Applied Mechanics and Materials Online: 2013-08-30 ISSN: 1662-7482, Vol. 371, pp 822-826 doi:10.4028/www.scientific.net/amm.371.822 2013 Trans Tech Publications, Switzerland Improvement of Process Failure Mode and Effects Analysis using Fuzzy Logic RACHIERU Nicoleta a, BELU Nadia b and ANGHEL Daniel Constantin c University of Piteşti, Faculty of Mechanics and Technology, Department of Manufacturing and Industrial Management, 110040 Pitesti, Targu din Vale Street, no. 1, Argeş, Romania a nrachieru@yahoo.com, b nadia_belu2001@yahoo.com, c daniel.anghel@upit.ro Keywords: quality improvement, process failure modes and effect analysis, risk evaluation, fuzzy sets. Abstract. Risk analysis increased in importance within environmental, health and safety regulation last few years. Process Failure Mode and Effects Analysis is one of the most used techniques to evaluate a process for strengths, weaknesses, potential problem areas or failure modes, and to prevent problems before they occur. The traditional PFMEA determines the risk priorities of failure modes using the Risk Priority Numbers by multiplying the scores of the risk factors like the occurrence (O), severity (S) and detection (D) of each failure mode. The method has been criticized to have several shortcomings. Fuzzy logic approach is preferable in order to remove the deficiencies in assigning the risk priority numbers. In this study, a fuzzy-based PFMEA is to be applied to improve the manufacturing process of rear bumper, injection part used in automotive industry. The fuzzy model PFMEA can provide the stability of process assurance. Introduction One of the most important quality management inductive analysis techniques is Failure Mode and Effects Analysis (FMEA). FMEA is an engineering method used to define, identify and eliminate potential failures, problems and errors from a system before they reach the customer [1]. It is used as a powerful tool for safety and reliability analysis of products and processes in a wide range of industries particularly, aerospace, nuclear, electronics and automotive industries. The automotive industry was first deployed FMEA by Ford in 1973, for the preventive detention of quality. There are several types of FMEA s: Concept of FMEA (CFMEA), Design FMEA (DFMEA), Process FMEA (PFMEA) used in the automotive field. The purpose of this paper is the Process FMEA analysis. PFMEA is used to analyze the already developed or existing processes. PFMEA focuses on potential failure modes associated with both the process safety / effectiveness / efficiency and the functions of a product caused by the process problems. Applying FMEA to a process means following a series of successive steps: analysis of the process, list of identified potential failures, evaluation of their frequency, severity and detection technique, global evaluation of problem, and apply of the corrective and preventive actions that could eliminate or reduce the chance of potential failures [2]. In quantification of the risk PFMEA uses indicator (RPN), defined as the product of the severity (S), occurrence (O), and detection (D) of the failure. Traditional PFMEA uses five scales and scores of 1 10, to measure the probability of occurrence, severity and the probability of not detection. Even through the traditional RPN model is simple and has been well accepted for safety analysis, it suffers from several weaknesses. In [3, 4] it is pointed out that the same RPN score can be obtained from a number of different score combinations of severity, occurrence, and detect. Although the same RPN is obtained, their hidden risk implications may be totally different. In [5] is suggested to give the occurrence factor the most weight in the RPN calculation because it affects the likelihood of a fault reaching the customer. In other words, interdependencies among various failure modes and effects are not taken into account [6]. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (ID: 130.203.136.75, Pennsylvania State University, University Park, USA-09/05/16,04:30:02)
Applied Mechanics and Materials Vol. 371 823 To overcome the above drawbacks, of the typical approach, fuzzy mathematics, developed for solving problems where parameter descriptions are subjective, vague and imprecise, was considered a promising tool for directly manipulating the linguistic terms used for the description of severity, occurrence and detection in order to assess risks associated to each failure mode [7]. The process of fuzzy logic is given in Fig. 1. Crisp Input Fuzzification Rules Fuzzy Output Defuzzification Fuzzy Input Fuzzy Logic / Inference Crisp Output Fig. 1. Fuzzy logic process [7] The methodology of the fuzzy RPNs is based on fuzzy set theory. The three inputs S, O and D are fuzzified and evaluated in a fuzzy inference engine built on a consistent base of IF-THEN rules. The fuzzy output is defuzzified to get the crisp value of the RPN that will be used for a more accurate ranking of the potential risks. Many studies have been published in technical fields where FMEA was used together with fuzzy sets. For example, Yang et al. [8] presented a new failure mode and effects analysis model of CNC machine tool using fuzzy theory. Chin et al. [9] proposed a framework of a fuzzy FMEA based evaluation approach for new product concepts. A new risk assessment system based on fuzzy theory is proposed in this paper to deal with the conventional PFMEA difficulties. It is realized a parallel between the typical and the fuzzy computation of RPNs, in order to assess and rank risks associated to failure modes that could appear in the manufacturing process of rear bumper, injection part used in automotive industry. Application Classical PFMEA Application. Using classical understanding the FMEA analysis was carried on the manufacturing process of rear bumper and the associated RPN numbers were calculated. In automobiles, a bumper is the front-most or rear-most part, ostensibly designed to allow the car to sustain an impact without damage to the vehicle's safety systems. They are not capable of reducing injury to vehicle occupants in high-speed impacts, but are increasingly being designed to mitigate injury to pedestrians struck by cars. The manufacturing process of rear bumper consists of the following: receiving material, drying material, injection, final inspection, packing, expedition. Specifically, we focused on injection operation of rear bumpers. When the RPN exceeds 100, it is necessary to take corrective action if the RPN is below 100 the risk is considered acceptable. In the injection operation in two case of possible failure, burrs, appeared RPN 108 and 112 which exceeds the acceptable limit (RPN=100). There had to take action, preventive maintenance plan of mould, so value RPN after application measure reduced to 72, which we consider as an acceptable risk. Results of PFMEA analysis are given in Table 1. After conventional PFMEA analysis, equal priorities (RPN=96) are assigned to failure mode FM1 - incomplete part for different causes (C3 - pressure of cylinder too low, C4 - insufficient quantity of material injected - incorrect adjustment). In order to obtain a risk prioritization that would reflect better the customer perception in terms of dissatisfaction, a fuzzy computation of the RPN was proposed.
824 Innovative Manufacturing Engineering Fuzzy PFMEA application. The fuzzy logic toolbox of Matlab software program has been used in calculating the values of RPN. A model was established for the FMEA technique having 3 inputs Process Injection Potential Failure Mode Incomplete part Burrs Burrs Blister Potential Effect of Failure FM1 FM3 FM3 FM4 S e v Table 1. Process FMEA Chart Potential O Current Controls Cause of c Failure c u Prevention Detection r 4 Temperature of mould too low C1 Temperature of cylinder too low C2 Pressure of cylinder too low C3 Insufficient quantity of material injected - incorrect adjustment C4 4 Clamping force too low - failure in the hydraulic system - C8 Clamping force too low incorrect adjustment C9 4 Clamping plan damaged / used C10 4 Temperature of mould too high C11 3 2 Adjustment sheet 6 48 / first part / Auto control 4 6 96 6 Starting 5 Starting 2 Starting 3 Preventive maintenance plan of mould 2 Starting Auto control D e t e c R P N 6 72 4 96 4 80 7 56 9 108 8 64 and 1 output variable, and given in Fig. 2. The RPN values were calculated by combining the associated 3 input factors. Five categories were associated to each fuzzy set: VL (very low), L, (low), M (moderate) and H (high), VH (very high). The output of the fuzzy system, FRPN, was scaled in the range 0...1000 in order to be compatible with the previous results. The severity, occurrence and detection values of the failures were identified with the help of expert opinions and by using an inference rules determined specifically. The rules were designed to take into account all possible situations.
Applied Mechanics and Materials Vol. 371 825 Table 2 presents the inference rules adopted for this application. Here are given some of the rules as an example. IF severity IS very law AND occurrence IS law AND detection IS very law then RPN IS very low. For Severity and Detection input variables was used Gaussian membership function (Eq. 1) defined by two parameters respectively center c and width σ. For Occurrence input variable was used Cauchy membership function (generalized bell) (Eq. 2) with the three parameters a, b,c. FUZZY RPN SEVERITY:L OCCURRENCE DETECTION VL VL VL VL L L FUZZY RPN Fig. 2. The Fuzzy FMEA model L VL VL L L M M VL L L M M H L L M M H VH L M M H H SEVERITY:VL OCCURRENCE DETECTION VL VL VL VL VL L L VL VL VL L L M VL VL L L M H VL L L M M VH L L M M H SEVERITY:VH FUZZY RPN OCCURRENCE DETECTION VL L L M M H L L M M H H M M M H H VH H M H H VH VH VH H H VH VH VH µ A (x) = exp µ A (x) = Table 2. Inference rules 1+ 1 1 2 x c a 2 x c σ SEVERITY:M FUZZY RPN OCCURRENCE DETECTION VL VL VL L L M L VL L L M M M L L M M H H L M M H H VH M M H H VH FUZZY RPN 2b SEVERITY:H OCCURRENCE DETECTION VL VL L L M M L L L M M H M L M M H H H M M H H VH VH M H H VH VH (1) (2) Mamdani min/max method of inference mechanism (input method: min; aggregate method: max) was used and the results were defuzzified by center of gravity method. There are different algorithms for defuzzification as well. These are Center of Gravity, Center of Gravity for Singletons, Center of Area, Left Most Maximum, and Right Most Maximum. Among these algorithms the most popular one is the center of gravity (centroid) technique. It finds the point where a vertical line would slice the aggregate set into two equal masses. Fig. 3 presents, as an example, the set of rules activated for the values corresponding to the failure mode FM1. As to the types of failure, the fuzzy RPN values provided in the model are given in Table 3 in comparison with the RPN values of classical FMEA.
826 Innovative Manufacturing Engineering FM Table 3. Conventional RPNs and Fuzzy RPNs Cause S O D RPN clasic RPN fuzzy FM1 C1 4 3 6 72 267 C2 4 2 6 48 237 C3 4 4 6 96 391 C4 4 6 4 96 488 FM2 C5 4 6 2 48 579 C6 4 4 5 80 406 C7 4 3 7 84 265 FM3 C8 4 5 4 80 408 C9 4 2 7 56 237 C10 4 3 9 108 203 FM4 C11 4 2 8 64 237 Conclusion The results obtained by fuzzy inference provide a hierarchy of potential risks that differs from the ranking established by conventional computation of the RPN: RPN=391 for C3: pressure of cylinder too low and RPN= 488 for C4: insufficient quantity of material injected - incorrect adjustment. The fuzzy inference does not allow identical values of RPNs to appear for different sets of risk factors. Results indicate that the application of fuzzy PFMEA method can solve the problems that have arisen from traditional FMEA, and can efficiently discover the potential failure modes and effects. It can also provide the stability of product and process assurance. The fuzzy PFMEA approach might be helpful to the management processes. In all the management processes in manufacturing areas it is quite possible to use this tool successfully. References Fig. 3. Set of rules activated by the failure mode FM1; fuzzy computation of risk priority number. [1] H. J. W. Vliegen, H. H. van Mal, Rational decision making: Structuring of design meetings, IEEE Transactions on Engineering Management, 37 (1990) 185-91. [2] Chrysler Corporation, Ford Motor Company, General Motors Corporation, Potential Failure Modes and Effects Analysis (FMEA). Reference Manual, 4 th ed., (2008). [3] H. C. Liu, L. Liu, N. Liu, L. X. Mao, Risk evaluation in failure mode and effects analysis with extended VIKOR method under fuzzy environment. Expert Systems with Applications, 39 (2012). [4] M. Ben-Daya, A, Raouf, A revised failure mode and effects analysis model. International Journal of Quality & Reliability Management, 3 (1993) 43 47. [5] F. Zammori, R. Gabbrielli, ANP/RPN: A multi criteria evaluation of the risk priority number. Quality and Reliability Engineering International, 28 (2011) 85 104. [6] Anonymous, A short fuzzy logic tutorial, (2010) available at http://www.cs.bilkent.edu.tr/~bulbul/depth/fuzzy.pdf, accessed: 21.02.2013. [7] Zh. Yang, B. Xu, F. Chen, Q. Hao, X. Zhu, Y. Jia, (2010). A New Failure Mode and Effects Analysis Model of CNC Machine Tool using Fuzzy Theory, Proceedings of the 2010 IEEE International Conference on Information and Automation, Harbin, China, pp. 582-587. [8] K-S. Chin, A. Chan, J-B. Yang, Development of a fuzzy FMEA based product design system, Int J Adv Manuf Technol 36 (2008) 633 649.
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