2.1. Classical FMEA method

The related literature shows that the FMEA method was applied for the first time in the 1960s by NASA and the United States Army. After that, the method was extended to cover multiple sectors, such as aerospace, automotive, and healthcare.

The FMEA method consists of identifying the associated risks, their consequences on the functionality of the process, potential causes, and the corresponding actions needed to prevent or detect the cause (^{Shamayleh et al., 2020}). Figure 1 presents the proposition of the steps that constitute the FMEA method's procedure.

Figure 1 Procedure of FMEA method. 

Our study focuses on improving the risk assessment step in the FMEA procedure. In the approach of FMEA, the assessment of failure modes (risks) consists of the calculation of the criticality of each failure mode, named risk priority number (RPN), based on three parameters: the occurrence (O), the non-detection (D), and the severity (S). In the classical FMEA, the RPN is obtained by multiplying these three parameters (^{Fattahi & Khalilzadeh, 2018}).

The point-scale used for O, D, and S are from 1 to 5, and the point-scale for the RPN is from 1 to 10. Then, the multiplication range goes from 1 to 125 (=5x5x5). Hence, the given results are multiplied by 10/125 in order to provide results of classical RPN (Equation 1).

Despite the meaningful use, many drawbacks and limitations are faced in the risk assessment step of the classical FMEA method, such as, among others:

Thus, developing a model to improve the FMEA method performance and surmount the cited drawbacks is essential. The FIS is used to perform this improvement.

2.2. Fuzzy FMEA

Fuzzy inference is one of the popular tools used to solve the constraints/problems of the classical FMEA method. The adoption of FIS to reduce the limitations of the FMEA method was in 1995 by Bowles and Pelæz. Later, fuzzy FMEA has been widely applied. In fact, several works propose fuzzy inference approaches in purpose to increase risk assessment efficiency in order to overcome weaknesses the classical FMEA (^{Na’amnh et al., 2021}). The fuzzy FMEA approach proved high effectiveness due to several reasons (^{Ahmadi & Mosallanezhad, 2018}): it allows the analyst to evaluate the risk associated with item risks directly using the linguistic terms that are employed in assessing the criticality of failure; (2) ambiguous, qualitative, or imprecise information, as well as quantitative data, can be used in the assessment and they are handled in a consistent manner; (3) it gives a more flexible structure for combining the severity, occurrence, and detectability parameters.

The FIS is the system that transforms crisp inputs using the theory of fuzzy logic (^{Zadeh, 1965}). Generally, the algorithm of the fuzzy inference applied to the FMEA method is presented as follows:

2.3. KNN technique

Risk assessment is a process that aims to decide whether the risk assessed is tolerable or not by determining class zones. Therefore, the problem searched by the risk assessment is a classification problem. One of the most influential and well-known techniques for classification problems is the KNN technique.

The KNN algorithm is a very simple and easy-to-implement algorithm. It is used mainly for classification purposes and comes under supervised machine learning types (^{Das et al., 2022}).

The KNN algorithm consists of classifying each point depending on its distances from points of data. The studied point is classified with the category of the K (where K is a natural number) nearest neighbors’ points (^{Ali et al., 2019}). Several means can be selected to calculate the distances, such as, the Euclidean Manhattan and Minkowsky equations.

The KNN is an algorithm composed of the following steps (^{Das et al., 2022}):

Step 1: Choosing the number K of neighbors.

Step 2: Taking the K-nearest neighbor of the new data point, according to the selected distance.

Step 3: Counting the number of data points in each category among the K neighbors.

Step 4: Assigning the new data point to the category where the most neighbors were counted.

2.4. SVM technique

The support vector machine (SVM) is classified as one of the supervised learning methods (^{Okabe & Otsuka, 2021}).

SVM is a sophisticated and popular machine learning method that was proposed by Vapnik in 1982 and extended to solve classification problems and has become exceedingly popular for neuroimaging analysis in recent years (^{Pisner & Schnyer, 2020}). It is a supervised learning method used for regression and classifications. The SVM algorithm consists of optimizing the linear threshold (named separation hyperplane) between points of the 2 classes. In case of nonlinear separation, the SVM is done using the projection of the dataset to a higher dimensional space where a determined hyperplane (support vector) separates the categories of the training data (^{Bajaj et al., 2023}).

In case of a multi-class problem, 2 tricks are adopted, “one-vs-one”, which is a binary classification, and “one-vs-all”, which is based on the separation of one class from the rest.

Performing the SVM algorithm is performed by following these steps (^{Gholami & Fakhari, 2017}):

Step 1: Preparation of the datasets: training data and test data.

Step 2: Selection of the adequate Kernel function: several kernel functions can be used as the linear, the gaussian, the cubic, etc.

Step 3: Execution of training algorithms (training data).

Step 4: Classification/prediction of unseen data (test data).

Step 5: Evaluation of the SVM classifiers’ performances.

2.5. The proposed model

Limited resources allowed to hospitals, especially in low-income countries, leads managers to prioritize the treatment of intolerable risks based on the RPN value of each risk and if the risk is easy to be treated or not. For this reason, another parameter is added to the three parameters defined in FMEA (O, D, and S), which is the control level (C).

That, values of fuzzy R²PNs are trained using KNN to provide a decision of tolerance about each risk. Figure 2 presents the design of the developed model.

Figure 2 Structure of the developed model. 

The present model consists of the following three sequential steps: calculating fuzzy RPN, calculating fuzzy R²PN, and classifying the risk using SVM and KNN. Two fuzzy inference systems are developed: the first FIS (fuzzy inference System1) is developed to compute the value of RPN, and the second FIS (fuzzy inference System 2) is developed to compute values of R²PN. Obtained results are classified using several machine learning classifiers. These classifiers are based on SVM and KNN techniques.

2.6. Application area: the hospital sterilization unit

The operation rooms and the medical departments use reusable instruments (RI) permanently. This multitude of uses for patients makes RI a way by which infections can be transmitted from one patient to another (^{Wilson & Nayak, 2013}). For this reason, the sterilization unit plays a pillar role in the hospital. Then, we select a sterilization unit for this study,the central sterilization unit of Ibn Sina Hospital of Rabat-Morocco (CSU).

As a part of the quality management system requirements, the CSU has implemented a risk assessment plan covering the processes of the unit: disinfection and cleaning, (2) packaging, (3) autoclaving (sterilization); (4) storage and distribution; and (5) resources support (maintenance, human resources…).

The risk assessment plan has been developed using the FMEA method procedure (Figure 1), and the evaluation of the risks has been performed according to the developed model.

3.1 Calculating fuzzy RPN and fuzzy R²PN values

In our case, five variables are used: O, D, and S as initial inputs, RPN as the output of FIS 1 and input of FIS 2, C as the input of FIS 2, and R²PN as the output of FIS 2. The scale-point used for the inputs is from 1 to 5 (O, D and S), and the scale-point used for the outputs is from 1 to 10 (RPN, C and R²PN).

The linguistic variables are: For the factors O, D, S, and RPN are defined as: [very low (VL); low (L); medium (M); high (H); very high (VH)], for the parameter C are defined as: [low (L); medium (M); high (H)] and for R²PN are defined as: [low priority (LP); priority medium (PM); high priority (HP)].

In the present study, the membership function form adopted in all input and output variables is the triangular form, which has the following mathematical formula (Equation 2):

Let X be a nonempty set. Let A be a set in X. And let μA be the triangular membership function (∀x∈A μA(x)ϵ0,1):

where a, b, c and d real numbers (a < b < c).

In concertation with the experts of the studied process (a hospital sterilization unit, see paragraph $4: application), the membership functions have been constructed based on the triangular form defined in mathematical function (2). With the same experts, a dataset of rules has been listed to construct the rule base of each developed FIS (FIS 1 and FIS 2). The different membership functions of the two FISs are illustrated in Figures 3, 4, 5 and 6.

Figure 3 Input variables “O, D and S.” 

Figure 4 Input/output variable “RPN (fuzzy RPN).” 

Figure 5 Input variable “C.” 

Figure 6 Output variable “R²PN.” 

As explained previously, all membership functions used in this study are based on the triangular form (Equation 2). Values of constants (a, b, c) assigned to each input/output variable in order to obtain ranges are given as follows:

2 lists of rules have been constructed: Appendix I and Appendix II provide the rules lists associated with FIS 1 and FIS 2, respectively. These lists of rules have been constructed based on experts of the FMEA team. After the construction of rules, the fuzzy inference engine step is conducted.

2 popular techniques are well-known to perform the fuzzy inference engines: Mamdani-type and Sugeno-type. The most used fuzzy inference engine is the Mamdani-type (^{Kumru & Kumru, 2013}). The Mamdani is easily implemented and widely used in various fields (^{Zulfikar et al., 2017}). For this reason, the present study adopts the Mamdani min/max approach for the two FISs used in this model.

Defuzzification is the process of obtaining a single number from the output of the aggregated fuzzy set. It transfers fuzzy inference results into a crisp output (^{Masoum & Fuchs, 2015}). There are several techniques for defuzzification, such as the center of gravity (COG), the mean of maximum and the center of gravity for singletons. The most popular technique is COG (^{Kumru & Kumru, 2013}), also used in this study. The mathematical formula of the COG is expressed in Equation (3) as follows.

3.2. Classification of risks using machine learning

a. KNN classification

The assessed and prioritized risks are assigned to 3 priority classes: low priority (acceptable), priority medium (periodic monitoring), and high priority (urgent). The KNN technique has been adopted to perform this classification. The present study selects the value of K=5 because this value is the most used (^{Das et al., 2022}).

The principle of KNN is that the classification algorithm first selects k closest samples for a test sample from all the training samples and then predicts the test sample with a simple classifier (^{Zhang et al., 2018}). For this reason, the available dataset has been divided randomly into two categories: 80% (n=36) for data and 20%(n=36) for the testing data (n’=10). .

The selected technique used to calculate the distance between points of the training data is the Euclidean distance, which is a distance commonly used. The mathematical formula of the Euclidean distance can be expressed in Equation (4) as follows:

where d (.,.) is the Euclidean distance and x and y are two points of the training data.

b. SVM classification

Similarly, the assessed and prioritized risks are assigned to 3 priority classes: low priority (acceptable), priority medium (periodic monitoring), and high priority (urgent).

In the present study, six kernel functions are performed: the linear, the quadratic, the cubic, the fine gaussian, the medium gaussian and the coarse gaussian. The approach adopted for the multi-class problem is the “one-vs-one” approach. As the KNN technique, the dataset has been divided randomly into two categories: 80% for training and 20% for the testing sets.

46 risks have been identified and assessed in the CSU. Based on experts’ estimations and the developed model, we obtained each risk’s fuzzy RPN. The description of the risk scenarios of each risk code is provided in Appendix III.

Each risk has been analyzed to estimate its level of control and how easily it can be treated. Hence, a level of control has been assigned to each risk based on experts’ and workers’ judgments. The combination of fuzzy RPN and C provides the value of R²PN. In order to perform the SVM and the 5-NN classifications, each data set was split randomly into 80% for training data (n=36) and 20% for the testing data (n’=10).

Table 1 and Table 2 present the results of the studied case study: The FMEA team identified 46 failure modes associated with the activity of the sterilization unit in the Ibn Sina hospital (Table 1, Column 1 in Table 1 & Appendix III). The team assigned each risk value to input factors O, D, and S using experiences in the CSU (Table 1, Columns 2, 3, and 4 in Table 1). The values obtained of the 46 RPNs using classical FMEA (Table 1, Column 6). The fuzzy approach of risks is then obtained (Table 1, Column 7) with classifications (Table 1, Column 8) using FIS 1 process. The FMEA team provides values of C (Column 9) to obtain values and classifications of R²PN (Table 1, Column 10 and Column 11, respectively) using the FIS 2 process.

After that, each result of risk prioritization is obtained using fuzzy approach (FIS 2). Finally, the types of data are generated randomly (80% training data and 20% testing data) (Table 2, Column 3) using machine learning models (SVM kernel functions and KNN) to learn from training data and predict the testing data (Table 2, Columns 3-10).

The proposed model is evaluated using the outputs of the present case study in order to prove its performance.

3.3. Evaluation of the model performance

The present study proposes a model for risk assessment using revised FMEA, fuzzy approach, the SVM and the KNN techniques. This model aims to improve the effectiveness of the risk assessment process in hospital sterilization units. Hence, we need to check out the model’s performance in this case to prove the achievement of the desired objective.

As presented previously (see paragraph 3: Proposed model), the model calculates the RPN and R²PN with a fuzzy inference approach and then classifies the risks according to the defined priority classes using the SVM and KNN techniques. Thus, the objective achievement consists of improving the performance of the two parts of the model.

According to the related literature, the fuzzy logic approach proves a significant ability to improve the efficiency of the FMEA method, then the performance of the risk assessment process, specifically in the healthcare sector. The advantages provided by the fuzzy logic to FMEA. These advantages are, among others:

For this reason, the FISs provide a high-efficiency level to the FMEA in the phase of measurement of criticalities.

Several metrics are used to evaluate the performance of the machine learning algorithms, such as the root mean square error (RMSE), the efficiency, and the coefficient of variation (^{Soltanali et al., 2022}). One of the most commonly and the simplest tools and metrics used for machine learning performance evaluation is the confusion matrix, the accuracy (ACC), the precision (PRE), the recall (REC) and the f-score (FS) (^{Ali et al., 2019}), which are extracted from the confusion matrix. The selected metrics are defined as follows (^{Ali et al., 2019}):

Six kernel functions are used to perform the SVM classification: linear, quadratic, cubic, fine gaussian, medium gaussian and coarse gaussian kernel functions. Each SVM model (kernel function) is evaluated using the metrics extracted from the confusion matrixes (Acc, Pre, Rec and FS) of training data and testing data. Results are illustrated in Table 3.

According to the results of the measured metrics in Table 3, the most performant SVM classifiers are the SVM models, which use the cubic and the medium gaussian kernel functions (all metrics are equal to 100% for training and testing data). The linear and the quadratic can be judged as the performant classifiers. The metrics associated with the training dataset exceed 90%. Nevertheless, despite the good results in the training step, the fine gaussian and the coarse gaussian kernel functions provide unperformed results in the testing data.

Similarly, the KNN classifier model is evaluated using the metrics extracted from the confusion matrixes (Acc, Pre, Rec and FS) of training data and testing data. Results are illustrated in Table 4.

According to the results of the measured metrics given in Table 4, the proposed KNN classifier in this study can be judged performant. The metrics associated with the training dataset exceed 90%. The metrics associated with the training data show that the classifier model is relatively performant in predicting new data.