Enhancing System Predictability and Profitability:
The Importance of Reliability Modelling in Complex Systems and
Aviation Industry
PRAWAR1, ANJALI NAITHANI1,*, H. D. ARORA1, EKATA2
1Department of Mathematics, Amity Institute of Applied Sciences,
Amity University Noida (Uttar Pradesh),
INDIA
2Department of Applied Science,
K.I.E.T Ghaziabad (Uttar Pradesh),
INDIA
Abstract: - Predicting the future has always been a human endeavor, ranging from antiquated methods such as
monitoring aquariums for indications of earthquakes to contemporary techniques that evaluate system
probabilities and capacities. Taking into account the current emphasis on improving product reliability by
customer demands and global competitiveness, we introduce the idea of reliability in the context of the Airbus
A320 airplane in this paper. When it comes to business and commercial aircraft, timetable compliance and
punctuality are critical components of an aircraft's profitability. For many operators of commercial aircraft,
reaching the 98% reliability criterion is a typical objective. This study examines the Airbus A320 in great
detail, concentrating on a particular system scenario that has two possible failure modes, one where gears do
not retract after takeoff and the other being when landing, the gears fail to extend. The organization bears
specific costs as a result of these shortcomings. The purpose of the study is to examine these expenses and offer
insights into the financial ramifications by performing a profit analysis. We examine the failure and repair
patterns by utilizing the Markov Process and Regenerative Point method. This study adds to our understanding
of the reliability issues facing the aviation sector and has applications for improving the Airbus A320 aircraft's
operational effectiveness and financial performance.
Key-Words: - aircraft reliability, Markov process in aviation, regenerative point technique, availability analysis,
failure rate, aircraft maintenance, profit analysis, and repair patterns.
Received: August 7, 2023. Revised: March 21, 2024. Accepted: April 14, 2024. Published: May 15, 2024.
1 Introduction
The demands of society are increasing day by day,
so to fulfill them, a good amount of technology is
put on the forefront by businesses, and many
advanced, complicated, and highly developed
systems are being introduced. To be at par with
international standards, industries are being more
responsive to the necessity to provide reliable
equipment. Failures are minimized, operational use
of systems is improved, and available operational
time is increased with the help of reliability and
maintainability. Reliability modeling was started
during World War II. Reliability program increases
the initial cost of every device, instrument, or
system, and it is also true that reliability decreases
as the system is made more complicated. To create,
plan, and execute the duty of the framework with its
arbitrary predominance of disappointments,
reliability is essential. The possibility that a
component, piece of equipment, or system will be
able to carry out its intended function as assigned
over a predetermined period under predetermined
conditions is known as its unwavering quality.
Researchers in [1], [2], found that reliability
modeling is a helpful method for predicting a
system's reliability by abstracting its dynamic
behavior. Understanding the system's numerical
representation is crucial to understanding its
dependability. The numerical representation of the
system reliability function describes the system
reliability in terms of the reliabilities of its
constituent elements. Later, [3], [4], [5], discussed
predicting model reliability, which has always been
a human endeavor, progressing from ancient
methods based on observational techniques to
contemporary approaches that can evaluate the
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probability and capacities of complex systems.
Improving product reliability [6], discussed machine
learning techniques that are becoming increasingly
important in the current environment to meet
consumer needs and remain globally competitive.
Moreover, [7], [8], studied and explored the
complex field of reliability in the particular context
of the Airbus A320 airplane. In business and
commercial aviation, [9], [10], an aircraft's capacity
to make a profit is closely correlated with how well
it arrives on time and follows its schedule. When
mechanical problems, [11], [12], [13], discussed
causes that affect the reliability of a system and
compromise its availability. Therefore,
demonstrating excellent reliability indices by [14] is
essential to any aircraft to guarantee its availability
when needed. Many commercial aircraft operators
share the objective of attaining a 98% dependability
standard. The Airbus A320, a mainstay of the
aviation industry, researchers, [15], [16], used
Markov regenerative techniques to further dive into
this area, and with insight into these findings, the
paper performs a thorough investigation. In
examining two crucial failure modes by [17], [18],
gears failing to down lock themselves during
landing and gears failing to up lock themselves after
takeoff—the study focuses on a particular system
situation. These mistakes have more repercussions
for the company than only disrupting operations;
they also incur additional expenses. Researchers,
[19], [20], studied the field of dependability, failure
analysis, mean time to system failure, and
availability has seen tremendous advancements and
breakthroughs in recent years, which have had a
significant impact on aviation systems. Cost-benefit
study of standby systems with waiting times aimed
at repair was studied by [21], by taking a cold
standby unit under consideration. reliability analysis
and life cycle cost optimization on Indian industrial
models was done by [22], and also studied the cost
optimization of the models. Researchers, [23],
[24], calculated and analyzed reliability, availability,
and maintainability of models already in working,
and studies also show that what kind of maintenance
techniques are good for similar system models. The
advances in intelligent reliability and maintenance
techniques of energy infrastructure assets were
discussed by [25]. Understanding that this field is
dynamic, our research incorporates these new
developments into examining the Airbus A320,
paying particular attention to the failure modes
found craft platform.
Research on reliability modeling in the aviation
sector frequently ignores particular parts or
subsystems in favor of concentrating on the overall
reliability of the system. Furthermore, a large
portion of the research is still theoretical in nature
and lacks empirical support and real-world case
studies, which calls into question its validity and
usefulness. Finally, a noteworthy deficiency exists
in the comparative examination of several reliability
modeling techniques, which hinders the
determination of the optimal ways for augmenting
reliability in intricate aviation systems. This paper
depicts the empirical implications and generates
cutoff points so the system remains profitable
despite the failure taken into consideration.
2 Problem Formulation
2.1 Notations
Table 1. Notations used in the model.
Notation
Meaning
FN , F’N
Failure of nose landing gear in takeoff and landing
resp.
OM, O’M
Main landing gear operative in takeoff and
landing resp.
FM, F’M
Failure of main landing gear in takeoff and
landing resp.
ON,O’N
Operative nose landing gear in takeoff and landing
resp.
FNr
Nose landing gear under repair
FMr
Main landing gear is under repair
FMw
The main landing gear is waiting for repair
O
Operative unit
ƛ1
The failure rate of nose landing gear during
takeoff
ƛ2
The failure rate of the main landing gear during
takeoff
ƛ’1
The failure rate of nose landing gear during
landing
ƛ’2
The failure rate of main landing gear during
landing
β1
Rate of allowed time to get repair started for nose
gear after landing
β2
Rate of allowed time to get repair started for nose
and main gear after landing
β3
Rate of allowed time to get repair started for main
gear after landing
p
The probability that landing gear is extended
successfully
q
The probability that the landing gear did not
extend after applying force
ƴ1
Rate of allowed time to extend nose landing gear
down using gravity
ƴ2
Rate of allowed time to extend nose main landing
gear down using gravity
ƴ3
Rate of allowed time to extend main gear down
using gravity
g1(t)
Repair rate for the nose gear
g2(t)
Repair rate for main gear
g3(t)
Repair rate after total failure
TF
Total failure of the system
ⓢ
Stieltjes Convolution
*
Laplace transform
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2.2 State Transition Diagram
Assumptions for the system
a. The initial state is considered to be the state of
working.
b. All the random variables follow arbitrary
distributions.
c. After every repair, the system becomes like a
new one.
d. The repairman remains with the system and is
immediately available whenever required.
e. The repairman is perfect; therefore, after each
repair/replacement, the system regenerates and
starts working as effectively as in new
condition.
f. If one or both main landing gear fail, then we
will take the total failure of the main landing
gear.
Figure 1 explains a system's state transition
diagram that shows the many operational stages and
transitions. When the system boots up, it is
completely functional and in state 0. States 1
through 6 are known as down states, denoting
situations in which the system is not running as
needed and must be repaired. Reduced states are
indicated by states 7, 8, and 9, where the system is
undergoing repair and will reactivate fully after the
work is successfully finished. State 10 denotes a
total failure state, implying there is no way to get
the system back to its working state. The variables
βn, ƛn, and ƛ'n are presented to measure certain
system elements. The time needed to finish the
repair procedure is represented by βn. The failure
rates during takeoff and landing are linked to the
factors ƛn and ƛ’n, respectively. The rate at which
the system is being repaired is indicated by the
repair rate, which is represented as gn(t), a function
of time. The paragraph offers a high-level summary
of the behavior and features of the system overall,
highlighting its operational and non-operational
states, repair procedures, and failure rates during
different operating stages. The notations used in the
model are in Table 1.
Fig. 1: State transition diagram of the system under
consideration
2.3 Transition Times
The transition from a regenerative state ‘i’ to ‘j’ or
to a failed state ‘j’ is independent of history before
reaching state ‘i’. Therefore, from the probabilistic
considerations, the distribution function of the
transition times can be expressed as:
q01 = ƛ1
q02 =
q03 =
q04 =
q05 =
q06 =
q17 =
q28 =
q39 =
q47 = p
q4,10=
q58=
q5,10=
q69=
q6,10=
q70 = g1(t)
q89 = g1(t)
q90 = g2(t)
q10,0 = g3(t)
Then, the average amount of time taken by the
framework to remain in a specific regenerative state
's' before traveling to some other regenerative state
'j' is :
=
µ1 =
-β1t dt=
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µ2 =
-β2t dt=
µ3 =
-β3t dt=
µ4=
4>t] dt =
µ5=
5>t] dt=
µ6=
6>t] dt= =
µ7=
6>t] dt =-g1*’(0)
µ8= -g1*’(0)
µ9= -g2*’(0)
µ10=-g3*’(0)
3 Measures of System Effectiveness
3.1 Mean Time to System Failure
Let φi(t) be the cumulative distribution function of
the first passage time from the initial state to a failed
state.
We have the following recursive relations f or φi(t):
φ0(t) = Q01(t) Ⓢ φ1(t) + Q02(t) Ⓢ φ2(t) + Q03(t) Ⓢ
φ3(t)+ Q04(t) Ⓢ φ4(t)+ Q05(t) Ⓢ φ5(t)+ Q06(t) Ⓢ
φ6(t)
φ1(t) = Q17(t) Ⓢ φ7(t)
φ2(t) = Q28(t) Ⓢ φ8(t)
φ3(t) = Q39(t) Ⓢ φ9(t)
φ4(t) = Q47(t) Ⓢ φ7(t) + Q4 10(t)
φ5 (t) = Q58 (t) Ⓢ φ8 (t) + Q5 10(t)
φ6 (t) = Q69 (t) Ⓢ φ9 (t) + Q6 10(t)
φ7 (t) = Q70 (t) Ⓢ φ0 (t)
φ8(t) = Q89(t) Ⓢ φ9(t)
φ9 (t) = Q90 (t) Ⓢ φ0 (t)
Also,D(0)= (1)
N(0)= (2)
N1=m01+m02+m03+m05+m06+p06µ6+p05µ5+p03µ9+p03
µ3+p06p69µ9+p01µ7+p01µ1+p02µ8+p02µ9+p02µ2+p05p58µ
9+p05p58µ8+ (3)
Using l’Hopital rule, MTSF =
=
(4)
3.2 Availability Analysis
Let AFi(t) denote the probability that the system is
in upstate at instant ‘t’, provided that the system
entered regenerative state ‘i’ at t = 0. After applying
the Laplace transform to the equations obtained, we
obtain the following recursive relations.
0(s) = 0(s)+ 01(s) . 1 (s) + 02(s) .
2(s) + 03(s) . 3 (s) + 04(s) . 4 (s) +
05(s) . 5 (s) + 06(s) . 6 (s)
1(s) = 1(s) + 17(s) . 7 (s)
2(s) = 2(s) + 28(s) . 8 (s)
3 (s) = 3(s)+39(s) . 9 (s)
4 (s) = 4(s) + 47(s) . 7 (s) + 4,10(s) .
10 (s)
5 (s) = 5(s) + 58(s) . 8 (s) + 5,10(s) .
10 (s)
6 (s) = 6(s)+ 69(s) . 9 (s) + 6,10(s) .
10 (s)
7 (s) = 70(s) . 0(s)
8 (s) = 89(s) . 9 (s)
9 (s) = 90(s) . 0(s)
10 (s) = 10,0(s) . 0(s)
D1’(0)=µ0+(p06p69+p05p58+p03+p02)+(p05p58+p02)
+(p01+p04p47)+(p06p6,10+p05p5,10+p04p4,10)+
p01+p02+p06µ6+p05µ5+p04µ4 (5)
N1(0) =
(6)
AF0=
=
(7)
3.3 Downtime of System
Let us assume that the system entered regenerative
state I at t=0. Then, the probability that the system is
in down mode at instant t is given by
DT0=
The recursive relations for downtime after applying
Laplace transform are as follows:
0(s) = 01(s) . 1 (s) + 02(s) . 2(s) +
03(s) . 3 (s) + 04(s) . 4 (s) + 05(s) . 5
(s) + 06(s) . 6 (s)
1(s) = 17(s) . 7 (s)
2(s) = 28(s) . 8 (s)
3 (s) = 39(s) . 9 (s)
4 (s) = 47(s) . 7 (s) + 4,10(s) . 10 (s)
5 (s) = 58(s) . 8 (s) + 5,10(s) . 10 (s)
6 (s) = 69(s) . 9 (s) + 6,10(s) . 10 (s)
7 (s) = 7 +70(s) . 0(s)
8 (s) =8 +89(s) . 9 (s)
9 (s) = 9+90(s) . 0(s)
10 (s) = 10,0(s) . 0(s)
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D2’(0)=µ0+p06µ6+p05µ5+p04µ4+(p06p69+p05p58+p03+
p02)(p05p58+p02)+(p01+p04p47)+(p06p6,10+p
05p5,10+p04p4,10)p01+p02 (8)
N2(0)=µ9
(9)
Finally, DT0=
=
(10)
3.4 Busy Period Analysis
Let us assume that the system entered regenerative
state ‘i’ at t=0. Then, the probability that the
repairman is busy at instant t is given by
Bi0=
The following recursive relations are obtained after
applying the Laplace transform:
0(s)=01(s).1(s)+02(s).2(s)+03(s).3(s)
+04(s).4(s)+05(s).5(s)+06(s).6 (s)
1(s) = 17(s) . 7 (s)
2(s) = 28(s) (t) . 8 (s)
3 (s) = 39(s) (t) . 9 (s)
4 (s) = 47(s) . 7 (s) + 4,10(s) . 10 (s)
5 (s) = 58(s) . 8 (s) + 5,10(s) . 10 (s)
6 (s) = 69(s) . 9 (s) + 6,10(s) . 10 (s)
7 (s) = 7 70(s) . 0(s)
8 (s) =8 89(s) . 9 (s)
9 (s) =
90(s) . 0(s)
10 (s) =
10,0(s) . 0(s)
D2’(0)=µ0+p06µ6+p05µ5+p04µ4+(p06p69+p05p58+p03+
p02)(p05p58+p02)+(p01+p04p47)+(p06p6,10+p
05p5,10+p04p4,10)p01+p02 (11)
N3(0)=
(12)
Finally, Bi0=
=
(13)
4 Results and Findings
4.1 Numerical Outcomes
Equation for profit
Profit(P)=C0*AF0-C1*DT0-C2*BI0-C3 (14)
C0 : revenue per unit time when the system is at
maximum efficiency.
C1 : loss incurred per unit time when system is in
down state.
C2 : cost per unit time when the repairperson is
busy.
C3 : fixed cost when the system is not working or is
down.
After using the following values for different
parameters calculated from the collected data: -
, ,
, ,
β1=β2=β3=12, ,
C0=200000,C1=300, C2=5000, C3=10000
p=0.99999, q=0.00001, ,
&
The various reliability indices obtained are in
Table 2 where the system generates a profit of
167157.224 INR with MTSF being 581632667
hours and the value of availability at 0.88804976
Table 2.Table for calculated reliability indices
S.No.
Parameters
Value
1.
Mean Time to System Failure
581632667 hrs
2.
Availability of System
0.88804976
3.
Downtime of the System
0.1011796
4.
Busy period for repairmen
0.084474805
5.
Profit generated
167157.2246
Fig. 2: Profit generated concerning Failure rates ƛ1
and ƛ2
4.2 Graphical Analysis
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Figure 2 shows the profit generated by the system
with variable failure rates taken one at a time, and it
depicts that when the failure rate ƛ1 goes below
0.0191085271, the system stops generating profit,
and similarly, for failure rate ƛ2, the profit is
negative after it falls below 0.016827519.
Fig. 3: Full Capacity Availability about Failure
Rates at ƛ1 and ƛ2
Figure 3 depicts the graphs plotted for the
availability of the system working at full capacity
concerning failure rates ƛ1 and ƛ2. It can be seen that
the availability of the system decreases with an
increase in failure rates (ƛ1 and ƛ2).
Fig. 4: Profit generated vs revenue generated while
the system works at full capacity
Figure 4 represents graphs plotted after finding
values of profit generated while the system is
working at full capacity considering revenue
generated per flying hour, and it shows that revenue
generated(C0) by the system cannot be less than
11,774 INR per flying hour for the airline to
generate profit.
According to these indices and statistics, the
system is no longer profitable below a certain failure
rate for both components. Furthermore, it suggests
that component ƛ1 failure rate affects profit creation
more than component ƛ2 failure rate. Moreover,
Figure 3 illustrates how the system's availability
drops as both components' failure rates rise. This
suggests that a higher failure rate causes a greater
frequency of system outages and a decrease in
system performance. Finally, Figure 4 shows that
the revenue produced by the system per flying hour
(C0) must equal or exceed 11,774 Indian rupees for
the airline to turn a profit. This is a critical value
that determines the profitability of the system.
5 Conclusion
This study has shown reliability modeling is
important for improving complex systems'
predictability. Reliability indices have been
analyzed, emphasizing downtime, busy periods, and
the resulting financial repercussions. This analysis
has provided important insights into the
optimisation of system failure minimization and
maintenance strategy. Organizations can ensure the
continuous availability of the system by taking early
measures to resolve possible faults, due to the
predictability that reliability modeling provides.
The results displayed in Table 1 highlight the
financial advantages of efficient reliability
modeling. The system's Mean Time Between
Failures (MTSF) of 581,632,667 hours, availability
of 0.88804976, and profit of 167,157.224 INR.
demonstrate the system's beneficial effects on
operational and financial aspects.
Moreover, decision-makers can benefit
significantly from the documented relationship
between profit, failure rates, and availability. Failure
rates hurt availability and profitability, as
demonstrated. Interestingly, the critical failure rate
levels (lambda 1 and lambda 2) that cause profit to
turn negative have been determined. This
knowledge enables to creation maintenance
schedules and performance standards to anticipate
problems before they arise.
Through disassembling a system and analyzing
its failure rates, researchers can learn more about
how it works and what influences success or failure.
This information can be applied to the analysis and
enhancement of comparable systems in many
industries such as healthcare and biomedical
engineering, transportation, and logistics, also in
energy and utilities resulting in higher
manufacturing process profitability and
productivity. Further disciplinary advancements and
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improvements could result from this research.
Businesses may reduce downtime, minimize losses,
and streamline processes with the help of reliability
modeling, which is adaptable and applicable to a
range of systems. The information gathered from
this research is essential for creating dependability
modeling techniques that improve system
performance and resilience as technology advances.
Reliability modeling ultimately contributes to the
strategic objectives of forward-thinking businesses
by mitigating losses that arise from system
unavailability.
5.1 Limitations of this Study
Its exclusive focus on the financial elements of
system failure and profitability is the main
shortcoming of this study. The wider ramifications
of system reliability are not fully reflected by
financial measurements, despite their obvious
importance. Additionally, because the study is
static, it ignores dynamic elements that over time
can have a substantial impact on the profitability
and reliability of systems, such as shifting market
conditions and technical improvements. Should
these dynamic components be disregarded, the
analysis might not fully convey the depth of the
connection between system profitability and
reliability.
5.2 Suggested Improvements of this Work
Several enhancements are proposed to resolve the
stated constraints. First and foremost, a more
thorough study that takes into account financial
measures in addition to a wider range of variables
including consumer effect and environmental
sustainability should be conducted. Moreover, by
evaluating the results' sensitivity to changes in
important factors or assumptions, sensitivity
assessments would strengthen the results'
robustness. Furthermore, adding new data sources
and incorporating more sophisticated reliability
modeling methods may enhance the analysis's
accuracy and dependability. Lastly, carrying out
validation research in actual environments would
validate the findings' validity and application in a
variety of circumstances.
5.3 Future Directions
There are several exciting directions this field may
take in the future. An examination of the
interactions among system profitability,
dependability, and other crucial performance
metrics can result in a comprehensive computation
of system optimization. Examining how new
technologies or market trends affect system
profitability and dependability would yield
insightful information for modifying plans of action
when conditions change. Proactive maintenance
techniques like condition-based monitoring and
predictive maintenance have the potential to
improve system profitability and dependability even
more. Maintaining operational effectiveness
requires evaluating reliability modeling's long-term
effects on system sustainability and resilience,
especially under changing regulatory environments.
Furthermore, investigating the applicability of
dependability modeling methodologies in other
industries and their scalability to larger or more
complex systems
Acknowledgement:
This research did not receive any specific grant from
funding agencies in the public, commercial, or not-
for-profit sectors. The authors would like to thank
the editor and anonymous reviewers for their
comments that helped improve the quality of this
work.
References:
[1] R. Malhotra, “Reliability and availability
analysis of a standby system with activation
time and varying demand,” in Engineering
Reliability and Risk Assessment, Elsevier,
2023, pp. 35–51, doi: 10.1016/B978-0-323-
91943-2.00004-6.
[2] Gitanjali, “Reliability Measurement of
Complex Industrial Redundant Systems
Using Semi-Markov Process and
Regenerative Point Technique,” in Recent
Advances in Metrology: Select Proceedings
of AdMet 2021, pp. 221-231. Singapore:
Springer Nature Singapore, doi:
10.1007/978-981-19-2468-2_25.
[3] O. KOCA, O. T. Kaymakci, and M.
Mercimek, “Advanced Predictive
Maintenance with Machine Learning Failure
Estimation in Industrial Packaging Robots,”
in 2020 International Conference on
Development and Application Systems
(DAS), IEEE, May 2020, Suceava, Romania,
pp. 1–6, doi:
10.1109/DAS49615.2020.9108913.
[4] M. K. Kakkar, J. Bhatti, G. Gupta, and K. D.
Sharma, “Reliability analysis of a three unit
redundant system under the inspection of a
unit with correlated failure and repair times,”
in AIP Conference Proceedings, Vol. 2357,
WSEAS TRANSACTIONS on MATHEMATICS
DOI: 10.37394/23206.2024.23.35
Prawar, Anjali Naithani, H. D. Arora, Ekata
E-ISSN: 2224-2880
328
Volume 23, 2024
No. 1. AIP Publishing.2022, doi:
10.1063/5.0080964.
[5] A. Tabandeh, G. Jia, and P. Gardoni, “A
review and assessment of importance
sampling methods for reliability analysis,”
Structural Safety, vol. 97, p. 102216, Jul.
2022, doi: 10.1016/j.strusafe.2022.102216.
[6] W. Zhang, X. Gu, L. Hong, L. Han, and L.
Wang, “Comprehensive review of machine
learning in geotechnical reliability analysis:
Algorithms, applications and further
challenges,” Appl Soft Comput, vol. 136, p.
110066, Mar. 2023, doi:
10.1016/j.asoc.2023.110066.
[7] L. Jun and X. Huibin, “Reliability Analysis
of Aircraft Equipment Based on FMECA
Method,” Phys Procedia, vol. 25, pp. 1816–
1822, 2012, doi:
10.1016/j.phpro.2012.03.316.
[8] J.-N. YANG and W. J. TRAPP, “Reliability
Analysis of Aircraft Structures under
Random Loading and Periodic Inspection,”
AIAA Journal, vol. 12, no. 12, pp. 1623–
1630, Dec. 1974, doi: 10.2514/3.49570.
[9] H. Pang, T. Yu, and B. Song, “Failure
mechanism analysis and reliability
assessment of an aircraft slat,” Eng Fail
Anal, vol. 60, pp. 261–279, Feb. 2016, doi:
10.1016/j.engfailanal.2015.11.032.
[10] A. Żyluk, K. Kuźma, N. Grzesik, M. Zieja,
and J. Tomaszewska, “Fuzzy Logic in
Aircraft Onboard Systems Reliability
Evaluation—A New Approach,” Sensors,
vol. 21, no. 23, p. 7913, Nov. 2021, doi:
10.3390/s21237913.
[11] M. S. EL-Sherbeny, M. A. W. Mahmoud,
and Z. M. Hussien, “Reliability analysis of a
two-unit cold standby system with arbitrary
distributions and change in units,” Life Cycle
Reliability and Safety Engineering, vol. 9,
no. 3, pp. 261–272, Sep. 2020, doi:
10.1007/s41872-020-00127-y.
[12] S. Gupta, S. Kanwar, H. D. Arora, and A.
Naithani, “Assessment of Reliability Factors
in Glass Manufacturing plant Using Boolean
Algebra and Neural network,” in 2022 12th
International Conference on Cloud
Computing, Data Science & Engineering
(Confluence), Amity University, Noida,
INDIA. IEEE, Jan. 2022, pp. 8–13. doi:
10.1109/Confluence52989.2022.9734199.
[13] H. D. Arora and A. Naithani, “Performance
analysis of Pythagorean fuzzy entropy and
distance measures in selecting software
reliability growth models using TOPSIS
framework,” International Journal of
Quality & Reliability Management, vol. 40,
no. 7, pp. 1667–1682, Jul. 2023, doi:
10.1108/IJQRM-11-2021-0398.
[14] C. A. Gabe, L. O. Freire, and D. A. De
Andrade, “Modeling dynamic scenarios for
safety, reliability, availability, and
maintainability analysis,” in Brazilian
Journal of Radiation Sciences, vol. 8, no.
3A, Feb. 2021, doi:
10.15392/bjrs.v8i3A.1464.
[15] V. P. Koutras, “A Markov Regenerative
Process Model for the Dependability and
Performance of a Two-Unit Multi-State
System under Maintenance,” Reliab Eng Syst
Saf, vol. 238, p. 109433, Oct. 2023, doi:
10.1016/j.ress.2023.109433.
[16] J. Bai, X. Chang, G. Ning, Z. Zhang, and K.
S. Trivedi, “Service Availability Analysis in
a Virtualized System: A Markov
Regenerative Model Approach,” IEEE
Transactions on Cloud Computing, vol. 10,
no. 3, pp. 2118–2130, Jul. 2022, doi:
10.1109/TCC.2020.3028648.
[17] K. Celikmih, O. Inan, and H. Uguz, “Failure
Prediction of Aircraft Equipment Using
Machine Learning with a Hybrid Data
Preparation Method,” Sci Program, vol.
2020, pp. 1–10, Aug. 2020, doi:
10.1155/2020/8616039.
[18] N. Zimmermann and P. H. Wang, “A review
of failure modes and fracture analysis of
aircraft composite materials,” Eng Fail Anal,
vol. 115, p. 104692, Sep. 2020, doi:
10.1016/j.engfailanal.2020.104692.
[19] A. D. Yadav, N. Nandal, S. Malik, and S. C.
Malik, “Markov approach for reliability-
availability-maintainability analysis of a
three unit repairable system,” OPSEARCH,
vol. 60, no. 4, pp. 1731–1756, Dec. 2023,
doi: 10.1007/s12597-023-00684-7.
[20] G. Kumar, M. K. Loganathan, and O. Yadav,
“Semi-Markov modeling applications in
system availability analysis,” in Engineering
Reliability and Risk Assessment, Elsevier,
2023, pp. 161–184. doi: 10.1016/B978-0-
323-91943-2.00012-5.
[21] A. kumar, “Cost-Benefit Study of a Cold
Standby Structure with Waiting Time Aimed
at Repair,” SSRN Electronic Journal, 2022,
doi: 10.2139/ssrn.4044551.
[22] L. Y. Waghmode and R. B. Patil,
“Reliability analysis and life cycle cost
optimization: a case study from Indian
industry,” International Journal of Quality &
WSEAS TRANSACTIONS on MATHEMATICS
DOI: 10.37394/23206.2024.23.35
Prawar, Anjali Naithani, H. D. Arora, Ekata
E-ISSN: 2224-2880
329
Volume 23, 2024
Reliability Management, vol. 33, no. 3, pp.
414–429, Mar. 2016, doi: 10.1108/IJQRM-
11-2014-0184.
[23] P. Tsarouhas, “Reliability, availability and
maintainability (RAM) analysis for wine
packaging production line,” International
Journal of Quality & Reliability
Management, vol. 35, no. 3, pp. 821–842,
Mar. 2018, doi: 10.1108/IJQRM-02-2017-
0026.
[24] U. Safder, P. Ifaei, K. Nam, J. Rashidi, and
C. Yoo, “Availability and reliability analysis
of integrated reverse osmosis - forward
osmosis desalination network,” Desalination
Water Treat, vol. 109, pp. 1–7, 2018, doi:
10.5004/dwt.2018.22147.
[25] H. Li, W. Peng, S. Adumene, and M. Yazdi,
“Advances in Intelligent Reliability and
Maintainability of Energy Infrastructure
Assets,” 2023, pp. 1–23. doi: 10.1007/978-3-
031-29962-9_1.
Contribution of Individual Authors to the
Creation of a Scientific Article
- Prawar carried out Investigation,
Methodology, Software, Writing-Orignal
draft, Writing- review & editing
- Anjali Naithani carried out Investigation,
Methodology, Software, Resources,
Writing- review & editing, Supervision
- H. D. Arora carried out Writing-review &
editing, Supervision, Validation.
- Ekata carried out Writing-review &
editing, Supervision, Validation.
Sources of Funding for Research
Presented in a Scientific Article or
Scientific Article Itself
No funding was received for conducting this
study.
Conflict of Interest
The authors have no conflicts of interest to
declare.
Creative Commons Attribution License
4.0 (Attribution 4.0 International, CC BY
4.0)
This article is published under the terms of
the Creative Commons Attribution License
4.0
https://creativecommons.org/licenses/by/4.0/
deed.en_US
WSEAS TRANSACTIONS on MATHEMATICS
DOI: 10.37394/23206.2024.23.35
Prawar, Anjali Naithani, H. D. Arora, Ekata
E-ISSN: 2224-2880
330
Volume 23, 2024
