# Application of the Structure Function in the Evaluation of the Human Factor in Healthcare

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Human Reliability Analysis in Healthcare

- data collection;
- task description;
- task simulation;
- human error identification; and
- human error quantification.

## 3. Structure Function for Mathematical Representation of Systems

_{i}, which takes on the value x

_{i}= 0 if the component fails in a stationary state or x

_{i}= 1, …, m

_{i}− 1 if the component performs from satisfactorily to perfect. The state vector

**x**= (x

_{1}, …, x

_{n}) defines the system’s component states. The system state (performance level) depends on its component states. The correlation between a system’s performance level and its component states is represented as the structure function:

**x**) = φ(x

_{1},…, x

_{n}): {0, …, m

_{1}− 1} × … × {0, …, m

_{n}− 1}→{0, …, M − 1},

**x**) is the functioning of the system state from failure (φ(

**x**) = 0) to perfect (φ(

**x**) = M − 1).

_{i}= 2, the structure function (Equation (1)) is a BSS that permits the analysis of two system states only: failure and working. The most utilized representation of the structure function is truth table. For example, consider a system of two components (n =2) that has three performance levels (M = 3) and component states defined as m

_{1}= 2 and m

_{2}= 4. The behavior of this system is described according to the rules: the system fails if the second component is rejected, or if the first component is rejected and the second component state is indicated as 1; the system performance level is 1 if the first component breaks down and the second component state is 2 or 3; and the system performance level is 2 if the two components are both functioning. The truth table of this system’s structure function is shown in Table 1.

_{i}agree with the system components x

_{i}(i = 1, …, n), and the target attribute B is the system performance level φ(

**x**). Therefore, calculation of the decision table for all possible values of the component states is determined to be the structure function of the system according to Equation (1).

- initial data preparation;
- representation of the system model by the FDT; and
- construction of the structure function based on the FDT.

## 4. Initial Data Preparation

_{i}sub-columns that indicate the i-th component states from 0 to (m

_{i}− 1) according to Equation (1). The last column has M sub-columns as the number of the system performance levels. Rows of this table are formed by samples of monitored systems or experts’ evaluations. The cells include values of component states and system performance levels. The number values in cells range from 0 to 1. These values can be provided by interviews of experts or possibilistic fuzzy clustering [63]. Per the first case, we have to take into account the differences in experts’ opinions of initial attributes. Therefore, all values of system performance levels and component states can be specified with a possibility ranging from 0 to 1. This range can be explained as the certainty degree of these values. If the value equals 1, then that expert’s certainty degree for this value is maximal (absolutely sure). These possibilities correspond to a membership function of the fuzzy data [64]. Note that the sum of these possibilities for each value equals to 1. This demand for initial data representation is caused by the method of FDT induction.

_{A}: U → [0,1], and an A-membership degree μ

_{A}(u) is assigned to each element u in U. μ

_{A}(u) gives us an estimation of u belonging to A. For u $\in $ U, μ

_{A}(u) = 1 means that μ is definitely a member of A and μ

_{A}(u) = 0 means that μ is definitely not a member of A, while 0 < μ

_{A}(u) < 1 means that μ is partially a member of A. If either μ

_{A}(u) = 0 or μ

_{A}(u) = 1 for all u $\in $ U, A is a crisp set. A is fuzzy set in the opposite case. The cardinality measure of the fuzzy set A is defined by M(A) = Σ

_{u}$\in $

_{U}μ

_{A}(u), which is the measure of the size of A.

_{1}and x

_{2}(that are interpreted as nursing mistakes) have only two possible states (m

_{1}= m

_{2}= 2): error (state 0) and absence of error (state 1). The doctor’s mistake can be modeled according to four levels (m

_{3}= 4) (i.e., from 0 (fatal error by the doctor) to 3 (doctor’s work is perfect)).

_{1}= 0) with a certainty of 0.9, and that no mistake has been made by this nurse (x

_{1}= 1) with a certainty of 0.1. The certainty of the second nurse having made a mistake is 1.0. Finally, the doctor’s work is determined to be perfect (x

_{3}= 3) with a certainty of 0.8, and to have included non-principal errors (x

_{3}= 2) with a certainty of 0.2. Similarly, the system performance (system medical error) is determined to have equaled 0 (non-operational, the fatal medical error) with a certainty degree of 0.3, or to have equaled 1 (partially operational, some imperfection in patient care) with a certainty degree of 0.7. We have interpreted all of these values according to the experts’ evaluations of possible values for input or target attributes. Note that the sum of these possibilities (certainties) for each value equals 1. The possibilities of the values permit data ambiguities to be specified. However, the information about investigated problems is not complete, as the data have not been obtained for all possible situations. To rectify this, the values of the input attributes and target attributes determined for the medical error analysis are defined by the membership functions in Table 3. The sums of the membership degrees of attribute values are given in the bottom row of Table 3.

## 5. FDT Induction for System Behavior Representation

_{i}$\in $

**A**, or with a system component in terms of reliability analysis. The non-leaf node of the attribute A

_{i}has m

_{i}outgoing branches. The s-th outgoing branch (s = 0, …, m

_{i}− 1) from the non-leaf node A

_{i}agrees with the value s of the i-th component (x

_{i}= s). The path from the top node to the leaf indicates the vector state of the structure function by the values of attributes, and the value of the target attribute corresponds to the system performance level. If some attribute is absent in the path, then all possible values are possible for the associated system component. The target attribute value B

_{w}agrees with one of the system performance levels and is defined as M values ranging from 0 to M − 1 (w = 0, …, M − 1).

**A**= {A

_{1}, ..., A

_{n}} and a target attribute B. The construction of the system’s structure function supposes that the system’s performance level is the target attribute and that component states (state vectors) are input attributes. Each input attribute (component state) A

_{i}(1 ≤ i ≤ n) is measured by a group of discrete values from 0 to m

_{i}− 1 that agree with the values of the i-th component states: {A

_{i}

_{,0}, …, A

_{i,j}, …, A

_{i,mi}

_{−1}}. The FDT assumes that the initial set is classified as class values B

_{j}of target attribute B.

**A**= {A

_{1}, A

_{2}, A

_{3}} and target attribute B for the system in Figure 2 are indicated in Table 4 according to FDT terminology. Each attribute is defined as follows: A

_{1}= {A

_{1,0}, A

_{1,1}}, A

_{2}= {A

_{2,0}, A

_{2,1}}, A

_{3}= {A

_{3,0}, A

_{3,1}, A

_{3,2}, A

_{3,3}} and B = {B

_{0}, B

_{1}, B

_{2}}. These attributes describe and structure the dataset in Table 3.

_{i}not yet associated with nodes of the previous levels in this FDT branch. This criterion is based on the information’s estimation [35]. We assign input attribute A

_{i}with the maximum values of this selection criterion as the current node of the FDT. We analyze the obtained results for choice of leaves. If the branch is not finished as a leaf, we recursively repeat the process for this branch.

**I**(B;${\mathrm{A}}_{{i}_{1}},\dots ,{\mathrm{A}}_{{i}_{q-1}}$,${\mathrm{A}}_{{i}_{q}}$) is an essential part of these criteria. This measure reflects how much information we obtain about target attribute B if we know the value of input attributes ${\mathrm{A}}_{{i}_{1}},\dots ,{\mathrm{A}}_{{i}_{q-1}}$ and ${\mathrm{A}}_{{i}_{q}}$. Conversely, the concept of entropy determines the measure of uncertainty for the value of the target attribute in cases where the corresponding values of the input attributes are known. These different cumulative information estimates permit the induction of an FDT with different properties. The algorithms for FDT induction and the criteria for building non-ordered, ordered or stable FDTs were originally proposed in [62].

_{q}in Equation (2) permits the selection of splitting attribute ${\mathrm{A}}_{{i}_{q}}$. This attribute will be associated with a node of the FDT.

_{j}of target attribute B is [35]

`.`The branch is finished as a leaf if the frequency of this branch is less than α.

_{j}of the target attribute B. These states can be interpreted as certainty degrees for these values. A value with maximal certainty is recommended as the target attribute of this branch. The second threshold β limits FDT growth too. The FDT branch is finished as a leaf if the maximal certainty degree of this branch more than threshold β. Therefore, an FDT branch is finished as a leaf when the certainty degree of any value B

_{j}of the target attribute is more than threshold β.

_{3}only. This attribute has four possible values: A

_{3,0}, A

_{3,1}, A

_{3,2}and A

_{3,3}. Similarly, target attribute B has three possible values: B

_{0}, B

_{1}and B

_{2}.

_{3}equals

**I**(B

_{0}; A

_{3,0}) +

**I**(B

_{0}; A

_{3,1}) +

**I**(B

_{0}; A

_{3,2}) +

**I**(B

_{0}; A

_{3,3}) +

**I**(B

_{1}; A

_{3,0}) + … +

**I**(B

_{2}; A

_{3,3}) =

**I**(B

_{0}; A

_{3,0}) = M(B

_{0}× A

_{3,0}) × (−log

_{2}M(B

_{0}) − log

_{2}M(A

_{3,0}) + log

_{2}M(B

_{0}× A

_{3,0}) + log

_{2}N) =

**H**(A

_{3}) = 12 × log

_{2}12 − 3.0 × log

_{2}3.0 − 3.0 × log

_{2}3.0 − 3.1 × log

_{2}3.1 − 2.9 × log

_{2}2.9 = 23.995.

**I**(B; A

_{i}) /

**H**(A

_{i}) for each i (i = 1,…,4). The minimal value 5.547/23.995 corresponds to the input attribute A

_{3}. Therefore, we assign attribute A

_{3}as a FDT root node (Figure 4).

_{3}has the maximum value of information estimation (Equation (2)). Therefore, this attribute is associated with the FDT root (top node). The data analysis starts with this attribute. This attribute can have the following possible values: A

_{3,0}, A

_{3,1}, A

_{3,2}and A

_{3,3}. The value of attribute A

_{3,0}stipulates target attribute B to be B

_{0}(the system is non-operational) with a certainty degree of 0.827. The other variants B

_{1}and B

_{2}of target attribute B can be chosen with a certainty degree of 0.170 and 0.003, respectively. Frequency f for branch A

_{3,0}is calculated as M(A

_{3,0})/12. The result equals 3.0/12 = 0.250. This frequency f = 0.250 shows the possibility of an occurrence of values A

_{3,0}when measuring the value of input attribute A

_{3}. The certainty degree of 0.827 for the value of B

_{0}is more than β = 0.80; therefore, we stop the process of constructing the FDT for this branch.

_{3}has other values (i.e., A

_{3,1}or A

_{3,2}), then value B

_{1}(the system is partially operational) of attribute B should be chosen with a certainty of 0.643 and 0.613, respectively. Similarly, for branch A

_{3,3}, the maximal value B

_{2}(the system is fully operational) of attribute B should be chosen with a certainty degree of 0.655, respectively. These certainty degrees are below the priory threshold for the target attribute (β = 0.80). Moreover, the frequencies of occurrence for values A

_{3,1}, A

_{3,2}and A

_{3,3}(frequencies of FDT branches) are equal to f(A

_{3,1}) = 3.0/12 = 0.250, f(A

_{3,2}) = 3.1/12 = 0.258 and f(A

_{3,3}) = 2.9/12 = 0.242, respectively. The frequency of each branch is higher than the given threshold α = 0.15. Therefore, these branches do not finish as leaves.

_{i}

_{,j}. Thus, the FDT can be represented by fuzzy decision rules [66]. The FDT in Figure 4 has eight leaves. We can formalize one fuzzy decision rule per each leaf. Of course, we have to use several fuzzy classification rules for analyses of new initial situations [62]:

- IF A
_{3}is A_{3,0}THEN B is B_{0}with certainty 0.827; - IF A
_{3}is A_{3,1}and A_{1}is A_{1,0}THEN B is B_{0}with certainty degree 0.616; - IF A
_{3}is A_{3,1}and A_{1}is A_{1,1}THEN B is B_{1}with certainty degree 0.822; - IF A
_{3}is A_{3,2}and A_{1}is A_{1,0}THEN B is B_{1}with certainty degree 0.672; - IF A
_{3}is A_{3,2}and A_{1}is A_{1,1}and A_{2}is A_{2,0}THEN B is B_{1}with certainty degree 0.756; - IF A
_{3}is A_{3,2}and A_{1}is A_{1,1}and A_{2}is A_{2,1}THEN B is B_{2}with certainty degree 0.651; - IF A
_{3}is A_{3,3}and A_{2}is A_{2,0}THEN B is B_{1}with certainty degree 0.589; and - IF A
_{3}is A_{3,3}and A_{2}is A_{2,1}THEN B is B_{2}with certainty degree 0.910.

## 6. Construction of the Structure Function Based on the FDT

**x**= (0 0 0) to

**x**= (1 1 3) must be classified into M classes of the system performance levels.

**x**= (0 0 0). Analysis based on the FDT starts with the attribute A

_{3}(Figure 4) that is associated with the third component. The value of this component state is 0 (x

_{3}= 0) for the specified state vector. Therefore, the branch for the attribute value A

_{3,0}is considered. The branch of this value has a leaf node, therefore the target attribute value at this node is defined as B

_{0}and analysis of other attributes is not necessary in this case. The system performance level for this state vector

**x**= (0 0 0) is 0 (the system is non-operational; fatal medical error) with a certainty degree of 0.827.

**x**= (1 0 1). We analyze attribute A

_{3}, and the value of this attribute is A

_{3,1}for this state vector. According to the FDT, the branch with attribute value A

_{3,1}is selected. Next, attribute A

_{1}is analyzed in a similar manner. The estimation of this attribute is implemented using a branch with an attribute value A

_{1,1}because the specified state vector includes x

_{1}= 1. The branch of this value has a leaf node; therefore, the target attribute can take any of the following possible values: value 0 (with a certainty degree of 0.006), value 1 (with a certainty degree of 0.822) and value 2 (with a certainty degree of 0.112). The value of the target attribute should be defined as the value with the maximal certainty degree, so the system performance level for the specified state vector is φ(

**x**) = 1 with a certainty of 0.822.

**x**= (0 1 1), the system state is 0, while for

**x**= (1 0 1), the system state is 1. Thus, it seems that in the event of one type of doctor error, the two nurses have different influences on the system. This outcome is inferred from the initial data. Each of the nurses has their own experiences, different qualifications and unique mistakes. Our algorithm can trace such influences, which was not obvious at the start.

## 7. System Evaluation Based on the Structure Function

_{j}[17]:

_{0}is system unavailability: U = A

_{0}; ${p}_{i,{s}_{i}}$ is the probabilities of the i-th component state s

_{i}, which represents the initial data for the system evaluation and is based on the structure function (s

_{i}= 0, …, m

_{i}− 1):

_{i,s}= Pr{x

_{i}= s

_{i}}.

_{1}= m

_{2}= 3) were considered for all versions: x

_{1}= the work of the nurse and x

_{2}= the work of the doctor. Device states (the third component x

_{3}) had only two states (m

_{3}= 2): error and functioning. The structure function for each system versions was formed using FDTs that were inducted based on data collected in the repositories. The constructed structure functions for three versions of the system are described in Table 9.

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Non-ordered FDT induction for the monitoring data from Table 1.

**Figure 5.**Scheme to evaluate the medical error as a result of familiarization problems and exploitation of new device.

**Figure 6.**Probabilities of the system’s performance levels for three versions: patient examination without device; patient examination with device’s exploitation for two months; and patient examination with device’s exploitation for one year.

**Figure 8.**Sensitivity of the medical errors according to mistakes by the nurse, mistakes by the doctor and device failure.

x_{1} | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |

x_{2} | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 |

φ(x) | 0 | 0 | 1 | 1 | 0 | 2 | 2 | 2 |

Structure Function | FDT |
---|---|

Number of the system components: n | Number of input attribute: n |

System component x_{i} (i = 1, …, n) | Initial attribute A_{i} (i = 1, …, n) |

The i-th system component state: {0, …, m_{i} − 1} | Attribute A_{i} values: {A_{i}_{,0}, …, A_{i,j}, …, A_{i,mi}_{−1}} |

System performance level φ(x) | Target attribute B |

System performance level values: { 0, …, M − 1} | Values of target attribute B: {B_{0}, …, B_{M}_{−1}} |

Structure function | Decision table |

No. | x_{1} | x_{2} | x_{3} | φ(x) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 0 | 1 | 0 | 1 | 2 | 3 | 0 | 1 | 2 | |

1 | 0.9 | 0.1 | 1.0 | 0.0 | 0.0 | 0.0 | 0.2 | 0.8 | 0.3 | 0.7 | 0.0 |

2 | 0.0 | 1.0 | 0.9 | 0.1 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.8 | 0.2 |

3 | 0.2 | 0.8 | 0.6 | 0.4 | 0.1 | 0.8 | 0.1 | 0.0 | 0.0 | 0.9 | 0.1 |

4 | 0.1 | 0.9 | 0.1 | 0.9 | 0.0 | 0.2 | 0.7 | 0.1 | 0.0 | 0.2 | 0.8 |

5 | 1.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 | 1.0 |

6 | 0.0 | 1.0 | 0.8 | 0.2 | 0.9 | 0.1 | 0.0 | 0.0 | 1.0 | 0.0 | 0.0 |

7 | 0.1 | 0.9 | 0.2 | 0.8 | 0.0 | 0.0 | 0.1 | 0.9 | 0.0 | 0.1 | 0.9 |

8 | 0.1 | 0.9 | 0.1 | 0.9 | 0.0 | 1.0 | 0.0 | 0.0 | 0.0 | 1.0 | 0.0 |

9 | 0.8 | 0.2 | 0.2 | 0.8 | 0.8 | 0.2 | 0.0 | 0.0 | 0.6 | 0.4 | 0.0 |

10 | 0.0 | 1.0 | 0.0 | 1.0 | 1.0 | 0.0 | 0.0 | 0.0 | 0.9 | 0.1 | 0.0 |

11 | 0.9 | 0.1 | 0.1 | 0.9 | 0.0 | 0.1 | 0.8 | 0.1 | 0.0 | 0.9 | 0.1 |

12 | 1.0 | 0.0 | 1.0 | 0.0 | 0.2 | 0.6 | 0.2 | 0.0 | 1.0 | 0.0 | 0.0 |

M(A) | 5.1 | 6.9 | 5.0 | 7.0 | 3.0 | 3.0 | 3.1 | 2.9 | 3.8 | 5.1 | 3.1 |

Structure Function | Attribute | Attribute’s Value | Attribute Value’s Description |
---|---|---|---|

x_{1} | A_{1} | A_{1,0} | The first nurse’s error |

A_{1,1} | The first nurse’s work without error | ||

x_{2} | A_{2} | A_{2,0} | The second nurse’s error |

A_{2,1} | The second nurse’s work without error | ||

x_{3} | A_{3} | A_{3,0} | The fatal error of the doctor |

A_{3,1} | The complex error of the doctor | ||

A_{3,2} | The non-principal error of the doctor | ||

A_{3,3} | The doctor’s work without error | ||

φ(x) | B | B_{0} | The system is non-operational (fatal medical error) |

B_{1} | The system is partially operational (some imperfection in patient care) | ||

B_{2} | The system is fully operational (patient care without any complication) |

**Table 5.**Ratio of the number of incorrectly constructed structure functions for different approaches.

No | Dataset | TS | NoA | NoC | Ratio of the Number of Incorrect Structure Functions | |||||
---|---|---|---|---|---|---|---|---|---|---|

FDT | ysFDT | C4.5 | CART | nBayes | kNN | |||||

1. | blood | 748 | 4 | 2 | 0.2363 | 0.2389 | 0.2263 | 0.2281 | 0.2493 | 0.3953 |

2. | breast | 106 | 9 | 6 | 0.4017 | 0.4454 | 0.3590 | 0.3567 | 0.3618 | 0.3586 |

3. | bupa | 345 | 6 | 2 | 0.4105 | 0.4224 | 0.3517 | 0.3527 | 0.4448 | 0.4339 |

4. | diagnosis | 120 | 6 | 2 | 0.0002 | 0.1578 | 0.0072 | 0.0074 | 0.0476 | 0.0000 |

5. | ecoli | 336 | 7 | 8 | 0.1816 | 0.2408 | 0.2918 | 0.2036 | 0.1520 | 0.2790 |

6. | haberman | 306 | 3 | 2 | 0.2652 | 0.2462 | 0.2749 | 0.2625 | 0.2537 | 0.4077 |

7. | heart | 270 | 13 | 2 | 0.1650 | 0.2575 | 0.2443 | 0.221 | 0.1635 | 0.3126 |

8. | ilpd | 579 | 10 | 2 | 0.2850 | 0.2854 | 0.2837 | 0.2828 | 0.4419 | 0.3991 |

9. | nursery | 12,960 | 8 | 5 | 0.0853 | 0.0833 | 0.0289 | 0.0427 | 0.0926 | 0.0982 |

10. | parkinsons | 195 | 22 | 2 | 0.0959 | 0.1522 | 0.1498 | 0.1289 | 0.2993 | 0.0839 |

11. | pima | 768 | 8 | 2 | 0.2417 | 0.2527 | 0.2547 | 0.2544 | 0.2462 | 0.3585 |

12. | thyroid | 215 | 5 | 3 | 0.0739 | 0.1059 | 0.0780 | 0.0955 | 0.0339 | 0.0568 |

13. | vertebral2 | 310 | 6 | 2 | 0.1714 | 0.1818 | 0.1916 | 0.1892 | 0.2202 | 0.2846 |

14. | vertebral3 | 310 | 6 | 3 | 0.1993 | 0.3027 | 0.1915 | 0.1903 | 0.1788 | 0.3412 |

15. | wdbc | 569 | 30 | 2 | 0.0368 | 0,0705 | 0.0641 | 0.0704 | 0.0674 | 0.0719 |

16. | wpbc | 194 | 33 | 2 | 0.2210 | 0.249 | 0.2400 | 0.2334 | 0.3378 | 0.4269 |

Component States (Values of Attribute A_{i}) | x_{1} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

x_{2} | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | |

x_{3} | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 | 0 | 1 | 2 | 3 | |

System performance level | φ(x) | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 2 | 0 | 1 | 1 | 1 | 0 | 1 | 2 | 2 |

Certainty degree | 0.827 | 0.616 | 0.672 | 0.589 | 0.827 | 0.616 | 0.672 | 0.910 | 0.827 | 0.822 | 0.756 | 0.589 | 0.827 | 0.822 | 0.651 | 0.910 |

Attribute | Attribute Values | Attribute Value’s Description |
---|---|---|

A_{1} | A_{1,0} | The mistake in work of the nurse |

A_{1,1} | The incorrect work of nurse | |

A_{1,2} | The perfect work of the nurse | |

A_{2} | A_{2,0} | The doctor’s mistake |

A_{2,1} | The incorrect work of the doctor | |

A_{2,2} | The perfect work of the doctor | |

A_{3} | A_{3,0} | The failure of the device |

A_{3,1} | The functioning of the device | |

B | B_{0} | The system is non-operational (medical error) |

B_{1} | The system is partially operational (complications in patient care) | |

B_{2} | The system is fully operational (perfect patient care) |

x_{1} | x_{2} | x_{3} | 1st Version | 2nd Version | 3rd Version | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |

0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |

0 | 1 | 0 | 0.3 | 0.4 | 0.3 | 0.3 | 0.4 | 0.3 | 0.3 | 0.4 | 0.3 |

0 | 1 | 1 | 0.3 | 0.4 | 0.3 | 0.2 | 0.5 | 0.3 | |||

0 | 2 | 0 | 0.2 | 0.6 | 0.2 | 0.3 | 0.5 | 0.2 | 0.3 | 0.5 | 0.2 |

0 | 2 | 1 | 0.2 | 0.6 | 0.2 | 0.3 | 0.5 | 0.2 | 0.3 | 0.3 | 0.4 |

1 | 0 | 1 | 0.4 | 0.3 | 0.3 | 0.3 | 0.5 | 0.2 | |||

1 | 1 | 1 | 0.1 | 0.6 | 0.3 | 0.1 | 0.6 | 0.3 | 0.1 | 0.4 | 0.5 |

1 | 2 | 0 | 0.1 | 0.6 | 0.3 | 0.3 | 0.3 | 0.6 | |||

1 | 2 | 1 | 0.1 | 0.4 | 0.5 | 0 | 0.3 | 0.7 | |||

2 | 0 | 1 | 0.4 | 0.3 | 0.3 | 0.4 | 0.3 | 0.3 | 0.2 | 0.5 | 0.3 |

2 | 1 | 0 | 0 | 0.6 | 0.4 | 0 | 0.6 | 0.4 | 0 | 0.6 | 0.4 |

2 | 1 | 1 | 0 | 0.6 | 0.4 | 0 | 0.3 | 0.7 | |||

2 | 2 | 0 | 0 | 0.3 | 0.7 | 0.1 | 0.3 | 0.6 | |||

2 | 2 | 1 | 0 | 0.3 | 0.7 | 0 | 0.3 | 0.7 | 0 | 0.3 | 0.7 |

Component States | x_{1} | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

x_{2} | 0 | 0 | 1 | 1 | 2 | 2 | 0 | 0 | 1 | 1 | 2 | 2 | 0 | 0 | 1 | 1 | 2 | 2 | ||

x_{3} | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | ||

System Performance Level | 1st ver. | φ_{1}(x) | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 2 | 2 | 0 | 0 | 1 | 1 | 2 | 2 |

2nd ver. | φ_{2}(x) | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 2 | 0 | 0 | 1 | 1 | 2 | 2 | |

3rd ver. | φ_{3}(x) | 0 | 0 | 1 | 1 | 1 | 2 | 0 | 1 | 1 | 2 | 2 | 2 | 0 | 1 | 1 | 2 | 2 | 2 |

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**MDPI and ACS Style**

Zaitseva, E.; Levashenko, V.; Rabcan, J.; Krsak, E.
Application of the Structure Function in the Evaluation of the Human Factor in Healthcare. *Symmetry* **2020**, *12*, 93.
https://doi.org/10.3390/sym12010093

**AMA Style**

Zaitseva E, Levashenko V, Rabcan J, Krsak E.
Application of the Structure Function in the Evaluation of the Human Factor in Healthcare. *Symmetry*. 2020; 12(1):93.
https://doi.org/10.3390/sym12010093

**Chicago/Turabian Style**

Zaitseva, Elena, Vitaly Levashenko, Jan Rabcan, and Emil Krsak.
2020. "Application of the Structure Function in the Evaluation of the Human Factor in Healthcare" *Symmetry* 12, no. 1: 93.
https://doi.org/10.3390/sym12010093