reliability project

8/7/2019 Reliability Project

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Adam Brown

DSES 6070 HV6

Reliability Project

Reliability of a Commuter Bicycle

Introduction

As a potential financial solution to todays ever-increasing fuel costs, one can

consider utilizing human powered vehicles for daily commutes. If an alternate means of

transportation is to be considered for the trip to and from work, it must be shown to be

nearly as reliable as the initial vehicle so as to not annoy ones boss or spouse with late

arrivals due to vehicle breakdown. However, depending on the individual, a slight

decrease in reliability between a car and a bicycle may be acceptable as a tradeoff for the

financial savings of fuel, automobile maintenance, and automobile depreciation. After

identifying the possible failure modes and assigning probabilities to each mode,

probabilities of system failure are calculated, as well as a mean time to failure.

Importance calculations are performed for each of the primary components in order to

identify the components with the greatest opportunity to improve the system as a whole.

The probabilities of failure for each component are based on the authors experience with

cycling and the local environmental considerations. The end result will be a probability

of system failure that would lead to a significantly late arrival. The analysis also

highlights particular modifications to the planned maintenance and care of the bicycle

that will reduce the probability of system failure.


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Methodologies

In the early phases of system development, precise component failure rates are

often not available to the system designers. This does not allow one to forgo all attempts

at maximizing system reliability until solid data is obtained. Rather, designers must

approximate values (at least maintaining an order of magnitude comparison between

related components) and identify the areas that offer the greatest room for improvement

for the system as a whole. The approach taken in this commuter bicycle analysis is

comparable to a system analysis in the early development phases of a program. While

hard data was not available for individual bicycle component failure rates, numbers had

to be approximated using experience and educated guesses.

An FMECA is used to map out all of the failure modes imaginable in the

alternative transportation system and an event tree is used to assign probabilities to

various situations involving different failures. A survivor function and a mean time to

failure is calculated for the system. Measures of component importance are then used to

identify the components with the greatest opportunity to improve the system as a whole.

Results

At first inspection it was surprising that the entire bicycle system is a series

configuration, with no redundancy in design to increase reliability. After studying the

bicycle market further, one can discern the manufacturers reasoning. The high end

bicycle market puts a massive emphasis on the overall weight of the complete system,

even to the point of riders trimming the excess off of their seat post tubes in order to

reduce the system weight by fractions of an ounce. Additional components added to the

system for redundancy will increase the system weight greatly. On the lower end of the


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quality (and price) spectrum are the Walmart bikes. The manufacturers of these

bicycles do not put nearly the emphasis on weight reductions, but they compete

aggressively for market share with the cheapest configuration possible. The addition of

redundant components to these bicycles would increase the weight of the bicycle (which

they do not generally concern themselves with), but more importantly, additional

components lead to higher material costs. Based on both the weight reduction and cost

reduction arguments presented here, it becomes clear why bicycle manufacturers have

stayed away from parallel component structures. It is also better understood why

competitive cyclists who must maximize the reliability of the system will spend in the

range of $250 for a single rear derailleur just because of an increase in quality, and

therefore, reliability.

The failure modes, effects, and criticality analysis was generated by separating the

bicycle system into individual components and brainstorming on how each component

could fail in a way that would affect the system performance. The resulting FMECA

table is shown in Figures 1 and 2 below.


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Figure 1 FMECA


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Figure 2 FMECA continued


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Following the development of the FMECA, the primary components of interest

were selected and a reliability block diagram was created for the system, as shown below

in Figure 3.

Figure 3 Reliability block diagram of the bicycle system.

An event tree, shown in Figure 4 below, presents the sequences of events that

would result in various outcomes. Probabilities are calculated for each of the outcomes

and presented on the right side of the figure.

Figure 4. Quantitative event tree for the bicycle system.

The survivor function for the system is given below. The mean time to failure

calculation, also shown below, results in a value of approximately 8 days.

Pedal Bottom Chain Hub Wheel Tire


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( )

days95712580

11MTTF

eetR

n

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i

t12580t

S

n

1i

i

..

.

==

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Based on the assumed component probabilities, the bicycle will provide for an

on time arrival rate of 92.8%. While this may be considered an appropriate reliability,

one should investigate which components to improve in order to result in a greater

reliability. This is accomplished by calculating various importance measures for each of

the components.

Birnbaums measure of importance can be defined as the probability that the

system is in such a state at time tthat component i is critical for the system. For the

series system being analyzed, Birnbaums measure of importance is calculated for a

single component by multiplying the probabilities of each of the other components

together, as shown below for the pedal. A summary of Birnbaums measures of

importance for all components is presented in Table 1. From these values one can see

that the wheel and tire show the most room for improvement, with the chain as a third

contender.

8827095095099909809990pppppI tirewheelhubchainbbBpedal ...... ===

Table 1 Birnbaums measure of importance for each component.

Component pi Birnbaum

Pedal 0.999 0.8827

BB 0.999 0.8827

Chain 0.98 0.8998Hub 0.999 0.8827

Wheel 0.95 0.9282

Tire 0.95 0.9282

The improvement potential of component i is the difference between the system

reliability with a perfectcomponent i, and the system reliability with the actual


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component i. For the series system being analyzed, the improvement potential for a

single component is calculated by multiplying the probabilities of all other components

together and then subtracting the product of all probabilities including the component

under question, as shown below. The improvement potential values agree with

Birnbaums measures of importance in classifying the tire and wheel as showing the

greatest potential for improved reliability.

Table 2 Improvement potential for each component.

Component pi Improvement PotentialPedal 0.999 0.0008827

BB 0.999 0.0008827

Chain 0.98 0.0180000

Hub 0.999 0.0008827

Wheel 0.95 0.0464100

Tire 0.95 0.0464100

The risk achievement worth is the ratio of the . . . system unreliability if

component i is not present . . . with the actual system unreliability. For the series system

being analyzed, the risk achievement worth is calculated as shown below. The values for

each component are summarized in Table 3. Based on the values in Table 3, the risk

achievement worth does not find any component more important than the others. This is

due to the bicycle being a system of series components.

46089509509990980999099901

950950999098099901

pppppp1

ppppp1I

tirewheelhubchainbbpedal

tirewheelhubchainbbRAWpedal

.......

..... =

=

=

Table 3 Risk achievement worth for each component.

Component pi Risk Achievement Worth

Pedal 0.999 8.460

BB 0.999 8.460

Chain 0.98 8.460

0008827095095099909809990999095095099909809990

pppppppppppI tirewheelhubchainbbpedaltirewheelhubchainbbIPpedal

............ ==

=


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Hub 0.999 8.460

Wheel 0.95 8.460

Tire 0.95 8.460

The risk reduction worth is the ratio of the actual system unreliability with the . . .

system unreliability if component i is replaced by a perfect component. For the series

system being analyzed, the risk reduction worth is calculated as shown below. The

values for each component are summarized in Table 4. Based on the values in Table 4,

the risk reduction worth has similar findings of Birnbaums measure of importance in

finding the wheel and tire to have the greatest potential for improvement.

0081950950999098099901

9509509990980999099901ppppp1

pppppp1Itirewheelhubchainbb

tirewheelhubchainbbpedalRRWpedal .

........... =

=

=

Table 4 Risk reduction worth for each component.

Component pi Risk Reduction Worth

Pedal 0.999 1.008

BB 0.999 1.008

Chain 0.98 1.180

Hub 0.999 1.008

Wheel 0.95 1.646

Tire 0.95 1.646

The criticality importance is the probability that component i is critical for the

system and is failed at time t, when we know that the system is failed at time t. For the

series system being analyzed, the criticality importance is calculated as shown below.

The values for each component are summarized in Table 5. Based on the values in Table

5, the criticality importance has similar findings of Birnbaums measure of importance in

finding the wheel and tire to have the greatest potential for improvement.

( )( )

( )( )( )

0074709509509990980999099901

9990188270

pppppp1

p1II


pedalBpedalCR

pedal

.......

..=

=

=

Table 5 Criticality importance for each component.


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Component pi Criticality Importance

Pedal 0.999 0.00747

BB 0.999 0.00747

Chain 0.98 0.15220

Hub 0.999 0.00747

Wheel 0.95 0.39260Tire 0.95 0.39260

The Fussell-Veselys measure is the probability that at least one minimal cut set

that contains component i is failed at time t, given that the system is failed at time t. For

the series system being analyzed, the Fussell-Veselys measure is calculated as shown

below. The values for each component are summarized in Table 6. Based on the values

in Table 6, the Fussell-Veselys measure has similar findings of Birnbaums measure of

importance in finding the wheel and tire to have the greatest potential for improvement.

( )( )

( )( )

0084609509509990980999099901

99901

pppppp1

p1I


pedalFVpedal

.......

.=

=

=

Table 6 Fussell-Veselys measure for each component

Component pi Fussell-Veselys

Pedal 0.999 0.00846BB 0.999 0.00846

Chain 0.98 0.16920

Hub 0.999 0.00846

Wheel 0.95 0.42300

Tire 0.95 0.42300

Conclusion

The analysis of the bicycle system resulted in a system reliability of 92.8% on

time arrival, with a mean time to failure of about 8 days. The components with the

greatest opportunity for improvement to the overall system were the wheels and tires, as

shown in the component importance calculations. Recommendations for improvement of

the system reliability would be to invest in high quality wheels and tire protection (such


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as Kevlar tube inserts) in order to improve these component reliabilities. A different

route with less debris on the roads could also be chosen in an effort to reduce the

frequency of flat tires.

Expanded analysis would include applying techniques to account for repairable

components and reduced functional capabilities (between new and failed). However,

additional research would need to be conducted to refine the component reliability

numbers before the results of the expanded analysis could be trusted.

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