Reliability Analysis Using Fuzzy FMEA To Design Sustainable Production Abstract Candra Setiawan, Grace Agustin Wijaya, Lusia Permata Sari Hartanti * Industrial Engineering Study Program of Universitas Pelita Harapan Surabaya, Indonesia. This research is to identify the machine s failures and reliability on X Company. Manufacturing industries have used automatic machines but it does not guarantee the machines find no failures. That is why industry must have good machine maintenance. X Company is an example of manufacturing industry that has no good maintenance since the machine often go down suddenly. Failure and reliability analysis is important task to do on this company. By doing the analysis, each failure cause and its properties will be known and so the further action needed. Keywords: reliability, fuzzy FMEA, failure. 1. Introduction Technology brings much impact to manufacturing industries. Manufacturing industries widely used state-of-the-art machines in their process. However, those machines are not free from failures so it s necessary to do maintenance. Maintenance can minimize the occurrence of failure. Maintenance is an risk management in term of reliability [1]. Reliability defined as percentage of a system, tools, or components operate perfectly under one condition and time period []. The life time of machines divided into three periods. On the first period, the failure rate is decreasing because poor components are replaced by good ones. Second period are usage time where the failure occurs randomly. The third period is worn out time where the failure rate is very high. Failure and reliability analysis is developing time by time. The traditional method (statistic) needs much data which is these data hardly to get because along the time, the circumstance also changes [3]. Then the researchers propose probability and non-probability methods to analyze. The method widely used is fuzzy methodology [1]. Fuzzy methodology is claimed as the most logical and effective method to involve the vague of human judgment. Root cause analysis is the most common method used to analyze the failures. The purpose of RCA is to avoid the failure by focusing on the cause of the failures []. Failure mode and effect analysis is a method used to identify the most critical components that cause the failure. FMEA. There are two stages on FMEA. First is correspondence to identifying failure and its effect, second is determining the criticality of each failures. There are two kind of criticality on FMEA, that are criticality number and risk priority number. CN is often used in high risk industry where as RPN used in common situation. RPN is calculated using the equation below. (1) 3 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
Where Of is frequency of the failures, Od is the probability failure undetected, and S is severity of the failures. Fuzzy FMEA is based on fuzzy theory that has more flexibility and meaningful to assess the risk of a failure []. There are few advantages of fuzzy FMEA [5]. (a) Allowing researchers to estimate using linguistic terms (b) Qualittive and quantitative data can be used (c) Allowing severity, non-detectability, and frequency of failures into flexible structure. Parameters on traditional FMEA are fuzzified with proper membership function. The results of each fuzzy input are evaluated in fuzzy inference engine that used if-then law and fuzzy logic operation to define criticaility of failure. The fuzzy result the be defuzzified to get fuzzy RPN score. The higher risk will produce higher score of fuzzy RPN. Fuzzy FMEA can be developed using toolbox on MATLAB (). As a manufacturing industry, X Company is expected to minimize the occurrence of failure. It s why failure and reliability analysis is important to do in X Company. The maintenance of X Company usually is held once a year and when the machine is suddenly down. It indicates that maintenance has been held by X Company is not optimum. X Company should give more attention to failure types, failure cause, and reliability of the machine to have optimum maintenance. By giving proper attention to these things, X Company will be able to decide whether the machine and its parts are still reasonable to be used. The objective of this research is to know the reliability of production machine of X company.. Material and Methods Steps needed to analyze the failures and reliability are: (a) Construct the root cause analysis (b) Construct the FMEA The Of is evaluated as the function of MTBF while S is evaluated as the function of MTTR. The score of Of shown on Table 1, the score of Od shown on Table, and the score of S shown on Table 3. Table 1. Score of Of Linguistic Score MIBF Very Low 1 > 3 years Low 3 1-3 years Moderate 5 6-1 months High 7 8 - months Very high 9 10 < months 33 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
Table. Score of Od Probability of Linguistic Score not detected (%) Very Low 1 0 5 6 15 Low 3 16 5 6 35 Moderate 5 36 5 6 6 55 7 56 65 High 8 66 75 9 76 85 Very high 10 86 100 Table 3. Score of S Linguistic Score MTTR Very Low 1 < 1 hour Low 3 < 1 day Moderate 5 6 1 days High 7 8 External intervention needed Very high 9 10 Production stop (c) Construct fuzzy FMEA In constucting fuzzy FMEA, the parameters (Of, S, and Od) are fuzzified using trapezoidal MF while RPN score is fuzzified using triangular-trapezoidal MF, shown on Figure 1 and Figure. Figure 1. Trapezoidal MF 3 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
Figure. Triangular-trapezoidal MF Then, it s needed to establish the fuzzy rule or if-then clause. The antecedent is based on linguistic term of Of, Od, and S while the consequence is based on the RPN linguistic terms. The linguistic term of RPN is calculated below [6]. F(x) indicates the normalized RPN (RPN/1000), x indicates the fuzzy RPN output, and a indicates shape factor which is around 0,8 [6]. The lingustic of fuzzy RPN shown on Table. Table. Linguistic of RPN Range Linguistic 0,000-0,167 Not Important 0,167 0,333 Minor 0,333 0,500 Low 0,500 0,667 Moderate 0,667 0,833 Important 0,833 1,000 Very Important When all the linguistic terms of parameter are known, then it defuzzified and ranked. (d) Analyze the reliability In analyzing the reliability, needed the to know the failure rate and the repair time of every failure. The failure rate and repair time then turned into fuzzy using triangular MF. Then, the fuzzy values are calculated on different confidence level using fuzzy transition expression below. () And then calculate the reliability using equation below reliability = e t (3) 35 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
3. Result and Discussion Machines used on X Company are involving shaker, grinder, and cutter. On one day production, shaker operates for hours, grinder for hours, and cutter for 1 hour. The failure of those machine shown on Figure 3. Figure 3. Root cause analysis The ranking of failure cause of the X Company is shown on Table 5. Table 5 Failure cause ranking Failure cause Of Od S RPN Rank FC11 FC1 7 8 7 56 11 8 5 FC13 3 6 9 16 3 FC1 5 8 8 30 FC1 3 9 108 6 FC 8 3 8 9 FC3 8 8 6 38 1 FC 5 8 160 FC31 9 9 16 3 FC3 7 3 10 FC33 8 10 160 FC3 6 6 7 7 The linguistic terms of RPN for every failure cause is shown on Table 6. 36 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
Table 6. Linguistic terms of RPN Failure Cause RPN x Linguistic FC11 FC1 56 11 0.30 0.388 N. Imp Low FC13 16 0.93 Low FC1 30 0.703 Imp FC1 108 0.379 Low FC 8 0.0 Minor FC3 38 0.758 High FC 160 0.89 Low FC31 16 0.93 Low FC3 0.181 Minor FC33 160 0.89 Low FC3 7 0.81 Minor By joining the linguistic terms for Of, Od, S, and RPN allowed to establish 11 fuzzy rules. After compute using MATLAB, the rank of the each failure cause can be assembled as shown on Table 6. Table 6. Fuzzy FMEA ranking Failure Cause FRPN FRPN Ranking FC11 FC1 0,5 0, 3 FC13 0, FC1 0,783 1 FC1 0, FC 0,5 3 FC3 0,783 1 FC 0, FC31 0, FC3 0,5 3 FC33 0, FC3 0,5 3 From the ranking above, it s inferred that failure causes are grouped and allow the X Company to decide what parts and machine got more attention easier. In failure and reliability analysis, it s also needed to know the failure rate and repair time of every failure cause. It is shown on Table 7. Table 7. Failure rate (λ) and repair time (τ) Failure Cause λ (/hour) τ (hour) FC11 FC1 0.0050 0.0006 1 FC13 0.00069 8 FC1 0.00167 0.5 FC1 FC 0.00139 0.0000 1 FC3 0.01000 1 37 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
FC 0.00 FC31 0.00139 FC3 0.0078 1 FC33 0.0008 7 FC3 0.0078 1 The values of each failure rate and repair time converted into fuzzy value using triangular MF with spread 15% on cut point 0,5. These values shown on Table 8. The spread then expressed into fuzzy transition expression on α cut from 0 to 1 with 0,1 increment. Table 9 shows the fuzzy transition expression values of failure rate and repair time. Table 8. Spread of failure rate and repair time Failure Cause FC 11 FC 1 FC 13 FC 1 FC 1 FC FC 3 FC FC 31 FC 3 FC 33 FC 3 Failure Rate (/ hour) Repair Time (hour) λ λ0 λ3 λ1 λ τ τ0 τ3 τ1 τ 0.005 0.001 0.008 0.003 0.006 0 3 8 1 9.000 3.00.600 3.700.300 0.000 0.0003 0.0005 0.000 0.0005 1.00 10.0 13.80 11.10 1.90 6 9 3 3 0 0 0 0 0 0 0.0006 9 0.0005 9 0.0008 0 0.0006 0.0007 8.000 6.800 9.00 7.00 8.600 0.0016 0.001 0.0019 0.0015 0.0017 7 9 0.500 0.5 0.575 0.63 0.538 0.0013 0.0011 0.0016 0.001 0.001 9 8 0 8 9.000 3.00.600 3.700.300 0.000 0.0170 0.030 0.0185 0.015 0 0 0 0 0 1.000 0.850 1.150 0.95 1.075 0.0100 0.0085 0.0115 0.009 0.0107 0 0 0 5 5 1.000 0.850 1.150 0.95 1.075 0.00 0.0018 0.005 0.000 0.003 9 6 6 9.000 1.700.300 1.850.150 0.0013 0.0011 0.0016 0.001 0.001 9 8 0 8 9.000 3.00.600 3.700.300 0.007 0.003 0.0031 0.005 0.009 8 6 9 7 9 1.000 0.850 1.150 0.95 1.075 0.000 0.0017 0.00 0.0019 0.00 8 7 0 3 7.000 5.950 8.050 6.75 7.55 0.007 0.003 0.0031 0.005 0.009 8 6 9 7 9 1.000 0.850 1.150 0.95 1.075 Table 9. Fuzzy transition expression DOMF LS Failure RS LS Repair Time RS 1.0 0.9 0.080 0.076 0.080 0.083 1.87 1.7865 1.87 1.8687 0.8 0.07 0.087 1.766 1.9111 0.7 0.069 0.090 1.7075 1.953 0.6 0.065 0.09 1.669 1.9985 0.5 0.06 0.098 1.6316.035 0. 0.058 0.0501 1.597.089 38 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
0.3 0.05 0.0505 1.5586.1363 0. 0.051 0.0508 1.531.181 0.1 0.07 0.051 1.88.39 0.0 0.0 0.0516 1.53.88 Based on Table 9, can be calculated the others variables such as reliability, availability, mean time between failures, and expected number of failures shown on Table 10 and Table 11. DOMF LS Reliability RS LS Availability RS 1.0 0.9 0.6190 0.61 0.6190 0.6168 0.9196 0.918 0.9196 0.917 0.8 0.635 0.616 0.939 0.915 0.7 0.6 0.657 0.680 0.61 0.610 0.960 0.981 0.919 0.9105 0.5 0.630 0.6080 0.9301 0.9081 0. 0.635 0.6058 0.930 0.9057 0.3 0.638 0.6036 0.9339 0.903 0. 0.6371 0.6015 0.9358 0.9007 0.1 0.639 0.5993 0.9376 0.8981 0.0 0.617 0.5971 0.939 0.8955 Table 11. MTBF and ENOF DOMF MTBF LS RS ENOF LS RS 1.0 0.9.676.793.676.563 0.7 0.9 0.7 0.500 0.8.913.5 0. 0.56 0.7 3.036.35 0.396 0.551 0.6 3.163.0 0.369 0.577 0.5 3.93.139 0.3 0.60 0. 3.6.01 0.315 0.66 0.3 3.563 1.95 0.88 0.651 0. 3.703 1.853 0.60 0.675 0.1 3.87 1.76 0.3 0.699 0.0 3.99 1.677 0.0 0.73. Conclusion From the research, it was inferred that reliability of the machines is between 0.5971 to 0.617, availability is between 0.8955 to 0.939, MTBF is between 1.6776 to 3.993, and ENOF is between 0.73 to 0.0. The reliability of the machines was considered very low to use in production. In that case, this research gives the X Company a proper consideration about renewing machines, especially most critical machine and also this research bring to the clear conclusion that X Company should care about the load because overload is the main problem (FC1 and FC3 get first rank). 39 Proceedings The 1 ST UMM International Conference on Pure and Applied Research (UMM-ICOPAR 015)
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