DOI 10.1007/s10845-013-0747-9
Applying the concept of exponential approach to enhance
the assessment capability of FMEA
Kuei-Hu Chang · Yung-Chia Chang · Pei-Ting Lai
Received: 3 October 2012 / Accepted: 16 February 2013 / Published online: 27 March 2013 © Springer Science+Business Media New York 2013
Abstract Failure modes and effects analysis (FMEA) has been used to identify the critical risk events and predict a sys-tem failure to avoid or reduce the potential failure modes and their effect on operations. The risk priority number (RPN) is the classical method to evaluate the risk of failure in con-ventional FMEA. RPN, which ranges from 1 to 1000, is a mathematical product of three parameters—severity (S), occurrence (O), and detection (D)—to rank and assess the risk of potential failure modes. However, there are some shortcomings of the conventional RPN method, such as: the RPN elements have many duplicate numbers; violate the assumption of measurement scales; and have not consid-ered the weight of S, O, and D. In order to improve the aforementioned shortcomings of the conventional RPN cal-culation problem, this paper presents an easy yet effective method to enhance the risk evaluation capability of FMEA. The new method is named exponential risk priority number (ERPN), which uses a simple addition function to the expo-nential form of S, O, and D to substitute the conventional RPN method, which is a mathematical product of three para-meters. Two practical cases are used to demonstrate that the ERPN method can not only resolve some problems of the conventional RPN method but also is able to provide a more accurate and reasonable risk assessment in FMEA.
K.-H. Chang (
B
)Department of Management Sciences, R.O.C. Military Academy, Kaohsiung 830, Taiwan
e-mail: evenken2002@yahoo.com.tw Y.-C. Chang· P.-T. Lai
Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 300, Taiwan
Keywords Risk assessment· Failure modes and effects analysis· Risk priority number · Exponential risk priority number· Data envelopment analysis
Introduction
Risk management is an important part of strategic ment in any organization. In order to perform risk manage-ment well, organizations require appropriate analysis tools with the capabilities of identification and treatment of these risks (Zhang et al. 2012). Many methods have been devel-oped for risk assessment (Hsiao and Lu 2008;Chang 2009; Chang and Cheng 2009; Karlsson et al. 2000; Chien and Zheng 2012; Hussain et al. 2012; Kubat and Yuce 2012). Failure modes and effects analysis (FMEA) is an important risk assessment tool to eliminate or reduce the probability of failure occurring by a potential failure process or prod-uct. For the purpose of ranking the risks of potential failure modes, the traditional FMEA uses the risk priority number (RPN) methodology. The RPN, which is the product of the severity (S), occurrence (O), and detection (D) of a failure mode, is ranging from 1 to 1000. The three parameters S, O, and D are used to describe each failure mode of a product or process, and each parameter can be assigned a rating from 1 to 10. However, there are some shortcomings of the conven-tional RPN method, such as: the RPN elements have many duplicate numbers; violate the assumption of measurement scales; and have not considered the weight of S, O, and D.
Gilchrist(1993) discussed the shortage of any cost evalua-tion of the failures in FMEA and thus developed an expected cost model; i.e., EC = CnPfPd, where C is the failure cost, n denotes the annual production quantity, Pf is the probabil-ity of failure, and Pdis the probability of the failure not to be detected. However,Ben-Daya and Raouf(1996) found some
problems of the expected cost model; it is difficult to estimate these probabilities at the design stage of a product, and the economic model completely ignores the important aspect of severity.Wang et al.(1995) proposed a methodology combin-ing FMEA and the Boolean representation method to identify and estimate risks of failures. However, it might be difficult to construct Boolean representation tables for some compo-nents of a system, especially during early phases of product design, since the relationships between components may be difficult to precisely represent.Sankar and Prabhu (2001) presented a modified approach to prioritize failure modes for corrective actions in FMEA. This technique extends the risk prioritization beyond the conventional RPN method. The ranks 1 through 1000 are used to represent the increasing risk of the 1000 possible severity-occurrence-detection combina-tions, called risk priority ranks (RPRs). The RPRs method has the advantage in solving the duplication problem of the conventional RPN method, but it requires a lot of time to deal with the risk-ranking process than what traditional RPN method does.
Moreover, the management of FMEA is usually con-fronted with several problems, such as the imprecise and vague linguistic information. To overcome this problem in the conventional RPN method, a lot of more reasonable and sys-tematic methods were proposed.Bowles and Pelaez(1995) were the first ones to propose a technique using membership function in FMEA. Their approach uses fuzzy logic to work with the linguistic terms directly in making the criticality assessment.Chang et al.(1999) used fuzzy linguistic terms that described the decision factors as Very Low, Low, Moder-ate, High, and Very High to evaluate S, O, and D and utilized the grey relational analysis to determine the risk priorities of failure modes.Pillay and Wang(2003) utilized fuzzy rules base and grey relation theory in FMEA. However, these meth-ods have the same problem of high duplication rate. There are also some studies that have applied fuzzy theory to incor-porate with FMEA to improve the traditional FMEA (such asBraglia et al. 2003;Sharma et al. 2005;Tay and Lim 2006; Wang et al. 2009;Xu et al. 2002;Yeh and Hsieh 2007;Chang et al. 2010).
Seyed-Hosseini et al. (2006) used the decision-making trial and evaluation laboratory (DEMATEL) to prioritize fail-ures in a system. DEMATEL was developed by the Battelle Memorial Institute (Gabus and Fontela 1973) through its Geneva Research Centre. DEMATEL is an effective method to analyze the relationships between components of a sys-tem regarding is type (direct/indirect) and severity. How-ever, Seyed-Hosseini et al.’s approach still could not solve the shortcomings of the conventional RPN method. When each cause of failure is assigned to only one potential failure mode, the risk ranking orders obtained by DEMATEL corresponds with the ones obtained by the conventional RPN method (Chang and Cheng 2011). Recently, some researchers
uti-lized data envelopment analysis (DEA), which is a well-known managerial tool, to evaluate the efficiency of a number of producers, to take the relative importance of risk factors S, O, and D into account. Chang and Sun(2009) applied the DEA technique to enhance assessment capabilities of FMEA.Chin et al.(2009) also used DEA to determine the risk priorities of failure modes. In the DEA approach used byChang and Sun (2009) andChin et al.(2009), existing complicated operations owing to multiplication and division are extensively applied to the values of S, O, and D. How-ever, likeBowles(2003) indicated—that one of the problems with the RPN method is the use of the ordinal ranking num-bers as numeric quantities—the same problem remains while applying DEA in FMEA from a statistical point of view. It is meaningless to directly perform mathematical operations to the values of S, O, and D, since they are actually on an ordinal scale.
As mentioned above, there are abundant studies to enhance the assessment capability of traditional FMEA, such us fuzzy theory, grey relation theory, ordered weighted aver-aging (OWA), DEA, and others. However, these approaches are obviously a lot more complicated than the conventional RPN method. That might be the main reason that hinders most engineers and analysts from applying them in prac-tice nowadays. Despite its simplicity, the shortcomings of the conventional RPN method still need to be improved. Therefore, this study developed a new method, named expo-nential risk priority number (ERPN), which uses a simple addition function to the exponential form of S, O, and D to enhance the risk evaluation capability of FMEA. The ERPN method is able to reduce the number of duplicate values in the conventional RPN method used in FMEA. Using the ERPN method, decision-makers can associate dif-ferent weights with respect to difdif-ferent risk factors for more practical applications. Two case studies are presented in this study to demonstrate the effectiveness of the proposed approach.
The rest of this article is organized as follows. “Failure modes and effects analysis” section discusses the traditional FMEA method and its shortcomings. “Methodology” sec-tion proposes a new approach, which uses a simple addisec-tion function to the exponential form of S, O, and D to sub-stitute the conventional RPN method. In “Simulations and comparison” section, a simulation example (safety assess-ments of fishing vessels) is adapted to demonstrate the effec-tiveness of the proposed new approach. Other than the new ERPN approach, results by using the conventional RPN method and DEA approach to the same case are compared and analyzed. In “Numerical verification” section, a practi-cal case is used to demonstrate an application of the ERPN method on a situation that considers the relative importance among the parameters S, O, and D. The final section makes conclusions.
Failure modes and effects analysis The development of FMEA
FMEA was first proposed by the aerospace industry in the 1960s, with their obvious reliability and safety requirements. Since then, it has been gradually used as a powerful tech-nique for system safety and reliability analysis of products and processes. Meanwhile, the military of the United States of America (USA) also started to apply the FMEA tech-nique and published the standard operational procedure MIL-STD-1629 of failure modes and effects criticality analysis (FMECA) in 1974 (US Department of Defense Washington, DC 1974), which then was revised as MIL-STD-1629A in 1980 (US Department of Defense Washington, DC 1980). Nowadays, the standard is still the one of the important FMEA references in the world.
In 1977, Ford Motor established the standard opera-tional procedure of FMEA and popularized the FMEA tech-nique. Afterwards, the automotive industry in the USA gradually adopted FMEA as a tool and divided it into two types: the design FMEA (DFMEA) and the process FMEA (PFMEA). In 1985, the International Electrotechnical Com-mission (IEC) published an international standard opera-tional procedure of FMEA called IEC 812, partly based on MIL-STD-1629A (International Electrotechnical Commis-sion 1985). In 1993, under the auspices of the American Society for Quality Control (ASQC) and the Automotive Industry Action Group (AIAG), Ford, Chrysler, and General Motors integrated the regulations of automotive companies to establish the FMEA reference manual to meet QS-9000 requirements. AIAG revised the FMEA reference manual several times since then (Automotive Industry Action Group
2008). Furthermore, FMEA is considered an important item for examining an analytic method by the international qual-ity certification system, such as ISO-9000, ISO/TS 16949, CE, and QS-9000 in recent years. Today, it is widely used in risk assessment and quality improvement in many industries, such as aerospace, nuclear, military, medicine, automobile, mechanical, and semiconductor. In the future, FMEA may not only be the techniques and mechanisms of product com-petitiveness in enterprise but also become the basic proce-dures for product development. The development of FMEA is shown in Table1.
Risk priority number (RPN) used in conventional FMEA The introduction of RPN
RPN is a mathematical product of three parameters, which ranges from 1 to 1000, for ranking and assessing the risk of potential failure modes. It is an index score calculated as the severity (S), occurrence (O), and detection (D) of a failure mode, which can be represented in a mathematical way; i.e., RPN = S× O × D. A failure mode that has a higher RPN is assumed to be more important and thus demands higher priority for corrective action than those with lower RPN val-ues. The detailed rating scales of the severity, occurrence, and detection used in FMEA are given in Tables2,3, and4, respectively.
The drawbacks of conventional RPN
From a management perspective, the conventional RPN cal-culation is easy to use and understand. However, the con-ventional approach to obtain RPN has been considerably
Table 1 The development of
FMEA Year Description
1963 FMEA was first proposed by aerospace industry
1965 The military of the US started to apply the FMEA technique 1974 The military of the US published the SOP of FMEA: MIL-STD-1629 1977 Ford Motor started to use FMEA
1980 The revised SOP of FMEA: MIL-STD-1629A
1985 The International Electrotechnical Commission (IEC) published SOP of FMEA: IEC 812
1993 Ford, Chrysler, and General Motor established the 1st edition FMEA reference manual 1995 The 2nd edition of FMEA reference manual was revised by AIAG
2001 The 3rd edition FMEA reference manual was revised by AIAG 2008 The 4th edition FMEA reference manual was revised by AIAG
2008-now FMEA is considered as an important examining item and analytic method by ISO-9000, ISO/TS 16949, CE, and QS-9000, and it has been widely used in risk assessment and quality improvement in many industries
Table 2 The rating scales of severity (Ford Motor Company 1988)
Effect Criteria: severity of effect Rank
Hazardous Failure is hazardous, and occurs without warning. It suspends operation of the system and/or involves noncompliance with government regulations
10 Serious Failure involves hazardous outcomes and/or noncompliance with government
regulations or standards
9 Extreme Product is inoperable with loss of primary function. The system is inoperable 8 Major Product performance is severely affected but functions. The system may not operate 7 Significant Product performance is degraded. Comfort or convince functions may not operate 6 Moderate Moderate effect on product performance. The product requires repair 5 Low Small effect on product performance. The product does not require repair 4
Minor Minor effect on product or system performance 3
Very minor Very minor effect on product or system performance 2
None No effect 1
Table 3 The rating scales of occurrence (Ford Motor Company 1988) Probability of failure Possible failure rates Rank Extremely high: failure almost inevitable 1 in 2 10
Very high 1 in 3 9 Repeated failures 1 in 8 8 High 1 in 20 7 Moderately high 1 in 80 6 Moderate 1 in 400 5 Relatively low 1 in 2000 4 Low 1 in 15000 3 Remote 1 in 150000 2 Nearly impossible 1 in 1500000 1
criticized for a variety of reasons. Significant criticisms include but are not limited to the following:
(1) The RPN elements have many duplicate numbers. Many scholars questioned that the RPN elements have many duplicate numbers (Bowles 2003;Wang et al. 2009;
Fig. 1 Histogram of RPN values generated from all possible combi-nations
Chang and Cheng 2010). There are 1000 possible com-binations of S, O, and D, but in fact, only 120 unique RPN values may result due to the duplicate numbers. For example, the RPN value of 120 appears 24 times from different combinations of S, O, and D; it is difficult to accept that these 24 different combinations of S, O, and D have the same priority. Figure1shows the thorough listing of frequency distribution for the 1000 RPN num-bers (Bowles 2003;Chang and Cheng 2010).
Table 4 The rating scales of detection (Ford Motor Company 1988)
Detection Criteria: likelihood of detection by design control Rank
Absolute uncertainty Design control does not detect a potential cause of failure or subsequent failure mode; or there is no design control 10 Very remote Very remote chance the design control will detect a potential cause of failure or subsequent failure mode 9 Remote Remote chance the design control will detect a potential cause of failure or subsequent failure mode 8 Very low Very low chance the design control will detect a potential cause of failure or subsequent failure mode 7 Low Low chance the design control will detect a potential cause of failure or subsequent failure mode 6 Moderate Moderate chance the design control will detect a potential cause of failure or subsequent failure mode 5 Moderately high Moderately high chance the design control will detect a potential cause of failure or subsequent failure mode 4 High High chance the design control will detect a potential cause of failure or subsequent failure mode 3 Very high Very high chance the design control will detect a potential cause of failure or subsequent failure mode 2 Almost certain Design control will almost certainly detect a potential cause of failure or subsequent failure mode 1
(2) Violate the assumption of measurement scales (Bowles 2003;Chang and Cheng 2011).
The first step of any statistical analysis is to identify the scale of measurements. Data can be classified into four different types of measurement scales: nominal scale, ordinal scale, interval scale, and ratio scale. It is not allowed for all measurements to have the same level of quantification. By definition, the values of S, O, and D of FMEA are classified as ordinal scale.Bowles(2003) mentioned that the calculation of multiplication and divi-sion are meaningless on ordinal scales, and addition and subtraction while sometimes meaningful, must be care-fully done, since they assume an equal interval between the category labels.
(3) Have not considered the weight of S, O, and D. Sankar and Prabhu(2001) mentioned that the three para-meters S, O, and D are assumed to be equally weighted with respect to one another in terms of risk. It neglects the relative importance among the three parameters and may not be able to correctly quantify the risk when con-sidering a practical application of FMEA.
(4) The RPN scale itself has some non-intuitive statistical properties.
Bowles (1998) pointed out that the FMEA scales for severity and detection are only qualitative. The state-ment in FMEA is often subjective, and the information in FMEA is described qualitatively in linguistic way, such as “likely”, “important”, or “very high” and so on. There-fore, it is difficult to precisely evaluate reliability of a product or process for the traditional FMEA. One of the shortcomings of the RPN method is that the RPN scale itself has some non-intuitive statistical properties. The initial and correct assumption observation is that the scale starts at 1 and ends at 1000, often leading to incorrect assumptions in the middle of the scale. Table5contains some common faulty assumptions (Sankar and Prabhu 2001).
Methodology
In order to improve the shortcomings of conventional RPN method and provide an easier yet effective approach than those approaches found in literature, this research proposes
a new method to substitute the use of RPN method used in conventional FMEA. The new method is named exponential RPN (ERPN), which uses a simple addition function to the exponential form of S, O, and D.
The exponential risk priority number (ERPN)
The conventional FMEA uses the mathematical product of the severity (S), occurrence (O), and detection (D) of a fail-ure mode to form the RPN values. However, multiplying the values of S, O, and Dmay cause some problems, since they are actually on an ordinal scale. It is actually meaning-less to perform multiplication directly to values in an ordinal scale. A general form of the exponential risk priority number (ERPN) proposed in this study is defined in Eq. (1).
ERPN(X) = XWs×S+ XWo×O+ XWd×D,
X ∈ Z and X ≥ 2 (1)
In Eq. (1), S, O, and D are the ratings of a failure as defined in the conventional RPN method. That is, S, O, and D are integers ranging between 1 and 10. X is defined as any positive integer that is no less than 2. X serves as a parameter in the ERPN method. Moreover, it is possible to assign different weights to S, O, and D to consider the rel-ative importance among the three parameters. Let WS, WO, and Wdbe the weights assigned to S, O, and D, respectively. Since X is unknown, the first step is to obtain an appropriate value X on the assumption that WS, WO, and Wdare set as 1. The process of determining an appropriate value of X is pre-sented and discussed in “Parameter determination in ERPN” section.
Parameter determination in ERPN
One of the problems of the conventional RPN method is it has too many duplicate numbers. For the purpose of search-ing an appropriate value of X , the number of unique values and the frequency associated with each unique value that ERPN(X ) could possibly generate for various X are calcu-lated for comparison. The number of unique values is the count of all possible values resulting from ERPN(X ) for a given X . The frequency of each unique value represents the number of possible combinations to generate that value. Table 5 RPN scale statistical data
Incorrect assumption Actual statistical data
The average of all RPN values is roughly 500 The average RPN value is 166
Roughly 50 % of RPN values are above 500 (The median is near 500) 6 % of all RPN values are above 500 (The median is 105) There are 1000 possible RPN values There are 120 unique RPN values
Fig. 2 Histogram of ERPN(2) values generated from all possible com-binations
Fig. 3 Histogram of ERPN(3) values generated from all possible com-binations
The smallest value of X is 2 per Eq. (1). All the possible values of ERPN(2) (= 2S+ 2O+ 2D) and the frequency of each value are computed. The histogram of ERPN(2) values generated from all possible combinations is given in Fig.2. Figure2clearly shows that there are 184 unique values gen-erated by ERPN(2). Recall that there are only 120 unique values in the conventional RPN method. Furthermore, the highest frequency of ERPN(2) is 6. In contrast, the highest frequency of the conventional RPN method is 24. Therefore, ERPN(2) has fewer duplicate numbers than the conventional RPN method.
Using the same procedure, the possible values of ERPN(3) and the frequency of each value are also computed. The his-togram of ERPN(3) values generated from all possible com-binations is given in Fig.3. Comparing Figs.2and3, although the highest frequency in both cases is 6, the number of values associated with the highest frequency of ERPN(3) is less than ERPN(2). Furthermore, there are 220 unique values gener-ated by ERPN(3), which is 36 more what ERPN(2) generates. Therefore, it would result in a better performance to assign X as 3 than as 2.
The trend of the number of unique values resulting from ERPN(X ) is shown in Fig.4. Therefore, it is appropriate to assign X as 3 while keeping the resulting ERPN numbers easy to interpret and effective to use. Some statistics of the values generated by different functions are summarized in Table6.
Actually, the number of unique values resulting from ERPN(X ), for X ∈ Z and X ≥ 2, can be calculated ana-lytically as follows. When X is a given number other than 2, there are three possible situations under which the resulting ERPN(X) = XS+ XO+ XDis a unique value: (1) when the
Fig. 4 The number of unique values resulted from ERPN(X) = XS+ XO+ XD
values of the three factors S, O, and D are totally different; (2) any two values of the three factors S, O, and D are same and the other one is different; and (3) the values of the three factors S, O, and D are all the same. Since S, O, and D could be any integer ranging from 1 to 10, situation (1) is able to generate C310 = 120 unique numbers. Situation (2) is able to generate C210 = 90 unique numbers. Ten unique numbers are generated by situation (3). Therefore, there are total of 220(=120 + 90 + 10) unique values resulting from ERPN(X ) as long as X is equal to or greater than 3. When X =2, the number of unique values resulting from ERPN(X ) only is 184, less than 220. The reduction in the number of unique values is resulting from the property that 2a+ 2a= 2a+1for a ∈ Z. For instance, (S, O, D) values of (3, 3, 2) and (4, 1, 1) would generate the same value of 20 in ERPN(2).
Since it makes no difference to adopt any value that is larger than or equal to 3 as the value of X , we recommend assigning X to be 3, because it could produce the most unique values and the easiest calculation. As a result, the new method to substitute the conventional RPN method is described in Eq. (2).
ERPN= 3Ws×S+ 3Wo×O+ 3Wd×D (2)
The properties of the new ERPN method
In brief, there are the following four properties of the new ERPN method proposed in this study.
(1) ERPN method uses a simple addition function to the exponential form of S, O, and D to substitute the multi-plication used in the conventional RPN method. Conse-quently, the problem of measurement scales found in the conventional RPN method is improved.
(2) ERPN method has fewer duplicate values than what the conventional RPN method has. That means that few fail-ure modes would be assigned to the same priority; thus, the risk evaluation capability of FMEA is enhanced.
Table 6 Comparison of statistics resulting different functions
Function Average Median Number of unique values Minimum Maximum
RPN = S× O × D 166 105 120 1 1000
ERPN(2)= 2S+ 2O+ 2D 613.8 518 184 6 3072
ERPN(3)= 3S+ 3O+ 3D 26571.6 13203 220 9 177147
ERPN(4)= 4S+ 4O+ 4D 419430 131328 220 12 3145728
ERPN(5)= 5S+ 5O+ 5D 3662109 781875 220 15 29296875
(3) The ERPN method could take the relative importance among the three parameters S, O, and D into considera-tion (the relative importance weights of S, O and D are obtained by FMEA team members based on their judg-ment).
(4) If it does not violate the premise of measurement scales, the ERPN method offers an easier way for identifying ranking-order for all failure modes in a system than the other proposed approaches.
Simulations and comparison
As aforementioned, a new approach named ERPN is pro-posed to overcome some shortcomings of the conventional RPN method in FMEA. The main shortcomings are: (1) the three parameters S, O, and D are assumed to be equally weighted with respect to one another in terms of risk; (2) dif-ferent combinations of S, O, and D may produce the same value of RPN, but their degree of hidden risk may be differ-ent; (3) the problem of the measurement scale; and (4) the RPN elements have many duplicate numbers. In order to ver-ify that the ERPN method proposed in this paper can improve some problems of conventional RPN method, a practical case of FMEA is used to demonstrate the new ERPN method. Besides, the traditional RPN method and the approach using data envelopment analysis (DEA) (Chang and Sun 2009) are also applied to the same case for comparison. The results of the three methodologies are analyzed and compared in “Comparison” section.
A practical case of FMEA
The practical case is obtained fromPillay and Wang(2003), which is an application of FMEA to a fishing vessel. The FMEA for the fishing vessel investigates four different sys-tems, which are structure, propulsion, electrical, and auxil-iary systems. Each system is considered for different failure modes that could lead to an accident with undesired conse-quences. The effects of each failure mode on the system and vessel are studied, along with the provisions that are in place or available to mitigate or reduce risk. For each of the failure
modes, the system is investigated for any alarms or condition monitoring arrangements that are in place. The failure modes of this case and their ratings on the three parameters S, O, and D are shown in Table7.
Application of the conventional RPN method
According to the conventional RPN method, the risk of each failure mode is assessed based on its severity, occurrence, and detection on a numerical scale from 1 to 10. RPN values are calculated by multiplying the three parameters of S, O, and D. A failure mode that has a higher RPN value is assumed to be more important and demands higher priority for corrective action than those with lower RPN values. The result of the conventional RPN method for this fishing vessel is carried out in Table8(Pillay and Wang 2003).
Application of the DEA approach
The DEA approach (CCR AR model) used byChang and Sun (2009) was implemented step by step to determine the risk priorities of failure modes in this case. The DEA approach calculates the relative performance or efficiency of a specific group. The efficiency score is evaluated mathematically by the ratio of weighted sum of outputs and weighted sum of inputs; a lower efficiency score implies a higher priority for corrective actions.
To apply the DEA approach in this case, the first step is to convert the FMEA data matrix to DEA data format. The out-put of each failure mode is set as 1. The inout-put-oriented CCR assurance region (AR) model with S, O, and D as inputs is employed to generate comprehensive risk scores for evalu-ating failure modes. The case data were computed by DEA EXCEL SOLVER, developed byZhu(2003). The result of applying DEA to this case is shown in Table9.
Application of the ERPN method
This case did not consider the relative importance among the three risk factors; i.e., Ws = Wo = Wd = 1 in Eq. (2). The results of this case by using the ERPN method are summarized in Table10.
Table 7 FMEA for a fishing vessel (Pillay and Wang 2003)
No. Description Component Failure mode Failure effect (system) Failure effect (vessel) Alarm Provision S O D 1 Structure Rudder bearing Seizure Rudder jam No steering ctrl No Stop vessel 8 1 3 2 Structure Rudder bearing Breakage Rudder loose Reduced steering ctrl No Stop vessel 8 1 3 3 Structure Rudder bearing Structural failure Function loss Reduced steering No Use beams 8 2 4 4 Propulsion Main engine Loss of output Function loss Loss of speed Yes None 8 8 5 5 Propulsion Main engine Auto shutdown M/E stops Loss of speed Yes Anchor 8 6 6 6 Propulsion Shaft and propeller Shaft breakage Loss of thrust Loss of speed No Anchor 8 2 1 7 Propulsion Shaft and propeller Shaft seizure Loss of thrust Loss of speed Yes Anchor 9 2 2 8 Propulsion Shaft and propeller Gearbox seizure Loss of thrust Loss of speed Yes Anchor 4 1 3 9 Propulsion Shaft and propeller Hydraulic failure Cannot reduce thrust Cannot reduce speed No Anchor 2 3 3 10 Propulsion Shaft and propeller Prop. blade failure Loss of thrust Loss of speed No Slow steaming 2 1 4 11 Air services Air services No start air press. Cannot start M/E No propulsion Yes Recharge receiver 2 4 3 12 Electrical system Power generation Generator fail No elec. power Some system failures Yes Use st-by generators 3 9 7 13 Electrical system Main switch Complete loss Loss of main supply No battery charging Yes Use emergency 24 V 3 8 6 14 Electrical system Emergency S/B Complete loss Loss of emer. supp. No emergency supp. No Use normal supply 7 3 4 15 Electrical system Main batteries Loss of output Loss of main 24 V Loss of main low volt Yes Use emergency 24 V 3 3 4 16 Electrical system Emer. Batteries Loss of output Loss of emer. supp. No emer. supp. No Use normal supply 8 1 3 17 Auxiliary system Fuel system Contamination M/E and gen. stop Vessels stops Yes Anchor 8 4 5 18 Auxiliary system Fuel system No fuel to M/E M/E stops Vessel stops No Anchor 7 2 7 19 Auxiliary system Water system No cooling water Engine overheat M/E auto cut-out Yes Use st-by pump 2 7 4 20 Auxiliary system Hydraulic System loss No hydraulics No steering Yes Stop vessel 8 9 9 21 Auxiliary system Lube oil system Loss of pressure Low pressure cut-off M/E stops Yes Use st-by pump 3 9 6
Table 8 FMEA for a fishing vessel by RPN
No. Description Component Failure mode S O D RPN
1 Structure Rudder bearing Seizure 8 1 3 24
2 Structure Rudder bearing Breakage 8 1 3 24
3 Structure Rudderbearing Structural failure 8 2 4 64
4 Propulsion Main engine Loss of output 8 8 5 320
5 Propulsion Main engine Auto shutdown 8 6 6 288
6 Propulsion Shaft and propeller Shaft breakage 8 2 1 16
7 Propulsion Shaft and propeller Shaft seizure 9 2 2 36
8 Propulsion Shaft and propeller Gearbox seizure 4 1 3 12
9 Propulsion Shaft and propeller Hydraulic failure 2 3 3 18
10 Propulsion Shaft and propeller Prop. blade failure 2 1 4 8
11 Air services Air services No start air press. 2 4 3 24
12 Electrical system Power generation Generator fail 3 9 7 189
13 Electrical system Main switch Complete loss 3 8 6 144
14 Electrical system Emergency S/B Complete loss 7 3 4 84
15 Electrical system Main batteries Loss of output 3 3 4 36
16 Electrical system Emer. Batteries Loss of output 8 1 3 24
17 Auxiliary system Fuel system Contamination 8 4 5 160
18 Auxiliary system Fuel system No fuel to M/E 7 2 7 98
19 Auxiliary system Water system No cooling water 2 7 4 56
20 Auxiliary system Hydraulic System loss 8 9 9 648
Table 9 The efficiency scores of each failure mode in the fishing vessel case by using DEA
No. DMU Efficiency score
1 1 1.0000 2 2 1.0000 3 3 0.6250 4 4 0.4783 5 5 0.4310 6 6 1.0000 7 7 0.8333 8 8 1.0000 9 9 1.0000 10 10 1.0000 11 11 1.0000 12 12 0.6667 13 13 0.6667 14 14 0.6250 15 15 0.7857 16 16 1.0000 17 17 0.5102 18 18 0.5000 19 19 1.0000 20 20 0.3165 21 21 0.6667
Table 10 ERPN for the fishing vessel case
No. Failure mode S O D ERPN
1 Seizure 8 1 3 6591 2 Breakage 8 1 3 6591 3 Structural failure 8 2 4 6651 4 Loss of output 8 8 5 13365 5 Auto shutdown 8 6 6 8019 6 Shaft breakage 8 2 1 6573 7 Shaft seizure 9 2 2 19701 8 Gearbox seizure 4 1 3 111 9 Hydraulic failure 2 3 3 63
10 Prop. blade failure 2 1 4 93
11 No start air press. 2 4 3 117
12 Generator fail 3 9 7 21897 13 Complete loss 3 8 6 7317 14 Complete loss 7 3 4 2295 15 Loss of output 3 3 4 135 16 Loss of output 8 1 3 6591 17 Contamination 8 4 5 6885 18 No fuel to M/E 7 2 7 4383 19 No cooling water 2 7 4 2277 20 System loss 8 9 9 45927 21 Loss of pressure 3 9 6 20439 Comparison
In order to evaluate the effectiveness of the new ERPN method, a case for a fishing vessel was performed by three approaches: the conventional RPN, DEA, and ERPN in sec-tions “Application of the conventional RPN method”, “Appli-cation of the DEA approach”, “Appli“Appli-cation of the ERPN method”. The results of the three methods are presented in Table 11. Some findings in this paper are discovered and analyzed as follows.
(1) The ERPN method can reduce the high duplication rate problem.
Table8clearly shows the basis of the conventional RPN method, both items No. 2 (S, O, and D are 8, 1, and 3, respectively) and No. 11 (S, O, and D are 2, 4, and 3, respectively) have the same RPN values of 24. Per the DEA method, the efficiency scores of both items are the same, with the value of 1 from Table9. Therefore, items No. 2 and No. 11 have the same priority for cor-rective actions based on the conventional RPN and DEA methods. However, these two items represent two failure modes that have different combinations of S, O, and D, which should lead to different risks. Using the proposed ERPN method, the resulting ERPN values (Table11) for items No. 2 and No. 11 are 6591 and 117, respectively; this means that item No. 2 has a higher risk than item No. 11 due to the fact that No. 2 has a quite large rating on its severity than No. 11. This illustration implies that the ERPN method is more effective in distinguishing the risks of failure modes than the other two methods. Furthermore, according to Table 11, the conventional RPN method generated 17 unique RPN values among a total of 21 items in this case; that is, the duplication rate is 19.05 %. The DEA approach yields 10 unique effi-ciency scores among these 21 items; that means that the duplication rate is 52.38 %. The number of unique ERPN values among these 21 items is 19; that means that the duplication rate is 9.52 %. Note that the two duplicate ERPN values are actually caused by the same combi-nations of S, O, and D. Nevertheless, the result shows that the ERPN method can reduce the problem of high duplication rate.
(2) The ERPN method can carry out more accurate risk rank-ing.
Based on Table11, it shows that the RPN values of item No. 7 with an (S, O, D) combination of (9, 2, 2) and No. 15 with an (S, O, D) combination of (3, 3, 4) are both 36. Using the DEA approach, the efficiency scores of items No. 7 and No. 15 are 0.8333 and 0.7857, respectively. This implies that items No. 7 and 15 have the same pri-ority according to the conventional RPN method, while
Table 11 Comparison of RPN, DEA, and ERPN approach
No. Failure mode RPN DEA Score ERPN Ranking RPN Ranking DEA Ranking ERPN
1 Seizure 24 1.0000 6591 14 13 10 2 Breakage 24 1.0000 6591 14 13 10 3 Structural failure 64 0.6250 6651 10 6 9 4 Loss of output 320 0.4783 13365 2 3 5 5 Auto shutdown 288 0.4310 8019 3 2 6 6 Shaft breakage 16 1.0000 6573 19 13 13 7 Shaft seizure 36 0.8333 19701 12 12 4 8 Gearbox seizure 12 1.0000 111 20 13 19 9 Hydraulic failure 18 1.0000 63 18 13 21
10 Prop. blade failure 8 1.0000 93 21 13 20
11 No start air press. 24 1.0000 117 14 13 18
12 Generator fail 189 0.6667 21897 4 8 2 13 Complete loss 144 0.6667 7317 7 8 7 14 Complete loss 84 0.6250 2295 9 6 15 15 Loss of output 36 0.7857 135 12 11 17 16 Loss of output 24 1.0000 6591 14 13 10 17 Contamination 160 0.5102 6885 6 5 8 18 No fuel to M/E 98 0.5000 4383 8 4 14 19 No cooling water 56 1.0000 2277 11 13 16 20 System loss 648 0.3165 45927 1 1 1 21 Loss of pressure 162 0.6667 20439 5 8 3
using the DEA approach, item No. 15 has a higher prior-ity than item No. 7. However, by the ERPN method, item No. 7 has a higher priority compared with No. 15. In fact, item No. 7 has a quite larger rate on severity than item No. 15; thus, it should be more reasonable to receive a higher priority than item No. 15 in taking corrective actions. This example indicates that the ERPN method we proposed can carry out a more accurate risk ranking for evaluating the orderings of failure modes.
From the above analysis, among the conventional RPN method, DEA approach, and the proposed ERPN method, the proposed ERPN method can not only achieve a more reasonable, accurate risk ranking for failure modes in FMEA but also reduce the high duplication rate problem found in the conventional RPN method.
Numerical verification
According to the conventional RPN method, the three para-meters S, O, and D are assumed to be equally weighted with respect to one another. It neglects the relative importance among the three parameters and thus may not be flexible enough in practical application of FMEA. In this section, a real case of PFMEA drawn from a mechanical factory in
Taiwan is used to illustrate the application of the pro-posed ERPN method. This example illustrates that the ERPN method can be applied to the case where different risk factors have different importance to decision-makers.
Case description
This case study is regarding the inlet plate manufactured via powder metallurgy by a mechanical factory located in Taiwan. This company has been in business for many years; it is not just a production facility and also has its own inde-pendent technology development team. All the products pro-duced by the company are widely used in industries all over the world. The inlet plate of this case regulates the fluid dis-placement per revolution of a hydraulic pump used in auto-mobiles engines, and it is shown in Fig.5. A PFMEA was carried out to improve the manufacturing process. The result-ing PFMEA table is summarized in Table12. The decision-maker assigned the relative weights of S, O, and D as 0.4, 0.35, and 0.25, respectively.
The proposed ERPN method
The relative importance weights of S, O and D are obtained by FMEA team members based on their judgment.
Fig. 5 Inlet plate
Table 12 The PFMEA for inlet plate
No. Process function/requirements Potential failure mode Potential effects of failure S O D 1 Premix powder Unstable apparent density and flow rate Unstable filling during compacting 5 2 6
2 Premix powder Unstable flow rate Unstable filling during compacting 5 2 6
3 Premix powder Wrong powder used Effect function 6 1 7
4 Compacting Damage of the tool Can not compact the parts 6 1 3
5 Compacting Damage of the tool Can not compact the parts 6 1 3
6 Compacting Damage of the tool Can not compact the parts 6 1 3
7 Compacting Damage Out of function 6 2 7
8 Compacting Crack Out of function 6 2 7
9 Compacting Crack Out of function 6 2 7
10 Compacting Unstable weight Out of function 5 3 3
11 Compacting Unstable weight Out of function 5 2 5
12 Compacting Length out of spec. Effect grinding process 5 2 5
13 Compacting Length out of spec. Effect grinding process 5 2 5
14 Compacting Depth out of spec. Effect assembly 5 2 5
15 Compacting Sectioned density out of spec. Out of function 4 3 5
16 Compacting Sectioned density out of spec. Out of function 4 3 5
17 Compacting Position Effect tapping 4 5 3
18 Compacting Without label Can not to retrace 4 2 6
19 Sintering Color change Poor appearance 6 1 7
20 Sintering Damage Poor function 6 2 7
21 Sintering O.D. out of spec Effect assembly 7 2 6
22 Sintering I.D. out of spec. Out of function 7 2 2
23 Sintering Improper hardness Out of function 5 2 2
24 Sintering Automatic temperature test is failure Can not get real temperature; affects the dimension and hardness
6 2 2
25 Sintering Position Effect tapping 4 5 2
26 Sintering Without label Can not retrace 4 2 5
27 Tapping Damage Poor function 6 2 2
28 Tapping Screw diameter is too small Effect assembly 5 2 2
29 Tapping Depth out of spec. Effect assembly 5 3 2
30 Tapping Profile out of spec. Effect assembly 5 3 3
31 Tapping Without label Can not retrace 4 2 3
32 Grinding Damages Out of function 6 2 2
33 Grinding Length out of spec. Effect assembly 5 2 2
Table 12 continued
No. Process function/requirements Potential failure mode Potential effects of failure S O D
35 Grinding Parallelism out of spec. Out of function 5 2 2
36 Grinding Flatness out of spec. Out of function 7 2 2
37 Grinding Roughness out of spec. Out of function 6 2 2
38 Grinding Rust Out of function 6 2 2
39 Grinding Without label Can not retrace 4 2 6
40 Brushing Burrs and dents Out of function 6 2 7
41 Brushing Without label Can not retrace 4 2 6
42 Steam treatment Rust Out of function 6 2 7
43 Steam treatment O.D. out of spec. Effect assembly 7 2 6
44 Steam treatment I.D. out of spec. Out of function 7 2 6
45 Steam treatment Improper hardness Out of function 5 2 6
46 Steam treatment Thickness of steam oxide out of spec Out of function 5 2 6
47 Steam treatment Roughness out of spec. Out of function 6 2 6
48 Steam treatment Without label Can not retrace 4 2 6
49 Q.C. Failure material out going Production shut down 6 2 6
50 Oil spray Too much oil Improper appearance 4 2 7
51 Oil spray Mixing in different oil Out of function 6 2 4
52 Oil spray Cleanliness out of spec. Out of function 7 2 5
53 Packaging/labeling Rust Out of function 6 2 7
54 Packaging/labeling Dirty, slag Out of function 6 2 7
55 Packaging/labeling Without label or wrong data Can not retrace 4 2 7
Using Eq. (2) while letting Ws = 0.4, Wo = 0.35, and Wd = 0.25, the ERPN values and the resulting ranking are organized in Table13.
As the same with the RPN values, a failure mode with a higher ERPN value is assumed to be more important and demands higher priority for corrective action than those with lower ERPN values. As a result, the risk ranking is based on their ERPN values. According to Table 13, items No. 20 and No. 21 with different (S, O, D) combinations of (6, 2, 7) and (7, 2, 6), respectively, have the same PRN values of 84. However, using the ERPN method, item No. 21 has a higher priority compared with No. 20; the severity has a higher weight than the detection in this case. This example indicates that the ERPN method can be implemented in the case where different risk factors have different importance to decision-makers, while the conventional RPN method could not. Considering the relative importance among the three parameters S, O, and D, the ERPN method seems to be more practical in the application of FMEA.
Conclusion
A new method named ERPN is developed in this study to improve some of the problems found in the conventional RPN method in FMEA. Different from those approaches
found in the literature that were also developed to improve the conventional RPN method, the ERPN proposed in this study is very easy to apply. This method used “Microsoft Office Excel” tool to make the calculation, which does not require other computer software to obtain the ranking result. An application of FMEA on a fishing vessel case (Pillay and Wang 2003) is presented to demonstrate the effective-ness of the new ERPN method. Other than the conventional RPN method, DEA (Chang and Sun 2009) is also applied to the fishing vessel case. The analysis of results shows that the proposed ERPN method can solve the shortcomings of the conventional RPN method, such as the high duplication rate problem. It can also provide an effective and easy way to identify the priority of failure modes. Another PFMEA case on an inlet plate drawn from a mechanical factory located in Taiwan is used to demonstrate that the ERPN method is capa-ble of taking the relative importance among the parameters S, O, and Dinto consideration.
In summary, the advantages of the proposed ERPN method are as follows:
(1) The new method ERPN uses a simple addition function to the exponential form of S, O, and D to substitute the multiplication function used in the conventional RPN method. The problem of measurement scales found in the conventional RPN is resolved this way.
Table 13 PFMEA for the inlet plate case by ERPN and RPN
No. S O D RPN RPN ranking ERPN ERPN ranking
1 5 2 6 60 22 16.3538 28 2 5 2 6 60 22 16.3538 28 3 6 1 7 42 51 22.2740 18 4 6 1 3 18 53 17.7150 25 5 6 1 3 18 53 17.7150 25 6 6 1 3 18 53 17.7150 25 7 6 2 7 84 1 22.9628 7 8 6 2 7 84 1 22.9628 7 9 6 2 7 84 1 22.9628 7 10 5 3 3 45 50 14.4489 47 11 5 2 5 50 35 15.1059 36 12 5 2 5 50 35 15.1059 36 13 5 2 5 50 35 15.1059 36 14 5 2 5 50 35 15.1059 36 15 4 3 5 60 22 12.9172 54 16 4 3 5 60 22 12.9172 54 17 4 5 3 60 22 14.9176 43 18 4 2 6 48 42 13.1534 48 19 6 1 7 42 51 22.2740 18 20 6 2 7 84 1 22.9628 7 21 7 2 6 84 1 29.0278 1 22 7 2 6 84 1 29.0278 1 23 5 2 6 60 22 16.3538 28 24 6 2 4 48 42 19.1243 23 25 4 5 3 60 22 14.9176 43 26 4 2 6 48 42 13.1534 48 27 6 2 7 84 1 22.9628 7 28 5 2 6 60 22 16.3538 28 29 5 3 5 75 16 16.1176 34 30 5 3 5 75 16 16.1176 34 31 4 2 6 48 42 13.1534 48 32 6 2 7 84 1 22.9628 7 33 5 2 5 50 35 15.1059 36 34 5 2 5 50 35 15.1059 36 35 5 2 5 50 35 15.1059 36 36 7 2 5 70 20 27.7799 5 37 6 2 5 60 22 20.0725 22 38 6 2 7 84 1 22.9628 7 39 4 2 6 48 42 13.1534 48 40 6 2 7 84 1 22.9628 7 41 4 2 6 48 42 13.1534 48 42 6 2 7 84 1 22.9628 7 43 7 2 6 84 1 29.0278 1 44 7 2 6 84 1 29.0278 1 45 5 2 6 60 22 16.3538 28 46 5 2 6 60 22 16.3538 28 47 6 2 6 72 18 21.3204 20
Table 13 continued
No. S O D RPN RPN ranking ERPN ERPN ranking
48 4 2 6 48 42 13.1534 48 49 6 2 6 72 18 21.3204 20 50 4 2 7 56 33 14.7957 45 51 6 2 4 48 42 19.1243 23 52 7 2 5 70 20 27.7799 5 53 6 2 7 84 1 22.9628 7 54 6 2 7 84 1 22.9628 7 55 4 2 7 56 33 14.7957 45
(2) To enhance the risk evaluation capability of FMEA, the proposed ERPN method is able to generate fewer dupli-cate values than what the conventional RPN method does. (3) The ERPN method offers an easier way to prioritize the failure modes in a system than any other approaches found in the literature.
Acknowledgments The author would like to express his sincerest gratitude to the anonymous referees for providing very helpful com-ments and suggestions which led to an improvement of the article. This work was supported in part by the National Science Council of the Republic of China under Contract No. NSC 99-2410-H-145-001 and NSC 101-2410-H-145-001.
References
Automotive Industry Action Group (AIAG). (2008). Potential failure mode and effect analysis (FMEA) reference manual. FMEA refer-ence manual (4th ed).
Ben-Daya, M., & Raouf, A. (1996). A revised failure mode and effects analysis model. International Journal of Quality and Reliability Management, 13(1), 43–47.
Bowles, J. B. (1998). The new SAE FMECA standard. In Processing annual reliability and maintainability, symposium, pp. 48–53. Bowles, J. B. (2003). An assessment of RPN prioritization in a failure
modes effects and criticality analysis. In Processing annual reliabil-ity and maintainabilreliabil-ity, symposium, pp. 380–386.
Bowles, J. B., & Pelaez, C. E. (1995). Fuzzy logic prioritization of failures in a system failure modes, effects and criticality analysis. Reliability Engineering and System Safety, 50(2), 203–213. Braglia, M., Frosolini, M., & Montanari, R. (2003). Fuzzy TOPSIS
approach for failure mode, effects and criticality analysis. Quality and Reliability Engineering International, 19(5), 425–443. Chang, C. L., Wei, C. C., & Lee, Y. H. (1999). Failure mode and effects
analysis using fuzzy method and grey theory. Kybernetes, 28(3–7), 1072–1080.
Chang, D. S., & Sun, K. L. P. (2009). Applying DEA to enhance assess-ment capability of FMEA. International Journal of Quality and Reliability Management, 26(6), 629–643.
Chang, K. H. (2009). Evaluate the orderings of risk for failure problems using a more general RPN methodology. Microelectronics Reliabil-ity, 49(12), 1586–1596.
Chang, K. H., & Cheng, C. H. (2009). A novel general approach to evaluating the PCBA reliability for components with different mem-bership function. Applied Soft Computing, 9(3), 1044–1056.
Chang, K. H., & Cheng, C. H. (2010). A risk assessment methodol-ogy using intuitionistic fuzzy set in FMEA. International Journal of Systems Science, 41(12), 1457–1471.
Chang, K. H., & Cheng, C. H. (2011). Evaluating the risk of failure using the fuzzy OWA and DEMATEL method. Journal of Intelligent Manufacturing, 22(2), 113–129.
Chang, K. H., Cheng, C. H., & Chang, Y. C. (2010). Reprioritization of failures in a silane supply system using an intuitionistic fuzzy set ranking technique. Soft Computing, 14(3), 285–298.
Chien, C. F., & Zheng, J. N. (2012). Mini-max regret strategy for robust capacity expansion decisions in semiconductor manufacturing. Jour-nal of Intelligent Manufacturing, 23(6), 2151–2159.
Chin, K. S., Wang, Y. M., Poon, G. K. K., & Yang, J. B. (2009). Failure mode and effects analysis by data envelopment analysis. Decision Support Systems, 48(1), 246–256.
Ford Motor Company. (1988). Potential failure mode and effects analy-sis. Instruction manual.
Gabus, A., & Fontela, E. (1973). Perception of the world problematique: Communication procedure, communicating with those bearing col-lective responsibility (DEMATEL report no.1). Geneva, Switzerland: Battelle Geneva Research Centre.
Gilchrist, W. (1993). Modelling failure modes and effects analysis. International Journal of Quality and Reliability Management, 10(5), 16–23.
Hsiao, T. Y., & Lu, C. N. (2008). Risk informed design refinement of a power system protection scheme. IEEE Transactions on Reliability, 57(2), 311–321.
Hussain, O. K., Dillon, T., Hussain, F. K., & Chang, E. (2012). Probabilistic assessment of loss in revenue generation in demand-driven production. Journal of Intelligent Manufacturing, 23(6), 2069–2084.
International Electrotechnical Commission, Geneva. (1985). Analysis techniques for system reliability-procedures for failure mode and effect, analysis. IEC812.
Karlsson, B., Karlsson, N., & Wide, P. (2000). A dynamic safety system based on sensor fusion. Journal of Intelligent Manufacturing, 11(5), 475–483.
Kubat, C., & Yuce, B. (2012). A hybrid intelligent approach for supply chain management system. Journal of Intelligent Manufacturing, 23(4), 1237–1244.
Pillay, A., & Wang, J. (2003). Modified failure mode and effects analysis using approximate reasoning. Reliability Engineering and System Safety, 79(1), 69–85.
Sankar, N. R., & Prabhu, B. S. (2001). Modified approach for prior-itization of failures in a system failure mode and effects analysis. International Journal of Quality and Reliability Management, 18(3), 324–335.
Seyed-Hosseini, S. M., Safaei, N., & Asgharpour, M. J. (2006). Repri-oritization of failures in a system failure mode and effects analysis
by decision making trial and evaluation laboratory technique. Reli-ability Engineering and System Safety, 91(8), 872–881.
Sharma, R. K., Kumar, D., & Kumar, P. (2005). Systematic failure mode effect analysis (FMEA) using fuzzy linguistic modeling. Inter-national Journal of Quality and Reliability Management, 22(9), 986–1004.
Tay, K. M., & Lim, C. P. (2006). Application of fuzzy inference tech-niques to FMEA. Applied Soft Computing Technologies: The Chal-lenge of Complexity, 34, 161–171.
US Department of Defense Washington, DC (1974). Procedures for performing a failure mode effects and criticality analysis. US MIL-STD-1629.
US Department of Defense Washington, DC (1980). Procedures for performing a failure mode effects and criticality analysis. US MIL-STD-1629A.
Wang, J., Ruxton, T., & Labrie, C. R. (1995). Design for safety of engineering systems with multiple failure state variables. Reliability Engineering and System Safety, 50(3), 271–284.
Wang, Y. M., Chin, K. S., Poon, G. K. K., & Yang, J. B. (2009). Risk evaluation in failure mode and effects analysis using fuzzy weighted geometric mean. Expert Systems with Applications, 36, 1195–1207. Xu, K., Tang, L. C., Xie, M., Ho, S. L., & Zhu, M. L. (2002). Fuzzy assessment of FMEA for engine system. Reliability Engineering and System Safety, 75(1), 17–29.
Yeh, R. H., & Hsieh, M. H. (2007). Fuzzy assessment of FMEA for a sewage plant. Journal of the Chinese Institute of Industrial Engi-neers, 24(6), 505–512.
Zhang, D. Y., Cao, X., Wang, L., & Zeng, Y. (2012). Mitigating the risk of information leakage in a two-level supply chain through opti-mal supplier selection. Journal of Intelligent Manufacturing, 23(4), 1351–1364.
Zhu, J. (2003). Quantitative models for performance evaluation and benchmarking: data envelopment analysis with spreadsheets and DEA Excel Solver. Boston: Kluwer.
