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FAILURE MODE IDENTIFICATION THROUGH CLUSTERING ANALYSIS

Srikesh G. Arunajadai Graduate Research Assistant

Department of Mechanical Engineering University of Missouri-Rolla

Rolla, MO 65409

Scott J. Uder Graduate Research Assistant

Department of Electrical Engineering University of Missouri-Rolla

Rolla, MO 65409

Robert B. Stone, Ph.D. 1

Associate Professor Department of Basic Engineering

University of Missouri-Rolla Rolla, MO 65409

573 341 4086 573 341 6593 (fax)

rstone@umr.edu

Irem Y. Tumer Ph.D. Research Scientist

Computational Sciences Division NASA Ames Research Center Moffett Field, CA 94035-1000

650 604 2976 itumer@mail.arc.nasa.gov

SUMMARY

Research has shown that nearly 80% of the costs and problems associated with product design are created

during product development and cost and quality are essentially designed into products during the conceptual

design stage. Failure identification procedures (such as FMEA, FMECA and FTA) and design of experiments

are currently being used for both quality control and the detection of potential failure modes during the design

stage or post-product launch. Though all of these methods have their own advantages, they do not provide the

designer with an indication of the predominant failures that should receive considerable attention while the

product is being designed. The work presented here proposes a statistical clustering procedure to identify

potential failures in the conceptual design stage. A functional approach, which hypothesizes that similarities

exist between different failure modes based on the functionality of the product/component, is employed to

identify failure modes. The various steps of the methodology are illustrated using a hypothetical design

example.

Keywords: clustering algorithm; conceptual design; failure-free design; failure mode; Failure Modes and

1 Corresponding Author. Revised manuscript submitted to Quality and Reliability Engineering Int’l Journal.

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Effects Analysis; function based design; product design; statistical based design.

BACKGROUND

Identification of potential failure modes during the product design process is critical for creating failure-

free designs. Industry currently uses procedures such as Failure Modes and Effects Analysis (FMEA), Fault

Tree Analysis (FTA), and Failure Modes, Effects, and Criticality Analysis (FMECA), as well as prior

knowledge and experience, to determine potential failure modes. These procedures require designers to have

both a broad knowledge of commonly occurring failure modes and an understanding of any connections or

causality between failures in order for the design to be successful. If sufficient knowledge is not available to

predict all of the realistically possible failure modes, then the current failure prevention procedures may be

insufficient.

Documenting Failure

Over the years many procedures have been developed to document failure data. Notable among them are

the FMEA, FMECA and the FTA. In this work, we take a new look at the principles of FMEA and present a

methodology for failure-free design of products.

The FMEA procedure is an offshoot of the Military procedure MIL-P-1629 [1] developed by the United

States Military as a tool to determine and evaluate equipment failures. Many industries have developed their

own standards of performing the FMEA: AIAG (1993) of the Automotive Industry Action Group; MIL-STD-

1629A (1984) of the US Department of Defense; SAE J1739 (1994) of the Society of Automobile Engineers;

and the VDA 96, Heft4, Teil 2 (1996) of the Verband der Automobileindustrie, Germany.

The traditional FMEA, when performed rigorously, contains valuable information about the failures of

various components but has two fundamental weaknesses: 1) the lack of a methodological guideline to

conduct the FMEA; and 2) the lack of a natural, repeatable language to record the information [2]. Current

Industrial FMEA practice is severely restricted in its usefulness and analytical power due to limitations of

spreadsheet based approaches to acquiring, representing, and reasoning with system failure knowledge. Thus

the standardization of the failure mode vocabulary would make the procedure more useful and repeatable.

In this work, we use a matrix-based method to help sort through the failure modes associated with

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products. A matrix approach for recording failure data was introduced as early as 1976 by Collins et al. [3]

and the concept of applying matrix techniques to FMEA was introduced in 1977 by Barbour [4] and

subsequently developed by Goddard and Dussault [5]. More recently the matrix technique has been employed

by Henning and Paasch [6] to represent the failure and replacement characteristics of a system.

Retrieving Failure Information – The Statistical Approach

Statistical tools have been employed for some time now in quality control and reliability measurement. A

structural approach based on probability theory for the design and safety analysis of aircraft began in the early

1960s [7]. The use of numerical probabilities may not be a prerequisite for performing system safety analyses,

but it provides valuable guidance to the designer in determining the architecture required and assessing its

failure tolerance. The prediction of system failure probabilities is not a precise science; however, the process

does provide an extremely good framework on which to hang engineering experience [7]. Lee [8] has

employed the Bayes networks to account for the conditional dependencies between states and events in the

causal chain and across causal chains. This approach constitutes a mathematically sound method for

representing and reasoning with joint probability distributions in an internally consistent manner. Traditional

FMEA ignores these connections and implicitly assumes that all failure states and events, together with their

causes and effects, are probabilistically independent.

Probabilistic design is concerned with the probability that a system will realize the function assigned to it

without failure. Onyebueke et al. [9] provide an overview of the Probabilistic Design Methodology (PDM)

with emphasis on the quantification of the effects of uncertainties for the structural variables and the

evaluation of failure probabilities. PDM takes into consideration reliability, optimization, cost parameters, and

the sensitivity of design parameters, which are ignored by the deterministic method and are extremely useful

in designs characterized by complex geometry, sensitive loads, and material properties. The method is limited

in use due to three identifiable factors: 1) most people are unaware of the capabilities of the PDM and the

available computer codes; 2) there is not yet a universal decision as to what constitutes an acceptable risk; and

3) there is very little information on most design parameters [9].

Bhonsle et al. [10] have developed a statistical distribution function called adaptive distributive function

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model which is compatible with collected data and produces conservative designs at low tail ends. Meeker

and Hamada [11] discuss the role of statistical process monitoring and designed experiments as tools for

quality improvement. They also differentiate between the traditional reactive approach where the reliability

requirements are not met at the time of delivery of the product and the proactive reliability assurance

approach. Yang and Xue [12] describe the application of the fractional factorial design of experiment method

to degradation testing and reliability design. Marco et al. [13], while describing the integration of the FMEA

and serviceability design, raise the need for calculating statistical and probabilistic occurrence measures for

each type of failure mode depending on component type, operational environment, or duty cycle.

The Function-Failure Method as a Step Toward Failure-Free Design

Standardization of a product function vocabulary to enable archival and retrieval of product design

knowledge has been a primary research area for many years [14-17]. We use the functional basis developed

by Hirtz et al. [14] and Stone and Wood [17] to link failure back to the more abstract product function.

Similar work has been suggested for the classification of failure modes. Collins [18] has described 23

different mechanical failures based on the characteristics of the manifestation of failure, the failure-inducing

agent, and the location of the failure. There are other classifications such as those based on the end effect of

the failure [19] and the design stage in which the failure mode might have been introduced [20]. Our current

work begins with the Collins classification and augments it such that each failure mode is identified with the

help of a primary and secondary identifier [21, 22, 24].

The work presented here employs the function-failure design method, a functional approach to guide the

determination of the potential failure modes a product may be subjected to once placed in its operating

environment [21-24]. The methodology involves the formation of a function-failure matrix that can be used as

a knowledge base to identify and analyze potential failures for new designs and redesign. The overall

procedure to create the knowledge base is outlined in Figure 1.

The function-component (EC) matrix is composed of columns of components (obtained from products’

bill of materials) and rows of functions (obtained from products’ bill of materials and the functional model).

The component-failure (CF) matrix is composed of rows of components and columns of failure modes. The

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CF matrix is populated using information derived from failure reports or from an FMEA rather than from

reliability testing. For this reason, the function-failure method is a “design tool” to aid in reliability

engineering. Entries in the EC matrix indicate the number of times a component was used to solve a function

across the range of products examined. Similarly, entries in the CF matrix indicate the number of times a

component experienced a particular failure across the range of products examined. The function-failure (EF)

matrix (which links product function to potential failure modes) is obtained from the matrix multiplication of

the two matrices:

EF = EC x CF. (1)

Through the function-failure (EF) matrix, product function is linked to potential failure modes by indicating

the number of times any component solving a particular function exhibited a failure.

FAILURE MODES STUDY – A FUNCTIONAL APPROACH

The function-failure approach described in [21-24] is used as a starting point in this research work. This

method, which seeks to eliminate operational failures, provides a standardized vocabulary to record failure

data and a matrix approach to store failure information. We go one step further in this paper to demonstrate

how the matrix approach aids in identifying critical failure modes and functions by making use of the

probabilistic characteristics of the observed failure modes.

General Observations

We know by experience that certain failure modes occur more frequently than others. The question we

want to answer is: given the functions of a product, are there particular failure modes that are more likely to

occur than others? Such information would be of immense importance in the conceptual design stage and

would allow the designer to take appropriate measures to ensure the best possible design. It is our hypothesis

that if the failure mode occurrence knowledge is easily accessible, the designer can focus on the appropriate

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analyses in an effort to prevent failure modes from occurring.

To test this hypothesis we examined a set of 41 electromechanical consumer products through laboratory

testing following the reverse engineering technique of Otto and Wood [25] to document component

function(s) and failure mode(s). Some of the products tested included an air purifier, palm sander, hand

vacuum, coffee maker, hair dryer, engraver, floor jack, grinder, jigsaw, leaf blower, popcorn popper, toaster

and a water purifier. The function-failure method was implemented across these 41 consumer products to

arrive at a single EC matrix, a single CF matrix, and an EF matrix (which is the result of the matrix

multiplication of the EC and CF matrices). The following observations were made from these three matrices.

Distribution of Failure Modes: The total number of occurrences of each failure mode was calculated

from the component-failure (CF) matrix. A Pareto chart was plotted for the occurrence of the failure modes

and is shown in Figure 2. This figure clearly indicates that certain failure modes occur more frequently than

others. In fact, 92% of the failures were accounted for by just 40% of the failure modes; i.e., 92% of the

failures were contributed by just 13 of the 32 failure modes. Thus by concentrating on these 13 failure modes,

the designer can be assured the major failures have been considered. To verify this fact we checked the

component-failure matrix to determine the number of failure modes that were overlooked per component. Of

the 1001 components in the matrix, 134 components exhibited failure from the 19 infrequently occurring

failures. Of these 134 components, 8 components exhibited 2 of the 19 failure modes while the remaining 126

components exhibited just 1 of the 19 failure modes. Thus, on average for the 1001 components, we

overlooked 0.141 failure modes per component. This calculation was performed by first calculating the

number of failure modes that were not addressed by the 13 primary failure modes. The average was then

calculated for the 1001 components.

Distribution of Failures Across Functions: The sum of each row corresponding to the given function in

the function-failure (EF) matrix indicates the number of failures experienced by the function for the time

period observed. A Pareto chart was plotted for the number of failures for a given function and is shown in

Figure 3. As seen in Figure 3, there are certain functions that exhibit more failures both in type of failures and

the number of occurrences. Only 42 of the 180 functions experienced at least 1% of the failures. With this

knowledge, the designer will know to focus his or her time and money developing solutions for those

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functions that exhibit a higher occurrence of failure.

Number of distinct failure modes with increasing functions: As the number of functions increase, the

number of distinct failure modes that are contributed by the new function decreases. That is, there is a limit

after which the addition of a new function does not contribute a new distinct failure mode. This fact reinforces

the hypothesis that the designer can concentrate on a particular set of failure modes as the additional functions

are very unlikely to add a substantial number of new distinct failure modes. Figure 4 shows the plot of the

number of distinct failure modes with increasing number of functions. For the 41 consumer products that were

considered, the plot indicates there are no new failure modes observed after 9 functions.

Number of distinct failure modes with increasing components: Similarly, as the number of

components increase, the number of new distinct failure modes observed in these components decrease. That

is, as the number of components increase, the probability that it would experience a new distinct failure

decreases. As shown in Figure 5, the number of distinct failure modes observed decrease as the number of

components increase.

Present Scope of Research

To summarize, our empirical study of 41 electromechanical consumer products provides a reliable

knowledge base on which to propose a new statistically based approach toward failure free design of

mechanical systems. Extending the function failure method to electrical systems is currently underway, so

electrical failure modes were not available at the time this work was performed. For this reason, the work

presented here strictly utilizes material-based mechanical failure modes.

The addition of new components or new functionality is not expected to significantly alter our findings.

For this paper, we focus on mechanical failure mode occurrence data. While typical FMEA approaches also

include severity and detectability data, we will be confined to occurrence data and the inherent statistical

knowledge it holds.

FAILURE MODES STUDY – A CLUSTERING APPROACH

The saying “time is money” is definitely true for product development in today’s highly competitive

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market. Thus, the key to success is to get the product to the customer in the shortest possible time ensuring

both maximum performance and safety. The issue is whether this can be accomplished without a substantial

increase in cost of product development.

Let us examine a simplified hypothetical design situation. Assume a product in which the function Stop

Gas is involved. From the function-component (EC) matrix, we retrieve the function Stop Gas and each of the

components that solve this function. We now have the reduced EC matrix shown in Table 1, which contains

possible component solutions to the function Stop Gas [21, 22, 24, 26]. The values of ‘1’ in this binary matrix

indicate the components shown solve the function indicated.

The designer’s decision as to which of the solutions to choose from the reduced EC matrix is partially

dependent upon the intended application. For example, the intended application for the function Stop Gas

could be a simple home product in which the component acts as an obstruction for stagnant air, or the

component could be intended to be used in a product for the highly complex aerospace industry where the seal

needs to stop the flow of gas at both high pressure and high temperature. Because this example does not have

an intended application and different types of rubber seals are prevalent in the morphological matrix, we

select a generic rubber seal (which could be a rubber piston seal, a rubber seal plug, a rubber barrel seal, or an

O-ring) as the solution to the function Stop Gas.

We now refer to the function-failure (EF) matrix in order to determine the failure modes exhibited by the

function Stop Gas. As indicated in Equation 1, the function-failure (EF) matrix is obtained from the matrix

multiplication of the function-component (EC) and the component-failure (CF) matrices. For matters of

convenience, the EF matrix was reduced to Table 2 (which only contains failures corresponding to the

function Stop Gas) by deleting rows and columns that did not pertain to this function. The values in Table 2

indicate the total number of instances each failure mode was observed (across the 41 products analyzed) for

the particular function. For example, there were four instances where components performing the function

Stop Gas experienced force induced deformation.

We see that the function Stop Gas has experienced 5 different failure modes for the time period observed.

The question now is whether the designer should concentrate on all the failures during design. In this rather

simple case, the difference between designing for 5 failures and 3 failures may seem trivial, but consider cases

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where a function exhibits many different kinds of failure or cases where multiple product functions must be

designed. A considerable advantage during the design process would be knowing if there is a particular set of

failures on which the designer should concentrate to ensure product safety and, at the same time, save cost and

reduce time of product development. A clustering approach is used to arrive at this set of failures.

Background: Cluster Analysis

Cluster analysis is a multivariate statistical procedure that begins with a data set containing information

about a sample of entities and attempts to reorganize these entities into relatively homogeneous groups.

Clustering analysis is helpful when a researcher tries to classify or group data into categories or groups when

neither the number of groups nor the members of the groups are known. Clustering has been proven as a

useful technique in exploratory data analysis when the sample is known to be non-homogeneous [27].

There are two main methods by which clustering analysis is performed: hierarchical clustering and K-

means clustering. For this work, we used hierarchical clustering due to the fact that the number of cases is

small (32 failure modes); the K-means method is more advantageous when there are a large number of cases

(greater than 200). In the hierarchical method, clustering begins by finding the closest pair of objects

according to a distance measure and combines them to form a cluster. The algorithm continues one step at a

time joining pairs of cases, pairs of clusters, or a case with a cluster until all the data are in one of the clusters.

The method is hierarchical, because once two cases or clusters are combined, they remain together until the

final step. The hierarchical clustering offers several methods for combining or linking clusters. In this work

we have used the complete linkage method, which is an extension of the above-described hierarchical

clustering [27]; a Euclidean distance is used as the distance measure.

The rule for the complete linkage method states that any candidate for inclusion into an existing cluster

must be within a certain level of similarity to all members of that cluster. This rather rigorous rule of the

complete linkage method has a tendency to find relatively compact, hyperspherical clusters composed of

highly similar cases.

The disadvantage of the cluster analysis is that, although the algorithm provides a means to form the

clusters, the final decision regarding the number of clusters and the membership in each cluster group is

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dependent on the researcher’s judgment. Most algorithms cluster the cases according to the number of clusters

input by the user. The designer steps through the algorithm a number of times, and, with the help of other

indicators such as dendograms (a tree diagram that depicts the clustering sequence), determines which is the

best set of clusters. Although designer judgment (which may be different from one designer to the next) is

required, the clustering method definitely provides a useful starting point for grouping data especially when

the data space is very large.

Technical Approach

As described in the previous sections, the cluster analysis is a multivariate statistical procedure that aids

in grouping or categorizing data. Our goal is to group failure modes based on their occurrence – i.e., we

would like to determine whether the failure should be considered by itself or whether it has a tendency of

accompanying other kinds of failure(s). To obtain the failure mode groupings, the cluster analysis is

performed on the failure similarity matrix, which is obtained by pre-multiplying the component-failure matrix

(CF) by its transpose [21, 24]. The similarity matrix, shown in Figure 6 in rearranged format, follows from the

matrix multiplication:

Λ = CFT x CF. (2)

Diagonal values in the similarity matrix indicate the number of individual occurrences of the particular

failure. Non-diagonal values represent joint occurrences. As an example of a joint occurrence, temperature

induced deformation and brittle fracture occurred together 21 times (i.e., 21 is the frequency of joint

occurrence). The importance of this matrix is derived from the frequency of both the individual and the joint

occurrences and the distance measures between joint occurrences. The closer one set of joint occurrences are

to another set of joint occurrences, the greater tendency these failure modes have to occur together.

The hierarchical clustering algorithm using the complete linkage method was performed using SPSS

(Statistical Package for the Social Sciences) software, a powerful statistical data analysis package from SPSS

Inc [28]. The input to the software was provided in the form of (1) the similarity matrix and (2) the number of

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clusters we desired (in the software output). The SPSS software calculated the distance measures internally

and used these distance measures along with the frequency of occurrences to suggest viable cluster

combinations. We applied the software ten different times while only varying the number of desired clusters

(i.e., used 6 through 15 as input to indicate the number of clusters we desired in the output). At this point, we

had ten distinct sets of clusters. Each set of clusters contained all of the failure modes, but the failure modes

were clustered differently in each set. After carefully studying the different cluster combinations, we grouped

the 32 failure modes identified in this work into 9 groups as shown in Table 3. Our interpretation of the set

containing 9 clusters follows.

Interpretation of the Cluster Groups

Cluster-1 and cluster-2 are single member clusters that contain direct chemical attack and force induced

deformation respectively. Single member cluster arise when the failure mode has a high frequency of

occurrence and it occurs with the majority of failure modes. Placing such failure modes in an individual group

is the equivalent of placing the failure mode in each and every cluster in order that it be considered in all

design situations. We call such clusters Type-I clusters. Note that five other failure modes occur more

frequently than direct chemical attack. However, these failure modes are not placed in a Type-I cluster due to

the fact that they have a tendency to occur with particular failure modes (i.e., they tend not to occur with the

majority of failure modes). Recall that the purpose of the clustering algorithm is to determine which failures

have a tendency of occurring together.

Clusters 3, 4, 5, 6, and 7 comprise failure modes that have a tendency to occur together. We call such

clusters Type-II clusters. The reader may notice the failure mode abrasive wear, which has 74 occurrences,

was placed in the same cluster as compression set, heat cracking, and installation damage, in which the

maximum occurrence is 5. Initially, one might wonder why abrasive wear was not placed in a single member

cluster. Recall that the distance measures between joint occurrences and the frequency of occurrences are used

to generate clusters. Single member clusters have a high frequency of occurrence and occur with the majority

of failure modes. Although abrasive wear occurred with many of the other failure modes, the frequency of

these joint occurrences (i.e., the number of times they occurred together) was relatively low. Abrasive wear

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occurred by itself on most occasions. Therefore, abrasive wear was grouped in a cluster having similar

distance measures.

Cluster-8 and cluster 9 contain failure modes that will be considered on an individual basis. These are

failure modes that have a very low rate of occurrence and do not show any particular characteristic of

occurring with other failures. The fact that these failure modes do not occur together raises the question as to

why they are placed in the same cluster. The reason for these failure modes being in the same cluster is

because these failure modes all have relatively large, yet similar, distance measures. As such, these failure

modes tend not to occur together. Thus, when dealing with failure modes in cluster-8 and cluster-9, we shall

only consider those particular failure modes rather than considering all of the failure modes within this

cluster. We call such clusters Type-III clusters.

After defining the cluster types, we rearranged the original similarity matrix by Type and cluster, as

shown in Figure 6, to verify that the occurrences within the similarity matrix were indeed clustered. The

figure shows a very clear pattern. The failure modes with the largest occurrences and joint occurrences that

also occur with the majority of failure modes are Type I clusters. The failure modes with very low

occurrences and joint occurrences and relatively large distance measures appear are Type III clusters. The

remaining failure modes, which we define as Type II, are those that have a moderate frequency of occurrence

and joint occurrence and relatively small distance measures.

The following section explains the general steps involved in using the cluster information.

Rules for Using the Cluster Information

To identify the failure modes that will be considered during the initial conceptual design stages, a three-

step approach is followed:

1. All Type-I clusters (i.e., single member clusters which have only one failure mode) are always

considered during the initial design stage.

2. For the given function (E) under consideration, we identify the maximum occurring failure mode

from the function-failure (EF) matrix. Engineering judgment may be exercised during this step. If the

designer decides that a particular failure mode is more important (than the maximum occurring

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failure mode) for the design at hand, then the designer may choose to consider one or both of these

failure modes for this step. When selecting the maximum occurring failure mode from the EF matrix,

the failures belonging to Type-I clusters are not considered as they have already been taken into

consideration during Step 1.

3. After having identified the maximum occurring failure mode, the cluster to which it belongs is

identified. If the failure mode belongs to a Type-II cluster we consider the entire cluster of failure

modes for the design. If the failure mode belongs to a Type-III cluster, only that failure mode is

considered and the other failure modes from the cluster are ignored.

Engineering judgment may certainly be exercised if the designer believes additional failure modes should

be considered.

We claim that by following Steps 1 through 3, we will identify a subset of the possible failure modes

corresponding to the design at hand. Let us denote the set of possible failure modes corresponding to the

design under consideration by Fd and the set of failure modes obtained from Steps 1 through 3 by F1-3. We

claim that

Fd

!

" ( F1-3 ∪ εd ), (3)

where εd is the set of failures that the Steps 1 through 3 did not yield for the design under consideration. For

this work, the number of failure modes that was overlooked was on average 0.295. That is, n (εd) = 0.295.

This shows that by following the failure mode clustering approach using only the most frequently occurring

failure mode for a given function, we can identify a subset of failure modes corresponding to the failure

modes of the design under consideration by overlooking approximately 0.295 failure modes. Thus Equation 3

can be closely approximated as:

Fd

!

" F1-3. (4)

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Table 4 shows the values of n (εd), which are the number of overlooked failures assuming only the most

frequently occurring failure mode is investigated. For example, if the predominant failure mode for a function

is determined to be abrasive wear, then the above described three-step approach indicates the component that

will solve this function should be designed to withstand failures belonging to cluster-1, cluster-2 and cluster-

3. Namely, the component would be designed to counter abrasive wear, compression set, heat cracking,

installation damage, direct chemical attack, and force induced deformation. According to Table 4, we would

have overlooked, on average, 0.55 failures per component when designing a component to counter the failures

from these three clusters using the clustering approach. For failures belonging to cluster-8 and cluster-9

(Type-III clusters), only that individual failure mode from cluster-3 along with cluster-1 and cluster-2 (Type-I

clusters) are considered. For this reason, the n (εd) values of all the failure modes corresponding to cluster-8

and cluster-9 would not be included in the calculation that determines overlooked failures. As more failure

mode observations are recorded in the function-failure matrices, n(εd) is expected to decrease.

Essentially, the question is: how many failure modes should be considered during conceptual design? The

number of failure modes considered should be small enough to effectively reduce the effort of the analysis yet

broad enough to capture the important correlations between failure modes.

APPLICATION TO THE ‘STOP GAS’ FUNCTION

We now apply the three-step method described in the previous section to the component that is desired to

solve the function Stop Gas.

1. We take into consideration Type-I clusters, which are cluster-1 and cluster-2 corresponding to failure

modes direct chemical attack and force induced deformation.

2. For the given function we identify the maximum occurring failure mode from the function-failure

matrix (EF). We find that the maximum occurring failure mode is force induced deformation. As

described in step 2 of the rules for using clustering information, the designer can use his or her

discretion when selecting this failure mode. Because the maximum occurring failure mode, force

induced deformation, occurs in a Type-1 cluster, it will be automatically be considered. In addition,

we select the failure mode compression set as we know this is an important failure mode associated

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with rubber failures. As you recall, we chose a rubber seal as the component solution from the

morphological matrix.

3. Next we identify the cluster to which the failure mode compression set belongs: cluster-3. Because it

is a Type-II cluster, we consider all of the failure modes within cluster-3.

Our subset F1-3 comprises direct chemical attach, force induced deformation, abrasive wear, compression set,

heat cracking and installation damage. The designer should consider these failure modes when designing a

rubber component (which could be a rubber piston seal, a rubber seal plug, a rubber barrel seal, or an O-ring)

to solve the function Stop Gas. We performed a cross check with the components identified as solving the

function Stop Gas in the component–failure matrix (CF) to determine what failure modes were exhibited and

if the value of n (εd) < 0.295. Table 5 shows the identified components, their failure modes, and the number of

failures modes that were not identified by the cluster approach.

As seen from Table 5, we missed just one failure mode for a single component. However, a careful

consideration reveals this component, an air tube cap, to be a plastic component. Had we decided to use a

plastic component, we would have selected cracking as our major failure in Step 2 of the cluster approach and

would still have found all of the failure modes for the component. The check of our work has another

advantage. We see that while all the rubber seals experienced the failure mode compression set, just one of

them experienced abrasive wear and installation damage. Thus clustering aids in retaining a collective failure

history of functions spanning the various components. As mentioned previously, the intended design

application should be taken into account when determining which of the failure modes resulting from the

clustering approach should ultimately be considered important for the design. If the seal is to be placed in a

home-product, then designing for force induced deformation or direct chemical attack may not be necessary.

However, if the seal will be in an aerospace application, then the designer may need to consider the failures

indicated by the Type-I clusters as the intended environment for the seal may contain reactive gas possessing

tremendous velocities.

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CONCLUSION AND FUTURE WORK

A clustering-based method aimed at producing failure-free designs has been described to assist the

designer in identifying potential failure modes during the conceptual design stage and deciding which failure

mode analyses are needed. The standardized vocabulary coupled with the matrix approach, introduced in

Tumer and Stone [21, 24], is used here as a basis for analyzing the statistical characteristics of failure mode

data. A discussion of the advantages of using a clustering-based approach for failure mode identification and

analysis planning is presented in detail as is the technical approach and a hypothetical example.

The clustering method was shown to overlook less than one failure per component (0.295 failures per

component on average) based on our study of 41 products. We expect the inclusion of additional products will

reduce this value. It is important to note that our aim is a “failure-free” design methodology, though currently

this approach is more accurately described as an attention-directing tool. Future work will seek to eliminate

the overlooked failure modes or, alternatively, quantify the risk of any overlooked failure mode.

Further research is needed to expand the failure mode classification to include more material specific

failures such as the failure of composite materials and to include more failures pertaining to the variety of

electrical components. The current work focused only on the occurrence data of mechanical failure modes.

ACKNOWLEDGMENTS

This work is supported by the National Science Foundation under grant DMI-9988817 and by the NASA

Ames Research Center under grant NCC 2-5423. Any opinions or findings of this work are the responsibility

of the authors, and do not necessarily reflect the views of the sponsors or collaborators.

BIOGRAPHIES

Srikesh Arunajadai received his Bachelors in Mechanical Engineering from Madras University

(1999) and a Masters in Mechanical Engineering from the University of Missouri-Rolla (2002). He is

currently pursuing his PhD in Biostatistics at the University of California-Berkeley. His research interests

include Statistical Genetics, Stochastic processes and applying statistics to a variety of fields from

engineering to epidemiology.

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Scott Uder graduated from the University of Missouri-Rolla in December of 2002 with an

undergraduate degree in Electrical Engineering and a minor in Computer Science. He will complete a M.S.

in Electrical Engineering at the University of Missouri-Rolla in May of 2003. Scott’s research involves

developing an electrical failure mode taxonomy and extending the function-failure design methodology to

identify failure modes in the conceptual stages of electrical system design.

Robert Stone is currently an Associate Professor of Basic Engineering in the Basic Engineering

Department of the University of Missouri-Rolla. He completed his Ph.D. in Mechanical Engineering from The

University of Texas at Austin in 1997. In addition to teaching fundamental engineering mechanics courses,

Stone has utilized his design background to develop an undergraduate interdisciplinary design methodology

courses and a graduate course covering and implementing cutting-edge product design methods. Dr. Stone’s

research interests lie in the area of design theory and methodology, specifically product architectures,

functional representations and design languages. He has received multiple awards related to his research in

product design and has authored a chapter on product architecture in a new product design text (Otto and

Wood, 2001). Prior to initiating his graduate work, Dr. Stone worked in the Missions Operation Directorate

of NASA-Johnson Space Center as a Space Shuttle Flight Controller.

Irem Tumer graduated from The University of Texas at Austin with a B.S. degree in mechanical

engineering in 1991 and then obtained a M.S.E. degree in mechanical engineering in 1995. Irem received her

doctorate in mechanical engineering from The University of Texas at Austin in 1998 and is currently a

researcher in the Computational Sciences Division at NASA Ames Research Center. Dr. Tumer’s research

interests include design for failure-free missions, vehicle health monitoring and diagnosis, fault detection,

failure analysis and modeling, function-failure similarity, variation analysis and modeling, failure and risk

identification, risk-based design, vibration monitoring, statistical analysis and signal processing.

REFERENCES

1. Procedures for performing a failure modes, effects, and criticality analysis. MIL-P-1629A. 1980.

2. Wirth R, Berthold B, Kramer A, Peter G. Knowledge-based support analysis for the analysis of failure

modes and effects. Engineering Applications of Artificial Intelligence 1996. 9(3): 219-229.

3. Collins JA. Failure of Materials in Mechanical Design: Analysis, Prediction, Prevention. 2nd ed., Wiley

18

Interscience. 1993.

4. Barbour GL, Failure modes and effects analysis by matrix methods. Proceedings of the Annual

Reliability and Maintainability Symposium. 1977. ASME: Piscataway, NJ.

5. Goddard PL, Dussault HB. The automated matrix FMEA-A logistics engineering tool. Proceedings of the

Society of Logistics Engineers’ 19th Annual Symposium. 1984. Soc of Logistics Engineers.

6. Henning S, Paasch R. Diagnostic analysis of mechanical systems. Proceedings of the Design Engineering

Technical Conferences. 2000. Baltimore, MD: ASME.

7. Cherry RW. The probabilistic approach to safety—successor failure? Proceedings of the Institution of

Mechanical Engineers. Part G, Journal of Aerospace Engineering 1995. 209(3):177-183.

8. Lee BH. Using Bayes belief networks in industrial FMEA modeling and analysis. Proceedings of the

Annual Reliability and Maintainability Symposium. 2001. IEEE: Philadelphia, PA.

9. Onyebueke LL, Onwubiko C, Chen FC. Probabilistic design methodology and the application of

probabilistic fault tree analysis to machine design. Proceedings of the 1995 Design Engineering

Technical Conferences. 1995. ASME: Boston, MA.

10. Bhonsle SR, VanKarsen CV, Michler JR. Statistical and mathematical approach for distribution function

model for low probability failures. International Gas Turbine and Aeroengine Congress and Exposition.

1991. ASME: Orlando, FL.

11. Meeker WQ, Hamada M. Statistical tools for the rapid development and evaluation of high-reliability

products. IEEE Transactions on Reliability 1995. 44(2): 187-198.

12. Yang K, Xue J. Reliability design based on dynamic factorial experimental model. Proceedings of the

Annual Reliability and Maintainability Symposium. 1997. IEEE: Piscataway, NJ.

13. Marco PD, Eubanks CF, Ishii K. Service modes and effects analysis: integration of failure analysis and

serviceability design. Computers in Engineering Conference. 1995. ASME: Boston, MA.

14. Hirtz J, Stone R, McAdams D, Wood K, Szykman S. A functional basis for engineering design:

reconciling and evolving previous efforts. Research in Engineering Design 2001. 13(2): 65-82.

15. Bluvband Z, Zilberberg E. Knowledge-based approach to integrated FMEA. Proceedings of ASQ’s 53rd

Annual Quality Congress. 1999. Anaheim, CA: ASQ.

16. Hawkins PG, Woolons DJ. Failure modes and effects analysis of complex engineering systems using

functional models. Artificial Intelligence in Engineering 1998. 12: 375-395.

17. Stone RB, Wood KL, Development of a Functional Basis for Design. Journal of Mechanical Design

2000. 122(December): 359-370.

18. Collins JA, Hagan BT, Bratt HM. The failure-experience matrix: A useful design tool. Journal of

Engineering for Industry 1976. 18:1074-1079.

19. Thornton CH. Reducing failures of engineered facilities. Combined Workshop of the National Science

Foundation and the American Society of Civil Engineers. 1985. pp 14-23. ASCE: Clearwater Beach, FL.

20. Svalbonas V. Causes of failure. Proceedings of the Pressure Vessel and Piping Technology: A Decade of

19

Progress. 1985: 1055-1067. SME.

21. Tumer IY, Stone RB. Analytical method for mapping function to failure during high-risk component

development. Proceedings of the Design Engineering Technical Conferences. 2001. Pittsburgh, PA:

ASME.

22. Arunajadai SG, Stone RB, Tumer IY. A framework for creating a function-based design tool for failure

mode identification. Proceedings of DETC02, DETC2002/DTM-34018, Design Theory and Methodology

Conference. 2002. ASME: Montreal, Canada.

24. Roberts RA, Stone RB, Tumer IY. Deriving function-failure information for failure-free rotorcraft

component design. Proceedings of DETC02, DETC2002/DTM-34166 Design for Manufacturing

Conference. 2002. ASME: Montreal, Canada.

23. Tumer I, Stone R. Mapping function to failure during high-risk component development. Research in

Engineering Design 2003 14(1): 25-33.

25. Otto K, Wood K. Product Design: Techniques in Reverse Engineering and New Product Design.

Prentice-Hall, 2001.

26. Strawbridge B, Stone R, McAdams D. A Computational Approach To Conceptual Design. Proceedings

of DETC2002. DETC2002/DTM-34001, Design Theory and Methodology Conference. 2002. ASME:

Montreal, Canada.

27. Aldenderfer MS, Blashfield RK. Cluster analysis: quantitative applications in social sciences. Sage:

Beverly Hills, CA 1984.

28. http://www.spss.com/. September 2, 2003.

1

Figure 1. A conceptual depiction of the function-failure method utilized to populate a function-failure

knowledge base for failure analysis.

0

100

200

300

400

500

600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

FAILURE MODES

NU

MB

ER

OF

OC

CU

RE

NC

ES

Figure 2. Failure mode distributions.

FAILURE MODE DISTRIBUTION

0

50

100

150

200

250

300

350

400

1

11

21

31

41

51

61

71

81

91

101

111

121

131

141

151

161

171

FUNCTION

NU

MBER O

F O

CCU

REN

CES

Figure 3. Failure modes for a given function.

2

DISTINCT FAILURE MODES WITH INCREASING FUNCTIONS

0

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 10 11 12 13 14

FUNCTION

DIS

TIN

CT

FA

ILU

RE

MO

DE

S

Figure 4. Distinct failure modes with increasing functions.

NEW FAILURE MODES WITH

INCREASING COMPONENTS

0

5

10

15

20

25

30

35

237 324 421 538 680 871 1001

COMPONENTS

FA

ILU

RE M

OD

ES

EXISTING FAILURE NEW FAILURE Figure 5. Distinct failure modes with increasing components.

3

Type

Cluster 1 2 3 3 3 3 4 4 5 5 6 6 7 7 7 7 7 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9Type

Clu

ste

r

FAILURE / FAILURE - (COMP)

DIR

ECT C

HEM

ICA

L A

TTA

CK

FO

RCE IN

DU

CED

DEFO

RM

ATIO

N

ABRA

SIV

E W

EA

R

CO

MPRESSIO

N S

ET

HEA

T C

RA

CKIN

G

INSTA

LLA

TIO

N D

AM

AG

E

AD

HESIV

E W

EA

R

DEFO

RM

ATIO

N W

EA

R

BRIT

TLE F

RA

CTURE

TEM

PERA

TU

RE IN

DU

CED

DEFO

RM

ATIO

N

CO

RRO

SIV

E W

EA

R

YIE

LD

ING

CRA

CK

ING

CREEP S

TRESS R

UPTU

RE

GA

LLIN

G A

ND

SEIZ

URE

HIG

H C

YCLE F

ATIG

UE

SU

RFA

CE F

ATIG

UE W

EA

R

CREEP B

UCKLIN

G

IMPA

CT D

EFO

RM

ATIO

N

AG

EIN

G

BIO

LO

GIC

AL C

ORRO

SIO

N

BLIS

TERIN

G

DUCTIL

E R

UPTURE

FRETTIN

G F

ATIG

UE

GA

LV

AN

IC C

ORRO

SIO

N

IMPA

CT F

RETTIN

G

IMPA

CT F

ATIG

UE W

EA

R

INTERG

RA

NU

LA

R C

ORRO

SIO

N

STA

RV

ED

JO

INT

TH

ERM

AL F

ATIG

UE

TH

ERM

AL R

ELA

XA

TIO

N

TH

ERM

AL S

HO

CK

1 DIRECT CHEMICAL ATTACK 108 54 18 0 1 1 2 2 1 11 30 16 11 6 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 3 0 3

2 FORCE INDUCED DEFORMATION 54 489 15 0 0 0 2 23 4 19 31 50 102 30 14 24 25 1 10 6 0 0 6 0 0 0 7 2 0 2 5 3

3 ABRASIVE WEAR 18 15 74 2 2 1 0 3 5 9 4 5 6 0 0 5 1 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0

3 COMPRESSION SET 0 0 2 5 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 HEAT CRACKING 1 0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 INSTALLATION DAMAGE 1 0 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4 ADHESIVE WEAR 2 2 0 0 0 0 121 101 0 1 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0

4 DEFORMATION WEAR 2 23 3 0 0 0 101 153 0 2 7 8 6 0 0 2 0 0 2 0 0 0 1 0 0 0 1 0 0 0 2 0

5 BRITTLE FRACTURE 1 4 5 0 0 0 0 0 34 21 11 5 0 0 3 10 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4

5 TEMPERATURE INDUCED DEFORMATION 11 19 9 0 0 0 1 2 21 159 17 23 4 0 4 12 1 0 0 0 0 0 0 0 3 1 0 11 0 3 0 6

6 CORROSIVE WEAR 30 31 4 0 0 0 0 7 11 17 75 23 2 0 1 10 0 0 0 0 1 0 0 1 0 0 1 0 0 3 0 1

6 YIELDING 16 50 5 0 0 0 10 8 5 23 23 136 0 0 1 5 0 0 0 0 0 0 5 1 0 0 0 2 0 1 6 1

7 CRACKING 11 102 6 0 0 0 0 6 0 4 2 0 147 29 11 21 12 0 1 8 1 0 0 0 0 0 0 0 0 0 0 0

7 CREEP STRESS RUPTURE 6 30 0 0 0 0 0 0 0 0 0 0 29 38 11 16 13 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0

7 GALLING AND SEIZURE 0 14 0 0 0 0 0 0 3 4 1 1 11 11 19 16 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

7 HIGH CYCLE FATIGUE 1 24 5 0 0 0 0 2 10 12 10 5 21 16 16 69 14 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0

7 SURFACE FATIGUE WEAR 0 25 1 0 0 0 0 0 1 1 0 0 12 13 14 14 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

8 CREEP BUCKLING 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0

8 IMPACT DEFORMATION 0 10 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 1 10 0 0 0 0 0 0 0 1 0 0 0 0 0

9 AGEING 0 6 1 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 14 0 0 0 0 0 0 1 0 0 0 0 0

9 BIOLOGICAL CORROSION 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

9 BLISTERING 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0

9 DUCTILE RUPTURE 0 6 0 0 0 0 0 1 0 0 0 5 0 0 0 1 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0

9 FRETTING FATIGUE 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

9 GALVANIC CORROSION 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 1 0 0 0 0

9 IMPACT FRETTING 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0

9 IMPACT FATIGUE WEAR 1 7 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 10 0 0 0 0 0

9 INTERGRANULAR CORROSION 1 2 1 0 0 0 0 0 0 11 0 2 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 16 0 0 0 0

9 STARVED JOINT 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0

9 THERMAL FATIGUE 3 2 0 0 0 0 0 0 0 3 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 2

9 THERMAL RELAXATION 0 5 1 0 0 0 3 2 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 23 0

9 THERMAL SHOCK 3 3 0 0 0 0 0 0 4 6 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 11

II

III

I II

I

III

Figure 6. Similarity matrix rearranged by type and cluster.

Table 1. Reduced EC matrix for the function Stop Gas.

FUNCTION / COMPONENT

RU

BBER P

ISTO

N S

EA

L

O-R

ING

RU

BBER S

EA

L P

LU

G

AIR

TU

BE C

AP

RU

BBER P

RESSU

RE G

AU

GE R

ING

SPA

CER

RU

BBER B

ARREL S

EA

L

STOP GAS 1 1 1 1 1 1 1

4

Table 2. Reduced EF matrix for the function Stop Gas.

Table 3. Cluster grouping of failure modes.

CLUSTER MEMBERS Type

Cluster-1 Direct Chemical Attack I

Cluster-2 Force Induced Deformation I

Abrasive Wear

Compression Set

Heat Cracking

Installation Damage

Adhesive Wear

Deformation Wear

Brittle Fracture

Temperature Induced Deformation

Corrosive Wear

Yielding

Cracking

Creep Stress Rupture

Galling and Seizure

High Cycle Fatigue

Surface Fatigue Wear

Ageing

Biological Corrosion

Blistering

Ductile Rupture

Fretting Fatigue

Galvanic Corrosion

Impact Fretting

Impact Fatigue Wear

Intergranular Corrosion

Starved Joint

Thermal Fatigue

Thermal Relaxation

Thermal Shock

Creep Buckling

Impact Deformation

IICluster-3

Cluster-4 II

III

Cluster-9 III

II

IICluster-6

Cluster-7 II

Cluster-5

Cluster-8

FUNCTION / FAILURE MODE

ABRASIV

E W

EAR

BRIT

TLE F

RACTU

RE

CO

MPRESSIO

N S

ET

CO

RRO

SIV

E W

EAR

CRACKIN

G

DEFO

RM

ATIO

N W

EAR

DIR

ECT C

HEM

ICAL A

TTACK

FO

RCE I

ND

UCED

DEFO

RM

ATIO

N

HEAT C

RACKIN

G

HIG

H C

YCLE F

ATIG

UE

INSTALLATIO

N D

AM

AG

E

TEM

PERATU

RE I

ND

UCED

DEFO

RM

ATIO

N

YIE

LD

ING

STOP GAS 1 0 3 0 1 0 0 4 0 0 1 0 0

5

Table 4. n (� d) values.

CLU

STER 1

CLU

STER 2

CLUSTER 3

CLUSTER 4

CLUSTER 5

CLUSTER 6

CLUSTER 7

CLUSTER 8

CLUSTER 9

ABRASIVE WEAR X X X 0.550

ADHESIVE WEAR X X X 0.115

AGEING X X X x

BIOLOGICAL CORROSION X X X x

BLISTERING X X X x

BRITTLE FRACTURE X X X 1.147

COMPRESSION SET X X X 0.000

CORROSIVE WEAR X X X 0.275

CRACKING X X X 0.190

CREEP BUCKLING X X X x

CREEP STRESS RUPTURE X X X 0.026

DEFORMATION WEAR X X X 0.156

DIRECT CHEMICAL ATTACK X X x

DUCTILE RUPTURE X X X x

FORCE INDUCED DEFORMATION X X x

FRETTING FATIGUE X X X x

GALLING AND SEIZURE X X X 0.473

GALVANIC CORROSION X X X x

HEAT CRACKING X X X 0.000

HIGH CYCLE FATIGUE X X X 0.666

IMPACT DEFORMATION X X X x

IMPACT FRETTING X X X x

IMPACT FATIGUE WEAR X X X x

INSTALLATION DAMAGE X X X 0.000

INTERGRANULAR CORROSION X X X x

STARVED JOINT X X X x

SURFACE FATIGUE WEAR X X X 0.100

TEMPERATURE INDUCED DEFORMATION X X X 0.360

THERMAL FATIGUE X X X x

THERMAL RELAXATION X X X x

THERMAL SHOCK X X X x

YIELDING X X X 0.365

0.295O

VERLO

OK

ED

FA

ILU

RE

AVERAGE

FAILURE MODE

Type-I Type-II Type-III

Table 5. Verification of failure modes for hypothetical design.

COMPONENT / FAILURE MODE

ABRASIVE W

EAR

CO

MPRESSIO

N S

ET

CRACKIN

G

FO

RCE I

ND

UCED

DEFO

RM

ATIO

N

IN

STALLATIO

N D

AM

AG

E

UN

ACCO

UN

TED

FA

ILU

RE

RUBBER PISTON SEAL 0 1 0 0 1 0

O-RING 0 0 0 1 0 0

RUBBER SEAL PLUG 0 1 0 0 0 0

AIR TUBE CAP 0 0 1 1 0 1

RUBBER PRESSURE GAUGE RING 0 0 0 1 0 0

SPACER 0 0 0 1 0 0

RUBBER BARREL SEAL 1 1 0 0 0 0

0.143AVERAGE UNACCOUNTED FAILURE/COMPONENT