-cut level. The constraint in Eq. 20 prevents taking negative efficiency score of the lower bound for the D M U j 0 at the given α-cut level. The constraint in Eq. 21 provides that the sum of the upper bounds of the weighted input data for the D M U j 0 is equal to 1 at the given α-cut level. The constraints in Eqs 22 and 23, and 24 give the assurance regions for the inputs and desirable and undesirable outputs data, respectively. The last constraint in Eq. 25 provides the sign constraints for the decision variables. E j 0 α U = max ∑ r = 1 s 1 u r g Y r j 0 g α U − ∑ p = 1 s 2 u p b Y r j 0 b α U (26)

Subject to; ∑ r = 1 s 1 u r g Y r j 0 g α U − ∑ p = 1 s 2 u p b Y r j 0 b α U − ∑ i = 1 m v i X i j 0 α L ≤ 0 , (27) ∑ r = 1 s 1 u r g Y r j 0 g α L − ∑ p = 1 s 2 u p b Y r j 0 b α L − ∑ i = 1 m v i X i j 0 α U ≤ 0 , j = 1 , … , n , j ≠ j 0 (28) ∑ r = 1 s 1 u r g Y r j 0 g α U − ∑ p = 1 s 2 u p b Y r j 0 b α U ≥ 0 , (29) ∑ i = 1 m v i X i j 0 α L = 1 , (30) Q I p q L ≤ v p v q ≤ Q I p q U , 1 ≤ p < q = 2 , … , m (31) Q O p q L ≤ u p g u q g ≤ Q O p q U , 1 ≤ p < q = 2 , … , s 1 (32) Q O p q L ≤ u p b u p b ≤ Q O p q U , 1 ≤ p < q = 2 , … , s 2 (33) v i ≥ ε , i = 1 , … , m ;   u r g ≥ ε , r = 1 , … , s 1 ;   u p b ≥ ε , p = 1 , … , s 2 , (34) where u r g , u p b , and v i are the weights for the rth desirable fuzzy output, pth undesirable fuzzy output and ith fuzzy input of the j 0 th DMU respectively, and ε is the non-Archimedean infinitesimal.

In Model 6), the objective function in Eq. 26 calculates the upper bound of the efficiency at any given α-cut level for the D M U j 0 . The constraint in Eq. 27 gives that the ratio of the upper bound of the desirable output data to the upper bound of the undesirable output data and the lower bound of the input data is less and equal than 1 for the D M U j 0 at the given α-cut level. The constraint in Eq. 28 also presents that the ratio of the lower bound of the desirable output data to the lower bound of the undesirable output data and the upper bound of the input data is less and equal than 1 for the other DMUs at the given α-cut level. The constraint in Eq. 29 prevents taking negative efficiency score of the upper bound for the D M U j 0 at the given α-cut level. The constraint in Eq. 30 provides that the sum of the lower bounds of the weighted input data for the D M U j 0 is equal to 1 at the given α-cut level. The constraints in Eqs 31–33 give the assurance regions for the inputs and desirable and undesirable outputs data, respectively. The last constraint in Eq. 34 provides the sign constraints for the decision variables.

The proposed models as mentioned above have some computational and practical implications, which are summarized below.

• They consider AR for inputs and outputs and perform together with the fuzzy multiattribute decision-making (FMADM) method, e.g., FCOPRAS, to increase their computational effort and reliability;

This section answers the question what indicators are to be measured in the design phase of TPM PMS. Turanoglu Bekar and Kahraman, (2016) proposed an outline for defining different types of PIs impacting TPM and evaluated these PIs using COPRAS-G and proposed FCOPRAS methods. A detailed list of the proposed TPM PIs is given in Table 3.

According to Table 3, “operational-related indicators” are the production losses observed while running the plant. Since these are the most common problems observed in production, they are the ones analyzed regularly. “Business-related indicators” consist of problems at the entire business level. “Organizational problems or labor unrest” are stated employee satisfaction and also may cause the production to shut down leading to production loss. “Employee satisfaction indicators” can include morale, teamwork, and industrial harmony. Some of these are “employee absentees”, “employee turnover rate”, and “refusal of extended hours or overtime” (Parida and Chattopadhyay, 2007). “HSE problems” cause production to be slowed down or stopped. An indicator of HSE problems is the number of HSE incidents (Muchiri and Pintelon, 2010). Human factors represented by maintenance technicians and other related staff (e.g., machine operators are in direct contact with the maintenance activities and efforts because of the autonomous maintenance concept in TPM) are the backbone of the maintenance system in any organization (Ljungberg, 1998; Cabahug et al., 2004). Qualified and well-trained machine operators and maintenance technicians are the driving force behind any effective maintenance measurement system (Simoes et al., 2011). As such, the effectiveness of the different facets of the performance system is very much dependent on the competency, training, and motivation of the human factor in charge of the maintenance system (Peach et al., 2016). In this context, human-oriented factors are proposed to measure TPM performance. These factors are divided into two groups, direct and indirect human-oriented factors. Proposed indicators for direct human-oriented factors are “Competence of maintenance personnel”, “experience of operators in production line”, “operator reliability”, and “training and continuing education”. The indirect human-oriented factor is addressed from two different points such as motivation management and work environment. Proposed indicators for the motivational management and work environment are “new ideas generated and implemented”, and “5S level”, respectively. Another proposed indicator is “the availability of maintenance personnel”. This indicator is very important when breakdowns occur and should urgently be repaired. Thus, the availability of maintenance personnel needs to be looked into, because otherwise, it can act as a performance killer.

This section answers the question how to evaluate the proposed indicators under some attributes in the evaluation phase of TPM PMS. The proposed TPM PIs are evaluated by COPRAS-G and the proposed FCOPRAS methods under some attributes determined by the committee according to the literature investigation. The committee consisted of three experts (TPM, Production, and Quality Managers), which were selected based on their knowledge and professional expertise about the subject under investigation according to the purposive sampling (Palys, 2008). Then, six criteria were identified, e.g., the specificity (i.e., clear and concentrated to keep away misunderstanding and it should contain measure suppositions and descriptions and be simply explained); the measurability (i.e., can be quantified and resemble other data; the attainability (i.e., is achievable, rational, and reliable under the conditions expected); the practicalness (i.e., conforms to the organization’s restrictions and is profitable); the timely (i.e., is available within the time frame given); and the cost of measure. The first five criteria are benefit attributes, while the last one is cost. The committee provided linguistic assessments for the six criteria and alternatives (TPM PIs) using the scales proposed by Jamalnia and Soukhakian (2009) as given in Table 4. It should be noted that the reader is referred to the study done by Turanoglu Bekar and Kahraman, (2016) for a more detailed explanation of the steps of the methods and the obtained result. Since the hierarchy between the experts in the committee was defined, thereby they were ranked in a fuzzy way, i.e.; 1 ∼ , 2 ∼ ,; 3 ∼ . Then, the fuzzy weights of the experts are calculated by using the Rank Reciprocal method (Malczewski, 1999). Then, the aggregated fuzzy weights of the criteria are achieved as in Table 4.

The experts gave the linguistic terms presented in Table 4 to each criterion with respect to all alternatives based on their own judgments to construct the fuzzy decision matrix. The proposed method requires aggregation, averaging and normalization process of the fuzzy decision matrix as explained in detail in Turanoglu Bekar and Kahraman, (2016). In the proposed FCOPRAS method, all fuzzy judgments were not converted to real numbers and all calculations were performed in accordance with the fuzzy arithmetic and ranking. The ranking results of the proposed FCOPRAS method based on the different α-cut levels from 0 to 0.9 are given in Table 5.

According to Table 5, the best alternative for all levels of α-cut is “the number of unplanned maintenance”. When transitioning from non-deterministic conditions (e.g., levels of α-cut being 0, 0.1, 0.2, and 0.3) to deterministic conditions (levels of α-cut approaching to 1), the ranking orders of the alternatives change. For example, at the deterministic conditions (e.g., levels of α-cut equal 0.6, 0.7, 0.8, and 0.9), while the best three alternatives are “the number of unplanned maintenance”, “MTTR”, and “MTBF”, the worst alternative is “refusal of extended hours or overtimes” for these α-cut levels. Furthermore, at the non-deterministic conditions (e.g., levels of α-cut equal 0, 0.1, 0.2, 0.3 and 0.4), while the best three alternatives are “the number of unplanned maintenance”, “quality defects”, and “reduced yield”, the worst alternative is “employee turn-over rate” for these α-cut levels. As a conclusion, the other alternatives have almost the same rankings for the different levels of α-cut.

The proposed FCOPRAS method was also compared to the other most popular FMADM methods, e.g., TOPSIS-F, fuzzy ARAS, VIKOR-F, fuzzy MULTIMOORA and fuzzy ELECTRE I (Kaya and Kahraman, 2010; Turskis and Zavadskas, 2010; Awasthi, et al., 2011; Balazentis et al., 2012; Hatami-Marbini et al., 2013; Kahraman et al., 2016). In order to measure the similarity between the ranks by the proposed FCOPRAS method and benchmarked FMADM methods, Spearman rank correlation coefficient (Gibbons and Chaakraborti, 2014) was calculated. The results of the Spearman test are given in Table 6.

According to Table 6, the minimum and maximum correlation coefficient values are provided as −0.159 (fuzzy MULTIMOORA-2 that is fuzzy reference point) and 0.826 (fuzzy ELECTRE I) for α = 0, respectively. Furthermore, the maximum and minimum correlation coefficient values are provided as 0.1 (fuzzy MULTIMOORA-2) and 0.922 (fuzzy ELECTRE I) for α = 0.5. Finally, these values are yielded as 0.167 (fuzzy MULTIMOORA-2) and 0.971 (fuzzy ELECTRE I) in case of α = 0.9. These values support the similarity of the results and indicate that the proposed method has high correlation or substantial relationship with the selected most popular FMADM methods. Additionally, the correlations between fuzzy VIKOR and the proposed FCOPRAS methods for α = 0, α = 0.5 and α = 0.9 are high (0.674, 0.811 and 0.870, respectively). This means that these methods produce rankings that are statistically similar since there is not enough evidence to accept the null hypothesis in accordance with significant values 0.003, 0.000 and 0.000, respectively. In summary, the maximal correlation values can be provided by the calculation of the proposed FCOPRAS with α = 0.5 and α = 0.9.

This section answers the question how to use the proposed TPM PIs to measure the performance of TPM in the implementation phase of TPM PMS. The GFDEA/AR models (see section 3.1.1) that integrate the proposed FCOPRAS and FDEA methods were implemented to evaluate the performance efficiency of TPM for four production lines in other words the DMUs as described at the beginning of Section 4.