3.1. Fuzzy Evaluation of Casting Workshop
A mechanical manufacturing business in Hunan, China was built in 1958, which covers an area of more than one point eight million square meters and has about five hundred workers. The registered capital of this mechanical manufacturing business is two billion yuan. The number of different types of equipment is more than 2800.
In recent years, this foundry business produced the first high performance driverless road roller in China, as well as the first environmentally friendly compacting machine for rubbish. Casting is a metal hot working process for producing components via mechanical manufacturing, which plays an important role in the national economy. Although it’s a service in social development, casualty accidents still occur. This study aims at adopting corresponding counter measures based on the safety evaluation result.
Analysis of the foundry site revealed that the factors affecting safety management of a casting workshop mainly include educational training, safety input, control of dangerous and harmful factors, hidden danger identification, and security systems. Therefore, the set of evaluated indicators is U={educational training(ET), safety input(SI), dangerous and harmful factors control(DHFC), hidden danger identification(HDI), security system(SS)}. The set of evaluation levels can be divided into V={Safe, Relatively safe, Generally safe, Relatively dangerous, Dangerous}.
After comparing the relative importance of evaluation indicators according to the analytic hierarchy process [
25,
26], the judgment matrix can be achieved as follows [
43].
Based on reference [
25,
26], we can see that the degree of preference may reach up to 9 in extreme circumstances for different industries and different evaluation indicators. For the casting workshop of the foundry enterprise, there is not much difference among the importance of different evaluation indicators in
Table 1. Taking ET and SI as an example, the scale of ET to SI is 2, indicating that the importance of ET is mildly (less than slightly) favored over SI. It should be noted that different weights of evaluation indicators can be achieved based on different degrees of preference. As mentioned in the Introduction, the weights achieved by the analytic hierarchy process mainly rely on subjective judgments from experts rather than actual data. Although the analytic hierarchy process might take full advantage of experts, different assessment results might be obtained from different experts.
The maximum eigenvalue was λmax = 5.1947, and the corresponding eigenvector was W = (0.2933, 0.5107, 0.387, 0.6738, 0.2223).
The consistency index was
, and the consistency ratio was
, which indicates the judgment matrix was a consistent matrix [
26].
The subjective weight can be calculated as follows after normalization.
After experts vote on the level of each indicator evaluated, the evaluation matrix can be constructed by the vote ratio as follows [
43].
For the evaluation matrix R, taking ET as an example, which means 12% of expert score 5, 20.1% of expert score 4, 35.4% of expert score 3, 20.7% of expert score 2 and 11.8% of expert score 1 for this indicator. The bigger the score, the higher the safety level of the casting workshop.
The fuzzy evaluation result can be obtained as follows, after application of Equation (1)
Therefore, the safety management evaluation result for the casting workshop was “Generally safe” based on the maximum membership principle.
3.2. Integrated Weight Determined by Least Square Method
The subjective weight method relies on the subjective judgments of experts, potentially resulting in variability in the assessment results. The objective weight method is based on actual data rather than expert judgments, but may not be exactly relevant to a given situation. The integrated weight method combines subjective and objective weight methods to include both expert judgments and data. The widely used integrated weight method is described as follows [
33,
44].
where,
,
and
indicate integrated, subjective, and objective weights, respectively;
n is the number of indicators evaluated;
is the preference coefficient.
For the preference coefficient
, there is no explicit computational method. Thus, in this study, a new algorithm was proposed to determine the preference coefficient based on the least square method [
35] as follows.
The error sum of square among integrated, subjective, and objective weights of the evaluated indicator can be calculated as shown below.
The least square method requires the least error sum of the square, so that Equation (21) achieves the minimum value.
Additionally, the method requires the derivation of the preference coefficient
to allow Equation (20) to achieve the minimum value so that the derivative is 0, as shown in Equation (22).
In Equation (22), the polynomial . For Equation (22) to be correct, the polynomial must be 0. Therefore, .
If we then input
into Equation (20), we obtain Equation (23)
Although Equation (23) has the same form as references [
33,
44], it has more explicit physical significance in this study due to application of the least square method, that is, the error sum of the square among integrated, subjective and objective weights achieve the minimum value.
The objective weights of the evaluation indicators can be achieved by the entropy weight method [
28,
29] and the evaluation matrix R, giving results of W
O = [0.12 0.202 0.281 0.244 0.153]′. The findings results show that there is significant difference among different weights of evaluation indicators, such as the weight of DHFC is more than twice over ET. The objective entropy weight method is mainly based on real data rather than expert judgments, taking advantage of the objectivity of real data.
Therefore, the integrated weights of the indicator evaluated can be determined based on Equation (23), as: WI = [0.1305 0.2235 0.233 0.283 0.13]′.
3.3. Cloud Model Evaluation of Sub-indicators
If we set the numerical range of safety level as [
1,
5], then the corresponding standard cloud models can be achieved. Taking C
3(
Ex3, En3, He3) as an example, the expectation
Ex3 can be calculated according to Equation (24) as follows.
The entropy
En3 can be calculated according to Equations (25) and (26) as follows.
The hyper entropy
He3 can be calculated according to Equation (27) as follows.
Then the standard cloud models of safety levels can be achieved in a similar way based on Equations (2)–(12), shown in
Table 2.
For the evaluation matrix, assuming that one thousand experts are taking part in the vote. Taking ET as an example, 120 experts score 5, 201 experts score 4, 354 experts score 3, 207 experts score 2 and 118 experts score 1 for this indicator. The cloud model of ET can be obtained via a backward cloud algorithm, the expectation
Ex can be calculated as follows.
The entropy
En can be calculated based on the backward cloud algorithm as follows.
The hyper entropy
He can be calculated based on backward cloud algorithm as follows.
The cloud models of other evaluation indicators can be achieved in a similar way, with the help of MATLAB software (The MathWorks Inc. Natick, MA, USA), shown in
Table 3.
The qualitative evaluation result can be obtained by mapping the cloud model, and its corresponding standard cloud models of ET into a cloud picture, shown in
Figure 3.
As shown in
Figure 3, the main cloud model of ET falls between the Relatively dangerous and Relatively safe standard cloud models, and the cloud drops of ET cloud model are most concentrated in the region of the Generally safe standard cloud model. Therefore, the qualitative evaluation result of ET was between Relatively dangerous and Relatively safe, and more inclined to Generally safe.
The assessment result of ET was the same in comparison against the expectation and corresponding safety levels (
Table 2), which was in line with Xu et al.’s intuitive understanding that the assessment result of the cloud model was mainly based on the expectation of the evaluation indicator [
45]. Safety level was worse when the expectation of the evaluation indicator was poor, which confirms that the introduced cloud model yields an accurate safety assessment. A qualitative assessment was obtained by comparing the cloud model of ET and its corresponding standard cloud models. The cloud drops of ET, as discussed above, are a good example of this, as most of the cloud drops fall between Relatively dangerous and Relatively safe, and are more inclined to Generally safe. The qualitative assessment result indicates that the safety level of ET was between Relatively dangerous and Relatively safe, and more inclined to Generally safe. Greater cloud model coverage area also indicates greater fuzziness in determining the corresponding safety level; in other words, the safety evaluation data were scattered across a very wide range and had large changes in safety levels. Safety indicators with greater cloud thickness also showed greater randomness; that is to say, the same safe score may have different membership degrees. For example, the membership degrees of cloud drops belonging to Relatively dangerous were from 0.3 to 0.8 in the case of the safety indicator of ET at score 2 (
Figure 3).
From the above analysis, the qualitative evaluation result of ET is more likely to be Generally safe, indicating that the performance of ET is not very high, and corresponding safety measures should be adopted.
It is necessary to calculate the similarity between cloud model of ET and corresponding standard cloud models, to determine the specific safety level to which it belonged. Therefore, the similarities between this cloud model and corresponding standard cloud model can be obtained using Equation (16), shown in
Table 4.
λ3 = 0.99992 was the maximum similarity of ET evaluation indicator, indicating the safe level of ET belonged to Generally safe. That is to say, the quantitative evaluation result of ET was Generally safe.
When determining the safety level of the evaluation indicator by the cloud model, the maximum similarity corresponding to the standard cloud model is the quantitative evaluation result based on the maximum membership principle. As shown in
Table 4, not all the maximum similarities of evaluation indicators are close to 1, which reflected the uncertainty conversion between qualitative concepts and their corresponding quantitative values, and the uncertainty conversion containing fuzziness and randomness. Compared with the fuzzy evaluation method, although not all the maximum similarities of evaluation indicators are close to 1, the distinction degree of similarities is more remarkable (
Table 4). Taking HDI as an example, although the maximum similarity is
λ3 = 0.127, which is about 488 and 24 times over
λ1 and
λ2 respectively.
The qualitative evaluation result of ET was between Relatively dangerous and Relatively safe, and more inclined to Generally safe. The quantitative evaluation result of ET was Generally safe. Therefore, by combining the qualitative and quantitative evaluation results, the evaluation result of ET was Generally safe.
The evaluation results of other sub-indicators can be obtained in a similar way, and the evaluation results of SI, DHFC, HDI and SS were all Generally safe.
3.4. Cloud Model Evaluation of Casting Workshop
The comprehensive cloud model of the casting workshop (CW) can be achieved via Equations (13)–(15), shown in
Table 3.
The qualitative evaluation result can be obtained by mapping the cloud model of the CW, and the corresponding standard cloud model into a cloud image, shown in
Figure 3.
As shown in
Figure 3, the main cloud model of CW falls between the Relatively dangerous and Relatively safe standard cloud models, with the cloud drops of the CW cloud model being most concentrated in the region of the Generally safe standard cloud model. Therefore, the qualitative evaluation result of CW was between Relatively dangerous and Relatively safe, and more inclined to Generally safe.
It is necessary to calculate the similarity between cloud model of CW and the corresponding standard cloud models, to determine the specific safe level to which it belonged. Therefore, the similarities between this cloud model and the corresponding standard cloud model can be obtained using Equation (16), shown in
Table 4.
λ3 = 0.60196 was the maximum similarity of CW evaluation indicator, indicating the safe level of CW belonged to Generally safe. That is to say, the quantitative evaluation result of CW was Generally safe.
The qualitative evaluation result of CW was between Relatively dangerous and Relatively safe, and more inclined to Generally safe. The quantitative evaluation result of CW was Generally safe. Therefore, by combining the qualitative and quantitative evaluation results, the evaluation result of CW was Generally safe.
3.5. Comparison by Grey Relational Analysis
To validate the integrated weight algorithm proposed in this study, we next used grey relational analysis to compare the safety assessment results [
16,
17,
18] with the cloud model. The process of grey relational analysis is illustrated below.
The dimensionless matrix of the evaluated indicator can be achieved as follows based on Equation (31).
The optimal index set was transferred into D* = [11111].
The grey relational coefficient was achieved based on Equation (32).
If the integrated weight of the indicator evaluated is
WI = [0.133 0.2315 0.231 0.2745 0.13]′, then, the grey relational degree of casting workshop can be determined as below, according to Equation (33).
The evaluation level for the casting workshop was “Generally safe” according to the grey relational degree.
The assessment result determined by grey relational analysis was the same as that obtained by the cloud model, in which indicator weights were determined using the revised integrated weight algorithm. Thus, the integrated weight method proposed and cloud model adopted in this study are feasible.
3.6. Cause and Effect–LOPA of Dangerous and Harmful Factors
The safety management assessment indicated conditions are likely to be Generally safe based on the above analysis. Accidents are probable in the foundry workplace, due to dangerous and potentially harmful conditions. Controlling potentially dangerous factors will help to improve the safe operation of the foundry. To do this, cause and effect–LOPA was applied to identify dangerous and harmful factors that contribute to accidents, as shown in
Figure 4.
As shown in
Figure 4, the causes that may lead to accidents in the casting workshop mainly including dust, noise, toxic gas, mechanical injury, empyrosis and electric shock, and each cause contains several sub-causes. Taking dust as an example, whose sub-causes are sand mixing, modeling, shakeout and fettling, that is, from sub-causes 1 to 4. In other words, the dust in the casting workshop is likely to be caused by sub-causes 1–4. Similarly, sub-causes of noise are from 5 to 7, sub-causes of toxic gas are from 8 to 10, sub-causes of mechanical injury are from 11 to 13, sub-causes of empyrosis are from 14 to 16, and sub-causes of electric shock are from 17 to 19. The causes and sub-causes that may lead to accidents in the casting workshop are shown in
Table 5.
In
Figure 4, to prevent accidents in the casting workshop and protect employee health, 18 IPLs should be adopted. Taking dust as an example, whose IPLs are wearing a mask, wet working and dust removal by ventilation, that is, from IPLs 1 to 3. In other words, the dust in the casting workshop can be eliminated by IPLs 1–3. Similarly, IPLs of noise are from 4 to 6, IPLs of toxic gas are from 7 to 9, IPLs of mechanical injury are from 10 to 12, IPLs of empyrosis are from 13 to 15, and IPLs of electric shock are from 16 to 18. The IPLs that can be adopted to prevent accidents and protect employee health are shown in
Table 6.
In this cause and effect–LOPA, foundry accidents were attributed to 6 causes and 19 sub-causes, and foundry accidents can be prevented by 18 IPLs. Causes 1 to 6 are all risk factors, which can lead to accidents in the casting workshop. Causes 1 and 2 may result in organ failure of the body and belong to low risk factors; Causes 3 to 6 can lead to serious casualties and belong to high risk factors. If the IPLs proposed in this study were not carried out, accidents may occur in the casting workshop. The safety level of the foundry can be improved by taking steps based on the cause and effect–LOPA identification of dangerous and harmful factors.
From the standpoint of safety management, to improve safe production in the casting workshop, management measures should also be adopted. First, improve the rules and regulations for the casting workshop. Second, strengthen the safety training. Third, the identification of dangerous and harmful factors and elimination of accident potential.