Risk Priority Evaluated by ANP in Failure Mode and Effects Analysis

Transcription

1 12-ICIT 9-11/4/07 in RoC Going for Gold ~ Quality Tools and Techniques Paper #: Page- 1 /6 Risk Priority Evaluated by ANP in Failure Mode and Effects Analysis Jih-Kuang Chen 1 Yu-Cheng Lee 2 1 Student of Ph.D., Institute of Technology Management, Chung Hua University 2 Associate Professor, Institute of Technology Management, Chung Hua University pony@qualinet.tw ycl@chu.edu.tw ABSTRACT FMEA has been widely adopted and has become standard practice in many manufacturing companies and service industries, even some special domains. Traditionally, to utilize the technology of FMEA to improve the decision is in the order from the bigger Risk Priority Number to the smaller ones, but many scholars questioned the RPN method, and proposed some new methods to improve. However, these methods do not consider the interdependence between the causes of failure and current method of control, and the current method of control may interact with the cause of failure. Therefore, these old methods may decrease the risk of certain failure mode, but may not eliminate the overall risks, even increase it. Hence, the research advances to estimate the weights of severity (S), occurrence (O) and detection (D), and get the new risk assessment data, by which to decide the priority of improvement, then to improve the above shortcomings. At last, the paper proves the method does decrease the overall risk by an actual case, thus to verify the feasibility and effectiveness of the method. Keyword: RPN; FMEA; ANP 1.0 Introduction Failure Mode and Effects Analysis (FMEA) is a kind of design and analysis technology of reliability of prevention, which is a structured systematic formula identifying the potential malfunction mode in design or manufacturing, then studying the influence of malfunction to the system and providing qualitative evaluation, then taking necessary correction measures and prevention methods while aiming at the problems lying in the systematic reliability. Then FMEA has been widely adopted and has become standard practice in Japanese, American, and European manufacturing companies [Hung et al, 1999]. Traditionally, using the technology of FMEA to improve decision is in the order from bigger Risk Priority Number (RPN) to smaller ones. But Gilchrist [1993]; Ben-Daya & Raouf [1996]; Kara-Zaitri & Fleming [1997]; Bowles [1998]; Sankar & Prabhu [2000] questioned the calculation of RPN. Therefore, some scholars have advanced some other methods to improve traditional RPN calculation methods before, such as Criticality Score Evaluate, Level of Risk, Critical Analysis and Matrix Method, etc. But the above methods are still similar to the traditional FMEA, which are all subjectively transforming the qualitative linguistic into quantitative fraction, then to assess the risk of failure by concept of utility function as the foundation to improve priority order. But the subjective appreciation caused difficulty in correct scoring by FMEA members. In order to improve the default of subjective appreciation of each factor in RPN, some new methods were raised in recent years, e.g. Bowles [1998] described multi-criteria Pareto ranking as an alternative method to the classical risk priority number calculation; Chang et al. [2001] applied the Grey theory to FMEA; Davidson & Labib [2003] integrated the AHP methodology with the FMEA applied to the Concorde accident. But the above methods did not consider the interaction of failure, one cause of failure may cause multiple failures, but may decrease some failures. One control measure may control a failure, but may cause another failure. Hence, these methods in the past may reduce risk of certain failure mode, but may not reduce the overall risks, even may increase the risk. Thus this research proposed to effectively consider the possible interdependence between the cause of failure and the possible control measures, even the possible feedback relationship, so that to effectively estimate the weights of severity, occurrence and detection, by which to obtain new risk assessment data and to decide the priority of improvement, then to improve the above defects. Finally, it proves that the method does reduce the overall risks by an authentic case, by which to verify the feasibility and effectiveness of the method. 2.0 Methodology As Franceschini & Galetto [2001] proposed, FMEA can be considered as a decision - making support tool for designers. The decision consists of defining the order to analyze the failure mode effects of the

2 12-ICIT 9-11/4/07 in RoC Going for Gold ~ Quality Tools and Techniques Paper #: Page- 2 /6 considered product. Characteristic indexes can be interpreted as evaluation criteria, while failure modes as the alternatives to be selected. Therefore, from the perspective of multiple attribute decision making, FMEA is the matter of choice among multiple guideline schemes. The researchers intended to analyze the potential failure modes in design or manufacturing, and choose the greatest failure risk to improve. From the structure of FMEA, the first guideline is Failure Mode; the second guideline is Failure Effect, with severity as the assessment guideline; the third guideline is Failure Cause with occurrence as the assessment guideline; the last is scheme, i.e. the result after assessment by the assessment guidelines. Hence, the scheme weight below each Failure Mode is the second weight; the product of the third weight and the fourth weight just fits the concept of RPN. However, since failures may interact with each other, one cause of failure may cause several failures, but may reduce some other failures. One control measure may prevent one failure from happening, but may cause another failure. Hence, it is appropriate to weight assess with Analytic Network Process (ANP) method by considering possible interdependence and influences of possible feedback. ANP was put forward by Saaty [1996], whose difference from Analytic hierarchy process (AHP) is it allows the inner dependence within cluster and outer dependence among clusters. It provides a complete structure, thus the researchers may find the interactions between elements and clusters from problems, then deduce the priority and proportion of each scheme. ANP method includes two parts: 1. The first part is control hierarchy, which refers to the network relationship of guideline and sub-guideline, influencing the internal relationship of systems. 2. The second part refers to the network relationship between elements and clusters. The network relationship shows the interconnection of guidelines, and calculates the limiting influence of each control guideline to form a super-matrix. Finally, each super matrix is to be given appropriate weight after comprehensive assessment in the priority order of control hierarchy. Meade & Roger (1997) believed that AHP method was basic operation, and divided into four phases, namely they were: 1. Mode construction and problem structuring; 2. Pair-wise comparisons matrices of interdependent; 3. Supermatrix formation; 4. Selection of best alternative. When ANP is applied to FMEA, it shall be explained according to the four phases: 1. In execution of FMEA, first reduce it to failure mode by function, each failure mode may cause one or several effects, each effect may come from one or more reasons. Since there is no inner or outer dependence between mode and effect, thus it can be regarded as the control hierarchy. Each cause may be controlled by one or more control methods at present. What deserves our attention is that there may be inner dependence between each cause, i.e. two causes may be influential to each other, in addition, so does each control. Besides this, control and cause are more likely to have outer dependence, i.e. change of each control may influence the previous cause. If the judgment weight guideline of effect is set as severity, the judgment weight guideline of cause shall be occurrence, and the judgment weight guideline of control is to be set as detection. 2. To establish pair-wise comparison matrix shall establish: (1) Failure Mode pair-wise comparison matrix; (2) The pair-wise comparison matrix of failure effect under each failure mode; (3) The pair-wise comparison matrix of failure cause under each failure effect; (4) The pair-wise comparison matrix of control method under each failure cause; (5) Pair-wise comparison matrix between causes; (6) Pair-wise comparison matrix between controls; (7) The pair-wise comparison matrix of failure cause under control method. 3. Organization of super matrix: Since the pair-wise matrixes in Item (1) and (2) are control hierarchy, and the weights of mode and effect can be known from evaluated eigenvector. Therefore, each weight under failure mode can be evaluated from super matrix. Super matrix consists of eigenvectors of each pair-wise comparison matrix from Item (3) to (7), the structure is as follows:

3 12-ICIT 9-11/4/07 in RoC Going for Gold ~ Quality Tools and Techniques Paper #: Page- 3 /6 The sub-matrix A to E correspond to the Item (3) to (7) of pair-wise comparison matrix in Step 2, since it is the un-weighted supermatrix, it should be transformed into weighted supermatrix, i.e. the sum of any line shall be 1. After several times of multiplication we can get a fixed converged extreme value, and the extreme value is fixed, i.e. limiting supermatrix. Finally we can get all the weights. 4. Finally, calculate all the risk priority evaluated (PRE) in the following method: RPE i = S i x O i x D i x 10 3 (1) Where: S i is the weight of each effect; O i is the weight of each cause; D i is the weight of each control. The cause to multiply 10 3 is because the coefficient of each hierarchy is between 0 and 1, in this way to convenience the comparison with traditional RPN method. The improvement of priority order is based on the magnitude of RPE. Besides whether the RPE of each item would drop after improvement, whether the integral RPE would drop is one of the important items to be considered. The integral TRPE is i= The assessment method for improvement effect (E.I.) can be expressed as: ( TRPE TRPEa ) E. I. = TRPEb (2) Where: TRPE b is TRPE before improvement; TRPE a is TRPE after improvement. b 3.0 Case study m 1 RPE i. Take the framework of an indoors gas cooker as an example, this is a product made by pig iron, the designing team used design FMA in designing the new framework, its modes, effects, causes and controls are listed in Table 1: Table 1: Failure modes; effects and control Failure mode stands for Dimension out of spec. which may bring the Effects in three items: No function; Can t assembly and Poor appearance. There are two items of potential causes of function: Calculation mistakes from Pattern Shrinkage and the rate of enameling stretch and Lack of strengthen connection or stress release when pattern designing needed; The potential cause of can't assembly lies in Calculation mistakes from pattern shrinkage and poor pouring; The potential cause of poor appearance lies in calculation mistakes from pattern shrinkage and poor casting. While the Controls

4 12-ICIT 9-11/4/07 in RoC Going for Gold ~ Quality Tools and Techniques Paper #: Page- 4 /6 are Experiment and evaluation; Decision from engineering experience; Experiment and pouring process control and Experiment and casting process control. The researching team was divided into two groups, the first group used the traditional FMEA method, its severities were 8, 7 and 6; its occurrences were 4, 3 and 4 respectively; its detection were 5, 3 and 5 respectively. The detailed assessment data was listed in Table 5, and the integral RPN was 492. The first group chose the higher RPN in the first two items as M1 and M3 of control, its RPN were 160 and 140 respectively. After corrective actions were taken, the RPNs in Item 4 were effectively reduced to 96 and 88 respectively. Its gross RPN was 376 (see Table 2), its improvement proportion was: ( ) = 23.5% 492 Table 2: Traditional FMEA evaluation The second group used the method proposed in the research, first compare effect in pairs, and evaluate its weights as follows: To observe causes, we can find that calculation mistakes from pattern shrinkage appeared for several times, therefore there was inter-dependence between causes; While in control, experiment and evaluation appeared for several times, therefore there was inter-dependence between controls. The change of each control may influence the cause, thus there was inner dependence relationship. Hence, the ANP method must be used in assessment, first evaluate the pair-wise comparison matrix of cause under each effect, the result is as follows: Then, evaluate the pair-wise comparison matrix of control under each effect; each cause; each control; assessment cause, then organize these eigenvectors into supermatrix, then transform it into the following weighted supermatrix:

5 12-ICIT 9-11/4/07 in RoC Going for Gold ~ Quality Tools and Techniques Paper #: Page- 5 /6 A fixed converged extreme value can be got after two times of multiplications, the extreme value is fixed, i.e. the limiting supermatrix: All weights can be got, see results in Table 6. The RPE value can be got by Formula (1). The second group recalculated the RPE after corrective measures, see results in Table 3: Table 3. RPE evaluation The improvement proportion can be got by Formula (2): ( ) = 33.4% The improvement proportion is larger than the figure by RPE method, from which we can find the RPE method is effective. 4.0 Conclusion The research advises to consider the possible inter-dependence between the failure cause and current control pattern, and there is inner dependence between current control method and failure cause. However, to use ANP as the RPE method of assessment, the method may effectively improve the defects arisen from the occurrence being linear relationship, and the detection being non-linear relationship; also it may improve different occurrence, detection and severity and may constitute same RPN value with totally different meanings; It gives meaning to the product of S, O and D because of its hierarchy structure. It also proves to improve priority by RPE not only improves the risk of individual failure mode, but also effectively reduces the overall risks by actual case, which is more effective than traditional RPN method.

6 12-ICIT 9-11/4/07 in RoC Going for Gold ~ Quality Tools and Techniques Paper #: Page- 6 /6 References AIAG. [1995]. Potential Failure Mode and Effects Analysis, Second edition, Chrysler Corporation, Ford Motor Company, General Motors Corporation. Ben-daya, M. and Raouf, A. [1996]. A revised failure mode and effects analysis model. International journal of quality reliability management, Vol.13, pp Bolwes, J.B. [1998]. The new SAE FMECA standard, Proceeding annual Reliability and Maintainability Symposium, pp Chang, C.L., Liu, P.H. and Wei, C.C. [2001]. Failure mode and effect analysis and grey theory, Integrated Manufacturing Systems, Vol.12, pp Davidson, G.G. and Libib, A.W. [2003]. Learning from failures: design improvements using a multiple criteria decision-making process, Proc. Instn Mech. Engrs, 217 Part G: Journal of Aerospace Engineering, pp Franceschini, F. and Galetto, M. [2001]. A new approach for evaluation of risk priorities of failure modes in FMEA, International journal of production research, Vol.39, No.13, pp Gilchrist, W. [1993]. Modelling failure modes and effects analysis, International Journal of Quality & Reliability Management, Vol.10, No.5, pp Hung, G.Q., Nie, M. and Mark, K.L. [1999]. Web-based failure mode and effect analysis, Computers & Industrial Engineering, Vol.37, pp Kara-Zaitri, C. and Fleming, P.V. [1997]. Applications of fizzy inference methods to failure modes effects and criticality analysis IFMECA, International Conference on Safety and Reliability, pp Mead L.M. and Rogers K.J. [1997]. Enhancing a manufacturing business process for agility, Portland International Conference on Management and Technology, pp Saaty, T.L. [1980]. The Analytic Hierarchical Process, McGraw-Hill, New York. Saaty, T.L. [1996], Decision Making with Dependence and Feedback: The Analytic Network Process, Pittsburgh, PA: RWS. Sankar, N.R. and Prabhu, B.S. [2001]. Modified approach for prioritization of failures in a system failure mode and effects analysis, The International Journal of Quality & Reliability Management, Vol.18, No.3, pp Authors Backgrounds Jih-Kuang Chen received the M.S. degree in industrial engineering and management from Chung Hua University, Hsinchu, Taiwan, in He is reading the Ph.D. degree in technology management in Chung Hua University. He is currently general manager for Qualinet Worldwide Ltd, Hsinchu, Taiwan. He has twelve years of experience in the electronics industry focusing on quality assurance technology and quality management system. His research interests include Taguchi method, experimental design, customer satisfaction, service quality and Taguchi-Mahalanobis system. Dr. Yu-Cheng Lee is an associate professor in the Department of Technology Management at the Chung Hua University, Taiwan, Republic of China. He is also appointed to the Chairman of this department since He received his PhD in Industrial Engineering from National Tsing Hua University in His major interests include customer satisfaction, quality engineering, experimental design, total quality management, Taguchi-Mahalanobis system and fuzzy theory. He has published a lot of papers in the international journals in the above-mentioned areas. He got Outstanding Teachers Award in 2002, 2003 and 2005 at Chung Hua University. He was appointed to be the member of Quality Engineering Committee under Chinese Society for Quality in the period of and Technical Committee of Chinese National Standard since He was elected to be the chairman of the Committee of Taiwan Customer Satisfaction under Chinese Society for Quality since 2005.