Reliability analysis, design improvements and maintenance ... · Amirkabir University of Technology, Tehran, Iran, 15875-4413 In the present paper, a complete process from reliability

American Institute of Aeronautics and Astronautics

1

Reliability Analysis, Design Improvements and Maintenance

Procedure Compilation of a Novel Remotely Piloted

Helicopter

Farnaz Kermanshahi1 , Mostafa Mohagheghi

2 and Sajed Sadati

3

Amirkabir University of Technology, Tehran, Iran, 15875-4413

In the present paper, a complete process from reliability evaluation to design modification is

proposed and also applied to a newly designed and manufactured Remotely Piloted Helicopter

(RPH) by the authors. First of all, a description of all platform subsystems is presented. After

that, function diagram and also product tree of the whole system is depicted for further analysis.

Then, the reliability of all parts and components are calculated through standard methods. The

procedure is followed by FMEA/FMECA execution and determination of critical components

and failures. Then, the reliability of the whole platform is calculated using standard block

diagrams. Finally, in order to improve the mission operational reliability of the considered RPH,

some modifications are implemented to the platform including configuration and mechanisms

design changes.

Nomenclature

C = criticality number

d = possibility of failure detection

FMEA = failure modes and effect analysis

FMECA = failure modes, effects and criticality analysis

MTBF = mean time between failures

MTTF = mean time to failure

n = severity of failure

P = probability of failure

pdf ( ) = probability density function

PN = probability number of component failure

RS(t) = reliability function

RPH = remotely piloted helicopter

T = lifetime of item (Fig. 2)

UAV = unmanned aerial vehicle

= failure rate

I. Introduction

No machine or vehicle is safe to be used unless it has approved by required safety and reliability regulations. In

addition, since any crash in aerial vehicles causes serious detriments, considering reliability aspects in aerial vehicles

is so essential. Although there are formularized methods to calculate the reliability for most of the systems, advent

of an organized and coherent procedure to evaluate the reliability of a Remotely Piloted Helicopter (RPH) will be so

valuable.

1 M.Sc. Graduated student of Aerospace department, Amirkabir University of Technology, Hafez Ave., Tehran,

Iran, AIAA member with ID 429399. 2 M.Sc. Graduated student of Aerospace department, Amirkabir University of Technology, Hafez Ave., Tehran,

Iran. 3 M.Sc. Graduated student of Aerospace department, Amirkabir University of Technology, Hafez Ave., Tehran,

Iran.

Infotech@Aerospace 201129 - 31 March 2011, St. Louis, Missouri

AIAA 2011-1545

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

Considering the growing international competition to ensure the reliability and the level of quality of the

industrial products, the need for developing methods to calculate the precise value of the reliability has been

increased. This can be seen, specially, in aerial systems where a small error may damage the whole system and

cause a catastrophe. This is more vital for unmanned systems which are developed to carry out missions

autonomously where the mission cancellation is energy, time and money consuming. Therefore, safe and reliable

operation has more importance in these vehicles. Besides, in recent years, there is a growth in use of unmanned

aerial vehicles due to their lower cost comparing to manned aerial vehicles. However this lower cost is considerable

when the reliability of unmanned systems is reasonable comparing to manned systems. In addition, the completion

of a mission is the goal of any system and a small undesired event can affect the mission quality. Therefore, the

reliability of aerial systems has considered in several studies. Indeed, the ability to perform reliable operations is an

important parameter in the design, fabrication and presentation of any product.

Several studies on reliability and design quality of aerial vehicles are carried out recently. Some of them are

based on theoretical formulation while the others present experimental results. On the other hand, some of these

literatures considered the reliability analysis in general form, while the others deal with a case study. Stamatelatos

presents the principal concepts of fault tree analysis and has emphasized on aerospace systems1. In this study, steps,

tools and application of fault tree analysis have been described by useful examples. As another example, a complete

study on reliability and availability of some current UAVs has been performed by Schaefer, based on flight

operation data which investigates the reliability of the aircraft as the mission reliability and includes three military

fixed wing UAVs operating in different environments2.

Reference 3 presents general aspects of reliability growth management of an advanced light helicopter. This

research has been performed during helicopter prototype development and contains reliability data analysis,

modeling reliability growth, methodology and benefits of reliability management. In Ref. 4 the main rotor of Bell

214 helicopter has been modeled as a serial-parallel system and the failure distribution of all components has been

determined based on given data. Then, reliability is calculated for different time periods including 2, 5 and 10 hours.

II. The Parvan Unmanned Helicopter Overview

Design, optimization and construction of an unmanned helicopter were parts of an academic project which has

been performed by a group of graduate and undergraduate students in Amirkabir university of technology (Tehran

Polytechnic).

The constructed helicopter, named Parvan, is a novel RPH which can lift up 2 kilograms payload and fly in 120

kilometers radius of action for about 1.5 hours5. The defined mission for this helicopter is traffic monitoring which

can be a useful tool for traffic control. An operational life of 100 hrs is considered in the design.

The second prototype of this unmanned helicopter with a full composite structure has been developed after

optimizations and reliability improvements to operate a full safe mission.

III. Reliability Concepts And Definitions

Reliability is the probability of desired system operation under a specified condition for determined time

duration6. The present work is based on the traditional reliability theory. In the so called theory, the system or its

components are only allowed to take two possibilities: either working or failed, but in a multistate system, both the

system and its components have more than two possible states, e.g. completely working, partially working or

Figure 1. Parvan unmanned helicopter


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partially failed, and completely failed. In fact, a multistate system reliability model provides more flexibility for

modeling of equipment conditions but it is also expensive and more complicated7.

Furthermore, there are some fundamental concepts defined in reliability studies such as Mean Time Between

Failures (MTBF) which states how long a repairable component will execute without failure. Definite relationships

are defined between the reliability and MTBF. For non-repairable components, Mean Time To Failure (MTTF) is

used instead of MTBF. In addition, mission reliability for aerial vehicles is defined as 100 minus the percentage of

times a mission is cancelled because of maintenance issues2.

Given the reliability function RS(t) for a system, the mean time-to-failure, MTTF, can be calculated by

integrating this function through time:

(1)

Besides, the failure rate of a system or component is the frequency of fails per hour or per determined hours. In

analytical approach, the failure rate of a system can be obtained by dividing system probability density function,

, by the reliability function:

(2)

where system probability density function (pdf) is the time derivative of the reliability function8:

(3)

However after performing some corrections during initial tests and debugging the system, the failure rate for a

given component tends to be constant until the component approaches the end of its life time. Therefore, failure rate

can be considered without change during normal useful life time9.

Figure 2. Typical failure rate history diagram9

With this assumption, in this paper failure rates are estimated through ground tests of the subsystems and the

whole system as well, and initial flight tests of Parvan unmanned helicopter.

Thus, with estimating MTBF or failure rate ( ), reliability (R) is formulated as follows:

(4)

Fa

ilu

re r

ate

Time T

Normal useful life

Wear out

period Debugging

period


4

Indeed, for reliability determination, negative exponential distribution is used. Any system consists of several

subsystems each of which includes different parts. While these components operate their own functions, the mission

of the system will be performed through interactions of these components. Therefore, for reliability calculations,

conventional systems can be separated to some serial and parallel components. For example, in the case of a system

with two statistically independent components in series format of operation, the system's reliability equation is given

by10

:

(5)

Also, the reliability of a system including two parallel components is:

(6)

Schematic diagrams of parallel and serial systems are shown in Fig. 3.

IV. Failure Analysis And Maintenance Procedures

A. Failure Mode Effect Analysis (FMEA)

In early 1950s a new technique used in the design and development of flight control systems which were named

failure modes and effect analysis (FMEA). Since then this method has received widespread acceptance in the

industry and has been introduced very well:

“FMEA is used to evaluate the design, at the initial stages from reliability aspects. The procedures demand

listing the potential failure modes of each and every component on paper and their effects on the listed subsystems.

There are seven main steps involved in performing failure modes and effect analysis: (i) establishing system

definition; (ii) establishing ground rules; (iii) describing system hardware; (iv) describing functional blocks; (v)

identifying failure modes and their effects; (vi) compiling critical items; (vii) documenting”7.

Indeed, the analysis of any potential failure state in a product or process which performed to determine failures

effects is named Failure Mode Effect Analysis.

B. FMECA Tables And Maintenance Procedure

Failure Modes, Effects and Criticality Analysis (FMECA) is a procedure by which potential failure modes in a

system are identified and analyzed11

. In this procedure every parts and components of the system is revised

separately to see the possibility of improper functioning. Each of these possibilities will lead to a chain of events

which may cause system failure. Indeed, FMECA procedure studies the probability and criticality of these failures

and identifies potential product weaknesses assuming a pessimistic viewpoint since the design procedure usually

approaches from an optimistic viewpoint. Thus, FMECA procedure usually starts from almost the beginning of the

product design to the final steps of the fabrication process. Since the objective of FMECA is to identify all modes of

failure within a system design, its first purpose is the early identification of all catastrophic and critical failure

possibilities, so they can be eliminated or minimized through design corrections at the earliest possible time.

Although FMECA is a great tool of reliability study, it can be used for other purposes. The use of this analysis can

be seen in maintainability, safety analysis, survivability and vulnerability, failure detection and isolation subsystem

design10

.

In the present work an FMECA table has been developed to find the most critical failure modes and hence, the

most critical group of components on the recently designed and fabricated unmanned helicopter (Parvan). Since in a

Figure 3. Parallel (left) and serial system (right).

B

A

B A


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helicopter system there are many complicated and coupled interactions between components, the whole system in

this case study is divided into several subsystems to observe which part of the system is the most critical one. The

criticality number (C) for each subsystem is attained by finding the average of the criticality numbers of its

components. Every component that its calculated criticality number is more than a predefined norm number, should

be revised and redesigned to meet the desired value which is achieved experimentally. Thus, in the present work,

reliability of the most critical subsystem is studied in detail and calculated precisely. The analysis and results are

presented in the next chapters of the paper.

The criticality number of each part is calculated using:

, (7)

where PN is the probability number of component failure, n is the severity of that failure and d is the possibility of

its detection. In the present study, these numbers are assumed to vary from 1 to 3 with respect to the component

specifications, operation and role. One can see that the possible minimum and maximum value for C will be 1 and

27 respectively. A norm of 12 is considered for criticality number, hence components with criticality numbers larger

than this norm, have been revised and redesigned to meet this norm and ensure safe operation.

Table 1 shows a sample of FMECA table and the results of analysis for estimating severity, detection and

probability numbers based on experimental data. In this table, P is the probability of the failure.

Table 1. A sample of FMECA table developed for component Hub. P is the probability of failure.

Part Number4

Part Name

Failure mode Failure cause

Detection technique

Failure effects

Preventive and

recovery precautions

P PN n d C

Pr H 03 Hub

M-5 screw (on the

horizontal shaft) might get loosened

- Undesirable

vibration

Extra flapping

and Unstable

flight

Blade unbalancing

and rotor vibration

Preflight check

(every 10 hrs)

1/3000 1 2 2 4

Bearing of hub

teetering damage

- Loss of lubricant

- Undesirable

vibration

Hub mechanism

s loose

- Delay in control

commands - Rotor

vibration

Preflight check

(every 10 hrs)

1/1000 2 2 2 8

Pr A 08 07

Regulator

Damaged

Due to any fault in its electronic

system

No power transmitted

to the avionics

-

Redundant part

1/1000 2 3

2

3 18

12

Regulator (After

revision) 2 3

Maintenance policy can be driven from two different viewpoints: 1) corrective; 2) preventive12

. According to this

fact, as it’s shown in Table 1, some preventive procedures are included in FMECA for Parvan RPH. The column

"preventive and recovery precautions" of FMECA table is used to determine some maintenance issues. These

precautions include three actions, a) Scheduled preflight checks: check of servos, fan casing, pinion, gear, main

shaft, control links, structure screws, tail swash plate, etc (before every flight) and main shaft lock, bearings,

mechanism screws, pulley and tail belt, etc (every 10 hrs), b) Replacement of distorted parts: clutch strip, main shaft

bearing, c) Some alarm gauges for undesirable conditions: low battery and governor alarm, engine temperature

4 The part numbers are assigned through Product Tree coding of the Parvan Helicopter.


6

sensor. For example, in avionics subsystem, some components such as connectors, batteries and regulator should be

checked in specified periods of time in order to ensure safe operation. The predetermined preventive procedures

have reduced failure probability and criticality of the components effectively.

C. Product Tree And Function Diagram

After fitting design, producing and configuring all components, product tree was provided to show level and

relations of components and subsystems. Concerning the complex system of a helicopter, for providing a detailed

product tree, Parvan unmanned helicopter is divided into 8 distinct groups from the assembly viewpoint. Therefore,

each group can be assembled separately to montage the whole vehicle. Indeed, product tree is a guide for assembling

groups and could be used for preparation of maintenance procedures and checking tables. One can see assembly

groups in Fig. 4 all together and product tree of engine group as the first assembly subsystem in Fig. 5.

Product tree is a static presentation of the system, while the function diagram shows components and subsystem

relations to demonstrate any defined flight modes. Furthermore, different levels of errors can be investigated through

these diagrams.

Parvan

Pr E 01

Engine

Pr F 02

Flybar

Pr H 03

Hub

Pr PT(1) 04

Power

Train 1

Pr PT(2) 05

Power

Train 2

Pr PT(3) 06

Power

Train 3

Pr T 07

Tail

Pr A 08

Avionics

Figure 4. Assembly groups provided for Parvan RPH

Pr E

Engine Group

Pr E 01 01

Engine

Pr 01 04

Engine

mount

Pr 01 02

Fan

Pr 01 05

Y - Pipe

Pr 01 06

Fuel pipe

Pr 01 03

Clutch

center

Pr 01 01 01

Fan lock nut

Pr 01 04 01

Mount nut

Pr 01 08

Linkages and

ball links

Pr 01 07

Governor

Pr 01 01 02

Ball link nut

Pr 01 02 01

Clutch center

nut

Figure 5. Product tree of engine group


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In this study, five operational modes are considered for Parvan helicopter and function diagram is extracted for

these modes which are: warm up, take off, hover, forward flight and landing. The function diagram of takeoff mode

is shown in Fig. 6. This function diagram starts with pilot command and describes main component tasks to result in

a safe take off. In addition, the severity of each component failures and effects of one component error in different

steps of operation can be seen in this diagram.

V. Reliability Calculations

A. Determination Of Subsystem’s Criticality

In order to have a good estimation for the reliability of the Parvan helicopter, detailed calculations has been

performed for most critical subsystems. Thus, the criticality number for subsystems should be determined by taking

the average of component criticality numbers of considered subsystem. For example, the criticality number of the

avionics subsystem which contains 8 components is:

(8)

(9)

Take Off

Mode

Ball Link

Pilot

Command

Radio and

Receiver

Engine

An increase

in rpm.

Cooling Fan

Rotates above the

engine and hardly

tries to cool it.

Clutch Shoes

get in contact with

Clutch bell and

causes the pinion

to rotate.

Pinion Gear

Is in contact

with Main Gear

and they both

rotate.

Main Gear

Main Shaft

Tail Gear

One Way Clutch

Flange and

Busch

For more performance

in autorotation.

Hub and blades

Experience increase in

pitch angle

Swashplate

And flybar Ball Links

Three control servos

Move the swashplate

upward so the pitch angle

increases.

Ball Links

Transmit servo command

Power

Train3 Shaft

Pin

Pin

Belt and

pulleysTail shaft

Tail hub

(pitch angle) is

changed to correct

body position.

Tail

Blades

Tail Servo

Might rotate and

change tail blade pitch

angle.

Tail links

Tail Swash

Plate

Battery

3.3 A, 4.8 V

Regulator

Makes the voltage

proper for the

receiver.

3.3 A, 7.4 V

Throttle Servo

Rotates in

consistent with pilot

command to

increase throttle.

Thrust

Is increased to

overcome the

weight

Skid

Takes off the

ground.

Tail Rotor Thrust

is changed to get

adapted with

main rotor torque.

Gyro

Senses yaw

perturbations of

body.

Blade drag

And hence its torque

is increased due to

the increase in pitch

angle.

Helicopter Body

Position is

changed.

Figure 6. Function diagram for takeoff mode of flight.


8

For reliability analysis, the 8 groups defined as assembly

groups have been reduced to 6 subsystems. Therefore, flybar and

hub are named as "control" subsystem and also power train 1 and

power train 2 groups are named as "gear box" subsystem.

Criticality numbers for all these subsystems are given in Table 2.

It can be seen that the control group is the most critical

subsystem.

B. Reliability Calculations For Helicopter Subsystems

In order to calculate the reliability for whole system, firstly

the helicopter modeled as a system with only serial components

and reliability determined by negative exponential distribution. In

this step, the initial failure rates from FMEA before taking

additional considerations and redesign to reduce the failure rate

were used and then total failure rate ( ) considering all components was obtained. This initial amount is 0.246.

Therefore system reliability for 2 hours mission duration is calculated as follows:

According to complexity of performing all the changes that have been achieved from additional considerations

of the system redesign, in the present study, only the control subsystem which is introduced as the most critical one,

considered as a sample, to calculate the reliability before and after considering redesign changes.

C. The Reliability Of Control Subsystem

Control subsystem is modeled as a set of serial-parallel components. The two main parts of these subsystem are

flybar and hub. For more exact reliability calculation of control subsystem, components relations are determined as

demonstrated in detailed diagrams of Fig. 7 and Fig. 9.

Table 2. Criticality number calculated

for every subsystem after taking

additional considerations for design and

maintenance

Subsystem Criticality number

1 Engine 5.78

2 Avionics 7.1

3 Gear Box 4.0

4 Control 7.38

5 Power Train 3 7.2

6 Tail 5.33


9

Hub

Center

(1)

2 Ball

Bearings

(7)

2 Ball

Bearings

Grip

(8)

M3 for

Cylinder

(10)

M3

Screw

M2

Screw

M2

Screw

(11)

Ball

Bearing

(12)

M3 for

Cylinder

(13)

GripM3 for

Cylinder

M3

Screw

M3

Screw

M2

Screw

M2

Screw

Ball

Bearing

M3 for

Cylinder

Thrust

Bearing

(3)

M5

Screw

(4)

M4

Screw

(5)

Blade

(6)

Thrust

Bearing

M5

Screw

M4

ScrewBlade

AND

Hub

Shaft

(2)

Hub

Shaft

M3

Screw

(9)

Figure 7. Hub block diagram

Since the two main parts of the control subsystem are serial, the reliability of this subsystem are given by,

(10)

The reliability calculations for these parts (hub and flybar) are presented separately in the following sections.

(a) (b) (c)

Figure 8. (a) Flybar and (b, c) hub

Mechanisms

Blade related components


10

1. Reliability calculations for hub

Considering block diagram of Fig. 7, it can be seen that hub center is in serial form with two independent parts,

i.e. blade related components and mechanisms. Therefore, the reliability of hub is:

(11)

In table 3, gross and revised failure rates are presented for hub. The reliability of hub is calculated using these

failure rates. It should be noted that the more accurate failure rate of components given in the right column of the

table, is calculated using equations presented in Ref. 13.

Table 3. Failure rates for hub components

component Gross estimate of failure rate

(per hr)

Revised and calculated

failure rate (per hr)

1 Hub center 1/5000 -

Blade component

s

2 Hub shaft 1/1000 -

3 Thrust bearing

1/1000 -

4 M5 screw 1/3000 0.000084

5 M4 screw 1/300 -

6 Blade 1/5000 -

Mechanisms

7 Ball bearing 1/1000 0.001243

8 Grip 1/5000 -

9 M3 screw 0.1 0.000042

10 M3 screw for cylinder

1/2000 0.000042

11 M2 screw 1/300 0 (Omitted joint)

12 Ball bearing 1/1000 0.001243

13 M3 screw for cylinder

1/2000 0.000042

Regarding to components relations, blade related components and so called mechanisms reliability can be

obtained as follows:

(12)

(13)

Substituting these values into Eq. 12, we have:

In this step, gross estimate of failure rates are considered.


11

2. Reliability calculations for flybar

Dividing flybar block diagram to two parts a and b, and assuming failure rate of 0.002 for all flybar joints, the

reliability is calculated in the same manner:

(14)

Where

And

Thus,

Finally, using Eq. 11 the reliability of control subsystem will be:

Considering design requirements, it seems that this is not a proper value of reliability for the most critical

subsystem of the Parvan Helicopter. Therefore, to improve system reliability, a set of design and fabrication changes

should be performed. Some of those changes have been made in the present work, such as:

- More depth threads

- Replacing uncertain parts with proper components

- Reducing temporary joints

Applying these changes and using precise failure rates which are given in Table. 3 once more, the reliability of the

control subsystem is obtained equal to 0.959 which is a reasonable value.

VI. Conclusion Remarks

For an unmanned helicopter as a dynamic and multidisciplinary system, the reliability plays an important role in

its operation success. First of all in the present study, based on FMECA procedure, failure modes, failure rates and

criticality number were obtained for all components and subsystems of the considered unmanned helicopter

(Parvan). In addition, in order to compare subsystems criticality, average criticality number is introduced and it was

found that the control subsystem has the most average criticality number. Then, the more detailed reliability

calculations were performed for control subsystem and it is observed that initial reliability value of the subsystem is

0.887. Finally, to improve the considered reliability, the components have been analyzed and some changes were

applied in the design and fabrication manner. Indeed, using more precise connections, simplifying some mechanisms

and increasing check time intervals are three most important changes.

Furthermore, containing main elements of the helicopter, function diagram shows the relationships of different

subsystems and fault propagation flow. Thus, according to this diagram, some redundancy and precautions could be

added to have safer mission operation.

M3 screw

M3 screw

3 serial M2 screw

M2 setscrew

ANDRing

Inner

frame

M3 screw

M3 screw

Outer

frame

Flybar

shaftFlybar

paddle

M2 setscrew

3 serial M2 screw

3 serial M2 screw

M2 setscrew

Flybar

shaftFlybar

paddle

M2 setscrew

3 serial M2 screw

Figure 9. Flybar block diagrams a b


12

Finally, in order to obtain a more precise value of reliability, some experimental tests can be performed on

critical components and more accurate data for failure rates of these components might be achieved.

Acknowledgments

The authors would like to thank Dr. Mehdi Mortazavi, associate professor of Aerospace department at Amirkabir

University of Technology, for his valuable comments and supportive manner throughout the whole project. As well,

the authors would like to thank Mr. Mohammad Sadegh Sajedi and Mr. Reza Mohammadi Ziazi, Aerospace

engineers, for their constructive collaboration in design, manufacturing and optimization the Parvan unmanned

helicopter.

References 1Stamatelatos, M., Vesely, W., Dugan, J., Fragola, J., Minarick, J. and Railsback, J., Fault tree handbook with aerospace

applications, Version 1.1, NASA, 2002. 2 Schaefer, R., “Unmanned aerial vehicle reliability study,” Office of the Secretary of Defense, Washington, DC, 2003. 3 Kumaraswamy, K.G., “Reliability Growth Management during Prototype Development,” Defense Science Journal, Vol. 52,

No. 4, 2002, pp. 385-392. 4Fallahi, H. and Mousa, A,. “Reliability Calculation of Bell 214 Main Rotor,” The 4nd conference of Iranian Aerospace

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5 Kermanshahi, F., Mortazavi, M., Mohagheghi, M., Sajedi, S., Mohammadi Ziazi, R., Sadati, S., Pourzand, H., and

Goudarzi, N., “Design, Optimization, and Building Flight Model of an Operational Unmanned Helicopter,” 2010 IEEE

Aerospace Conference, AIAA Technical Co-Sponsor, Big Sky, Montana, pp. 1-10. 6 Lombardo, D.C., and Fraser, K.F., Importance of reliability assessment to helicopter structural component fatigue life

prediction, DSTO Aeronautical and Maritime Research Laboratory, Australia, 2002. 7 Pham, H., Handbook of reliability engineering, Springer Verlag, 2003. 8 Mettas, A., and Savva, M., “System reliability analysis: the advantages of using analytical methods to analyze non-

repairable systems,” Reliability and Maintainability Symposium 2001, Proceedings Annual, 2001, pp. 80-85. 9 VA, A., Engineering Design Handbook Helicopter Engineering. Part One. Preliminary Design, Storming Media, 1974. 10 Billinton, R., and Allan, R.N., Reliability evaluation of engineering systems: concepts and techniques, Springer, 1992. 11 Rothbart, H.A., Mechanical design handbook: measurement, analysis, and control of dynamic systems, McGraw-Hill

Professional, 2006. 12 Wang, H., and Pham, H., Reliability and optimal maintenance, Springer Verlag, 2006. 13Handbook of Reliability Prediction Procedures for Mechanical Equipment, Naval Surface Warfare Center Carderock

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Documents

Reliability analysis, design improvements and maintenance ... · Amirkabir University of Technology, Tehran, Iran, 15875-4413 In the present paper, a complete process from reliability