Home Role of individual component failure in the performance of a 1-out-of-3 cold standby system: A Markov model approach
Article Open Access

Role of individual component failure in the performance of a 1-out-of-3 cold standby system: A Markov model approach

  • Layla Hindi EMAIL logo and Hussein K. Asker
Published/Copyright: February 28, 2024
Become an author with De Gruyter Brill

Abstract

The current work assesses the availability and reliability of repairable 1-out-of-3 cold standby systems, undergoing switching failure, by the Markov models, where a finite set of differential equations govern the repairable system. A numerical approach based on KAOS programming in MATLAB is employed to solve the differential equations. Thus, numerical solutions for the time-dependent availability can then be obtained. The Laplace transform method is used for the reliability model to find the explicit form of the reliability function and the mean time to failure (MTTF) of the system. An availability estimation model for a 1-out-of-3 cold standby system is developed and the main electrical power network, local electricity generator, and domestic electricity generator are studied. Finally, the model is analyzed to illustrate the effect of both failures and repair rates as well as component capacity partitioning on system availability and MTTF.

1 Introduction

Electrical power plays an increasingly important role in all aspects of human life and in various electrical fields, system availability assessment has been extensively investigated. Particularly, a stable power supply system is essential and critical in many electrical energy systems, such as the main electrical power network (MEPN), and private generators. These generators are either local, set up to provide power for each block, or used in houses for domestic purpose. In modern technological life, the power supply system is widely applied in various industries. In modern technological life, a reliable power supply system is widely applied across various industries due to its high availability. The MEPN in Iraq is an important source of energy. Because of the increasingly long blackouts in MEPN, people resorted to using private generators. Availability depends on the types of breakdowns that should be included in the analysis [1]. One of well-known methods used to improve system reliability and availability is increasing the redundancy in the system [1]. Redundancy is an effective tool to improve the availability of a system by adding plug-ins [2]. The status of these plug-ins determines the type of the redundancy. It is categorized into three parts: active redundancy, standby redundancy, and active/standby redundancy [3]. Standby redundancy system is a configuration of units in the sense that this system fails when all the units fail. The word “standby” means that only one (or a given number) unit operates at a time, while the other operating units are on hold to be switched at the failure of operating unit [3], as shown in Figure 1. This system contains three units, A which is the initial (at time t = 0) operating unit, and B and C are the standby units while S is the switch of changeover device. Standby redundancy generally falls into three kinds: Unloaded (cold) standby, loaded (hot) standby, and light (warm) standby [2].

Figure 1 
               Standby system with three units.
Figure 1

Standby system with three units.

In the current study, the unloaded (cold) standby system is investigated. Hence, a cold standby system is examined in detail in the following sections in light of previous studies.

The cold standby system does not carry any load during the hold time before activation. Nonetheless, the redundant units are reserved in a dormant mode where the failure rates of cold standby components are usually zero before activation. On the other hand, the active units undergo a high failure rate of (λ) [3,4].

Asker examined a repairable standby system of two units with a changeover (or switch) that works with a standby (cold or partially loaded) unit either imperfectly or flawlessly. In light of the studied considerations, eight models for the standby system were obtained [3]. Wang and Kececioglu investigated the inherent availability, which is a significant performance index for a repairable system, and is usually estimated from the times-between-failures and the times-to-restore data [5]. Pérez-Ocón and Montoro-Cazorla discussed that the system comprises n units, the other units are either in repair, or in cold standby, or on hold for repair, only the working unit can fail [6]. Zhang and Wang investigated the two-component cold standby repairable system with one repairman and use of priority. It is assumed that component M after repair is not “as good as new” [7]. Zhang and Wang clarified that a deteriorating cold standby repairable system, consisting of two dissimilar components and one repairman, assumes that the successive working times form a decreasing geometric process while the consecutive repair times constitute an increasing geometric process [8]. Leung et al. presented the research on a cold standby repairable system consisting of two dissimilar components and one repairman. It is supposed that distributions of working time and distributions of repair time of the two components are both exponential, and component 1 receives priority for repairing [9]. Manglik and Ram explained the analysis of reliability of a four-components system arranged in series. Subsystems A, B, and C have a single unit whereas subsystem D has three units. In this system, one unit is active and the other two are cold standby arranged in a paralleled way [10]. Jia et al. studied a two-unit standby system without repair, to introduce the active switching policy in which the standby unit is activated at either a pre-fixed time or the failure time of active unit and considering the perfect and imperfect switching [11]. Grida et al. addressed the effect of plug-in economy of scale on achieving a high level of availability [4]. Peng et al. scrutinized a cold standby system that has two diverse components. The highly applicable phase-type (PH) distribution is employed to show the life and maintenance time of components of the system in a unified manner. A reliability of systems of the model is structured for wider applicability [12]. Akhavan Niaki and Yaghoubi studied the closed-form equations, derived using the Markov method, to calculate the reliability function and the mean time to failure (MTTF) of a 1-out-of-n cold standby system with non-repairable component under imperfect switching [13]. Danjuma et al. suggested the reliability of a system with three components, A, B, and C, joined in series in a parallel manner. The system was assessed through the Markov birth–death process, resulting in clear expressions for availability and system breakdown mean time. The results indicate that indicators of system effectiveness such as availability and mean time to system failure fall with failure rates and rise with repair rates [14]. Raghuvanshi et al. examined the cost-benefit analysis of a two identical unit cold standby system model using regenerative point technique with the basic tools of probabilistic argument and Laplace transform, and various important measures of system effectiveness useful to system designers and operations managers have been obtained [15]. Kaur and Bhardwaj presented the improvement in the system effectiveness of a two unit cold standby repairable systems by taking into account the failure possibility of a unit in standby mode. So, whenever an operating unit crosses a prefixed period (called maximum operation time) or the repair of the unit is not completed within a prefixed period (called maximum repair time), it is sent for preventive maintenance. The expressions for various explicit measures of system effectiveness are derived by adopting semi-Markov approach and regenerative point technique [16]. Hindi and Asker (2023) developed a 1-out-of-3 cold standby system with perfect switching. An availability estimation model for a repairable 1-out-of-3 cold standby system is developed and studied on the real industrial application of the MEPN, local electricity generator, and domestic electricity generator, where Markov model is employed for system reliability. The analysis of the model showed relatively high availability of electricity and that the MEPN cannot be dispensed with. A 1-out-of-3 system performed better and is more stable due to its higher level of capacity [17]. Based on the aforementioned studies, this work is complementary to the study by Hindi and Asker [17], and due to frequent outages of the MEPN in Iraq causing people to resort to local electricity generators besides domestic generators, this study investigates a 1-out-of-3 cold standby system model. It consists of three components and each component expresses the following: The first component represents the MEPN, the second component represents the local generator, and the third component represents the domestic generator. A 1-out-of-3 cold standby system denotes a prioritization hierarchy in the usage and maintenance of its components under specific assumptions: cold standby mode, imperfect switching, and a backup that is itself a 1-out-of-3 system. The whole process is shown and explained with the help of a Markov transition chart in Figure 2.

Figure 2 
               The transition of the 1-out-of-3 cold standby system from one state to another is succinctly represented through a Markov transition diagram. The detailed transitions and their corresponding probabilities can be found in Table 1, which provides the transition matrix for the system.
Figure 2

The transition of the 1-out-of-3 cold standby system from one state to another is succinctly represented through a Markov transition diagram. The detailed transitions and their corresponding probabilities can be found in Table 1, which provides the transition matrix for the system.

The remainder of this study is structured as follows: Section 2 provides a comprehensive description of the system under consideration, and describes system state by using the transition matrix. Section 3 presents the description of availability of two cold standby repairable systems and calculates the stationary availability of system. Section 4 presents the description of MTTF of cold standby system and calculates the MTTF of the system. Section 5 presents the numerical results of evaluation and analysis of the impact of diverse reliability metrics on the performance of the 1-out-of-3 cold standby system. Section 6 gives the discussion and conclusion, and the algorithm of the KAOS programming technique using MATLAB is also given.

2 System description and assumptions

Assume that the system under discussion is a 1-out-of-3 cold standby system with imperfect switching, which consists of three components: A is the initial operational component, and B and C are the two cold standby components. As shown, component A is the MEPN, component B is the local power generator, and component C is the household electricity generator. The assumptions are detailed as follows:

  1. The switch is imperfect and maintainable.

  2. Switch has priority in maintenance.

  3. Component A is priority in use and maintenance, then component B and component C, respectively.

  4. Each of the switch and component has a constant operating failure rate (λ), and a constant repair rate (µ).

  5. The system remains in working condition (running) even when the switch fails as long as component A, B, or C is in the state of operation, i.e., not failing.

  6. The system fails in two cases:

  1. In the case of the failure of the switch with the failure of the instantaneous operating component (A or B or C).

  2. The failure of all components (A, B, and C).

Table 1

Transition probability matrix

P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10 P 11 P 12 P 13 P 14 P 15 P 16 P 17 P 18 P 19
P 1 −(λ A +λ S) λ A 0 λ S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
P 2 μ A −(μ A +λ S +λ B) λ B 0 λ S 0 0 0 0 0 0 0 0 0 0 0 0 0 0
P 3 0 0 −(λ S +λ C +μ A) 0 0 λ S λ C 0 0 0 μ A 0 0 0 0 0 0 0 0
P 4 μ S 0 0 −(μ S +λ A) 0 0 0 λ A 0 0 0 0 0 0 0 0 0 0 0
P 5 0 μ S 0 0 −(μ S +λ B) 0 0 0 λ B 0 0 0 0 0 0 0 0 0 0
P 6 0 0 μ S 0 0 −(μ S +λ C) 0 0 0 λ C 0 0 0 0 0 0 0 0 0
P 7 0 0 0 0 0 0 μ A 0 0 0 0 0 μ A 0 0 0 0 0 0
P 8 0 μ S 0 0 0 0 0 μ S 0 0 0 0 0 0 0 0 0 0 0
P 9 0 0 μ S 0 0 0 0 0 μ S 0 0 0 0 0 0 0 0 0 0
P 10 0 0 0 0 0 0 μ S 0 0 μ S 0 0 0 0 0 0 0 0 0
P 11 μ B 0 λ A 0 0 0 0 0 0 0 −(μ B +λ A +λ S) λ S 0 0 0 0 0 0 0
P 12 0 0 0 0 0 0 0 0 λ A 0 μ S −(λ A +μ S) 0 0 0 0 0 0 0
P 13 0 0 0 0 0 0 λ A 0 0 0 0 0 −(λ A +λ S +μ B) λ S μ B 0 0 0 0
P 14 0 0 0 0 0 0 0 0 0 λ A 0 0 μ S −(λ A +μ S) 0 0 0 0 0
P 15 μ C 0 0 0 0 0 0 0 0 0 0 0 0 0 −(μ C +λ S +λ A) λ S 0 λ A 0
P 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 μ S −(μ S +λ A) λ A 0 0
P 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 μ S μ S 0
P 18 0 0 0 0 0 0 λ B 0 0 0 0 0 0 0 μ A 0 0 −(λ B +λ S +μ A) λ S
P 19 0 0 0 0 0 0 0 0 0 λ B 0 0 0 0 0 0 0 μ S −(λ B +μ S)

Utilizing the specific transition rates presented in Figure 2 and Table 1, we can formulate the subsequent equations representing the state probabilities of the 1-out-of-3 cold standby system.

(1) d p 1 ( t ) d t = 2 λ p 1 + μ p 2 + μ p 4 + μ p 11 + μ p 15 ,

(2) d p 2 ( t ) d t = λ p 1 ( 2 λ + μ ) p 2 + μ p 5 + μ p 8 ,

(3) d p 3 ( t ) d t = λ p 2 ( 2 λ + μ ) p 3 + μ p 6 + μ p 9 + λ p 11 ,

(4) d p 4 ( t ) d t = λ p 1 ( λ + μ ) p 4 ,

(5) d p 5 ( t ) d t = λ p 2 ( λ + μ ) p 5 ,

(6) d p 6 ( t ) d t = λ p 3 ( λ + μ ) p 6 ,

(7) d p 7 ( t ) d t = λ p 3 μ p 7 + μ p 10 + λ p 13 + λ p 18 ,

(8) d p 8 ( t ) d t = λ p 4 μ p 8 ,

(9) d p 9 ( t ) d t = λ p 5 μ p 9 + λ p 12 ,

(10) d p 10 ( t ) d t = λ p 6 μ p 10 + λ p 14 + λ p 19 ,

(11) d p 11 ( t ) d t = μ p 3 ( 2 λ + μ ) p 11 + μ p 12 ,

(12) d p 12 ( t ) d t = λ p 11 ( λ + μ ) p 12 ,

(13) d p 13 ( t ) d t = μ p 7 ( 2 λ + μ ) p 13 + μ p 14 ,

(14) d p 14 ( t ) d t = λ p 13 ( λ + μ ) p 14 ,

(15) d p 15 ( t ) d t = μ p 13 ( 2 λ + μ ) p 15 + μ p 16 + μ p 18 ,

(16) d p 16 ( t ) d t = λ p 15 ( λ + μ ) p 16 ,

(17) d p 17 ( t ) d t = λ p 16 μ p 17 ,

(18) d p 18 ( t ) d t = λ p 15 + μ p 17 ( 2 λ + μ ) p 18 + μ p 19 ,

(19) d p 19 ( t ) d t = λ p 18 ( λ + μ ) p 19 .

In a steady-state condition, the time derivatives of the state probabilities are expressed as follows:

(20) i = 1 19 p i ( t ) = 1 ,

and let F = 12λ 6 + 26λ 5 μ + 27λ 4 μ 2 + 20λ 3 μ 3 + 12λ 2 μ 4 + 5λμ 5 + μ 6,

So

(21) p 1 = λ 3 μ 3 + 3 λ 2 μ 4 + 3 λ μ 5 + μ 6 F ,

(22) p 2 = 2 λ 5 μ 3 + 7 λ 4 μ 4 + 9 λ 3 μ 5 + 5 λ 2 μ 6 + λ μ 7 ( 2 λ 2 + 2 λ μ + μ 2 ) F ,

and let E = 4λ 4 + 6λ 3 μ + 5λ 2 μ 2 + 3λμ 3 + μ 4

(23) p 3 = 4 λ 7 μ 3 + 16 λ 6 μ 4 + 25 λ 5 μ 5 + 19 λ 4 μ 6 + 7 λ 3 μ 7 + λ 2 μ 8 EF ,

(24) p 4 = λ 3 μ 3 + 2 λ 2 μ 4 + λ μ 5 F ,

(25) p 5 = 2 λ 5 μ 3 + 5 λ 4 μ 4 + 4 λ 3 μ 5 + λ 2 μ 6 ( 2 λ 2 + 2 λ μ + μ 2 ) F ,

(26) p 6 = 4 λ 7 μ 3 + 12 λ 6 μ 4 + 13 λ 5 μ 5 + 6 λ 4 μ 6 + λ 3 μ 7 EF ,

(27) p 7 = ( 2 λ + μ ) ( 4 λ 5 + 4 λ 4 μ + λ 3 μ 2 ) F ,

(28) p 8 = 4 λ 4 μ 2 + 2 λ 3 μ 3 + λ 2 μ 4 F ,

(29) p 9 = 4 λ 8 μ 2 + 14 λ 7 μ 3 + 20 λ 6 μ 4 + 15 λ 5 μ 5 + 6 λ 4 μ 6 + λ 3 μ 7 EF ,

(30) p 10 = 4 λ 6 + 4 λ 5 μ + λ 4 μ 2 F ,

(31) p 11 = 4 λ 8 μ 4 + 20 λ 7 μ 5 + 41 λ 6 μ 6 + 44 λ 5 μ 7 + 26 λ 4 μ 8 + 8 λ 3 μ 9 + λ 2 μ 10 ( 2 λ 2 + 2 λ μ + μ 2 ) EF ,

(32) p 12 = 4 λ 8 μ 4 + 16 λ 7 μ 5 + 25 λ 6 μ 6 + 19 λ 5 μ 7 + 7 λ 4 μ 8 + λ 3 μ 9 ( 2 λ 2 + 2 λ μ + μ 2 ) EF ,

(33) p 13 = 8 λ 7 μ + 20 λ 6 μ 2 + 18 λ 5 μ 3 + 7 λ 4 μ 4 + λ 3 μ 5 ( 2 λ 2 + 2 λ μ + μ 2 ) F ,

(34) p 14 = 8 λ 7 μ + 12 λ 6 μ 2 + 6 λ 5 μ 3 + λ 4 μ 4 ( 2 λ 2 + 2 λ μ + μ 2 ) F ,

and let M = 48 λ 10 + 17 6 λ 9 μ + 324 λ 8 μ 2 + 408 λ 7 μ 3 + 393 λ 6 μ 4 + 299 λ 5 μ 5 + 181 λ 4 μ 6 + 87 λ 3 μ 7 + 32 λ 2 μ 8 + 8 λ μ 9 + μ 10 ,

(35) p 15 = 8 λ 8 μ 2 + 28 λ 87 μ 3 + 38 λ 6 μ 4 + 25 λ 5 μ 5 + 8 λ 4 μ 6 + λ 3 μ 7 M ,

(36) p 16 = λ 4 ( λ + μ ) ( 2 λ + μ ) ( 4 λ 2 μ 2 + 4 λ μ 3 + μ 4 ) M ,

(37) p 17 = 8 λ 9 μ + 20 λ 8 μ 2 + 18 λ 7 μ 3 + 7 λ 6 μ 4 + λ 5 μ 5 M ,

and let N = 96λ 12 + 448λ 11 μ + 1,048λ 10 μ 2 + 1,640λ 9 μ 3 + 1,926λ 8 μ 4 + 1,729λ 7 μ 5 + 1,353λ 6 μ 6 + 835λ 5 μ 7 + 491λ 4 μ 8 + 167λ 3 μ 9 + 50λ 2 μ 10 + 10λμ 11 + μ 12

(38) p 18 = [ λ 4 μ ( λ + μ ) ( 4 λ 2 + 4 λ μ + μ 2 ) ( 4 λ 3 μ + 8 λ 2 μ 2 + 5 λ μ 3 + μ 4 ) ] M ,

(39) p 19 = [ λ 5 μ ( λ + μ ) ( λ 2 + 2 λ μ ) ( 2 λ + μ ) ( 4 λ 2 + 8 λ μ + μ 2 ) ] M .

3 Availability of two cold standby repairable systems

Availability is the probability that the system is operating at a specified time (t), which is always associated with the concept of maintainability. Availability depends on both failures and relies on repair rates [10].

3.1 Calculation of the stationary availability of system

The system is in operation when it is in either the state p 1 , p 2 , p 3 , p 4 , p 5 , p 6 , p 11 , p 12 , p 13 , p 14 , p 15 , p 16 , p 18 , and p 19 . Therefore, the general form to calculate the stationary availability of system is as follows:

(40) V AAIM = [ p 1 ( ) + p 2 ( ) + p 3 ( ) + p 4 ( ) + p 5 ( ) + p 6 ( ) + p 11 ( ) + p 12 ( ) + p 13 ( ) + p 14 ( ) + p 15 ( ) + p 16 ( ) + p 18 ( ) + p 19 ( ) ] .

Using equations ((21)–(26), (31)–(36), (38), and (39), equation (40) can be rewritten as follows:

V AAIM = λ 3 μ 3 + 3 λ 2 μ 4 + 3 λ μ 5 + μ 6 F + 2 λ 5 μ 3 + 7 λ 4 μ 4 + 9 λ 3 μ 5 + 5 λ 2 μ 6 + λ μ 7 ( 2 λ 2 + 2 λ μ + μ 2 ) F + 4 λ 7 μ 3 + 16 λ 6 μ 4 + 25 λ 5 μ 5 + 19 λ 4 μ 6 + 7 λ 3 μ 7 + λ 2 μ 8 EF + λ 3 μ 3 + 2 λ 2 μ 4 + λ μ 5 F + 2 λ 5 μ 3 + 5 λ 4 μ 4 + 4 λ 3 μ 5 + λ 2 μ 6 ( 2 λ 2 + 2 λ μ + μ 2 ) F + 4 λ 7 μ 3 + 12 λ 6 μ 4 + 13 λ 5 μ 5 + 6 λ 4 μ 6 + λ 3 μ 7 EF + 4 λ 8 μ 4 + 20 λ 7 μ 5 + 41 λ 6 μ 6 + 44 λ 5 μ 7 + 26 λ 4 μ 8 + 8 λ 3 μ 9 + λ 2 μ 10 ( 2 λ 2 + 2 λ μ + μ 2 ) EF + 4 λ 8 μ 4 + 16 λ 7 μ 5 + 25 λ 6 μ 6 + 19 λ 5 μ 7 + 7 λ 4 μ 8 + λ 3 μ 9 ( 2 λ 2 + 2 λ μ + μ 2 ) EF + 8 λ 7 μ + 20 λ 6 μ 2 + 18 λ 5 μ 3 + 7 λ 4 μ 4 + λ 3 μ 5 ( 2 λ 2 + 2 λ μ + μ 2 ) F + 8 λ 7 μ + 12 λ 6 μ 2 + 6 λ 5 μ 3 + λ 4 μ 4 ( 2 λ 2 + 2 λ μ + μ 2 ) F + 8 λ 8 μ 2 + 28 λ 87 μ 3 + 38 λ 6 μ 4 + 25 λ 5 μ 5 + 8 λ 4 μ 6 + λ 3 μ 7 M + ( λ 4 ( λ + μ ) ( 2 λ + μ ) ( 4 λ 2 μ 2 + 4 λ μ 3 + μ 4 ) M + [ λ 4 μ ( λ + μ ) ( 4 λ 2 + 4 λ μ + μ 2 ) ( 4 λ 3 μ + 8 λ 2 μ 2 + 5 λ μ 3 + μ 4 ) ] M + [ λ 5 μ ( λ + μ ) ( λ 2 + 2 λ μ ) ( 2 λ + μ ) ( 4 λ 2 + 8 λ μ + μ 2 ) ] M .

So,

(41) V AAIM = 8 λ 5 μ + 16 λ 4 μ 2 + 16 λ 3 μ 3 + 11 λ 2 μ 4 + 5 λ μ 2 + μ 6 12 λ 6 + 2 6 λ 5 μ + 27 λ 4 μ 2 + 20 λ 3 μ 3 + 12 λ 2 μ 4 + 5 λ μ 5 + μ 6 .

4 System MTTF

MTTF is the predicted elapsed time between inherent failures of a system during operation. MTTF can be calculated as the average time between failures of a system [10]. According to Markov model and a property of the Laplace transform, the MTTF of the system is given by

MTTF = E ( t ) = 0 R ( t ) ( t ) d t .

According to Asker ([3], p. 13), the MTTF of the system can be determined by considering the failed state of the system state p 7 , p 8 , p 9 , p 10 , and p 17 as an absorbing state. Now suppose that the initial state at t = 0 is state 0, by deleting the row and column of the transition rate matrix corresponding to the absorbing states p 7 , p 8 , p 9 , p 10 , and p 17 and taking Laplace transitions (with s = 0) of Transition Probability Matrix in Table 1, we obtain transition probability matrix MTTF of the system given in Table 2.

Table 2

Transition probability matrix MTTF of the system

P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10 P 11 P 12 P 13 P 14
P 1 ( λ A + λ S ) λ A 0 λ S 0 0 0 0 0 0 0 0 0 0
P 2 μ A ( μ A + λ S + λ B ) λ B 0 λ S 0 0 0 0 0 0 0 0 0
P 3 0 0 ( λ S + λ C + μ A ) 0 0 λ S μ A 0 0 0 0 0 0 0
P 4 μ S 0 0 ( μ S + λ A ) 0 0 0 0 0 0 0 0 0 0
P 5 0 μ S 0 0 ( μ S + λ B ) 0 0 0 0 0 0 0 0 0
P 6 0 0 μ S 0 0 ( μ S + λ C ) 0 0 0 0 0 0 0 0
P 7 μ B 0 λ A 0 0 0 ( μ B + λ A + λ S ) λ S 0 0 0 0 0 0
P 8 0 0 0 0 0 0 μ S ( λ A + μ S ) 0 0 0 0 0 0
P 9 0 0 0 0 0 0 0 0 ( λ A + λ S + μ B ) λ S μ B 0 0 0
P 10 0 0 0 0 0 0 0 0 μ S ( λ A + μ S ) 0 0 0 0
P 11 μ C 0 0 0 0 0 0 0 0 0 ( μ C + λ S + λ A ) λ S λ A 0
P 12 0 0 0 0 0 0 0 0 0 0 μ S ( μ S + λ A ) 0 0
P 13 0 0 0 0 0 0 0 0 0 0 μ A 0 ( λ B + μ A + λ S ) λ S
P 14 0 0 0 0 0 0 0 0 0 0 0 0 μ S ( λ B + μ S )

By using the appropriate transition rates depicted in Table 2, we can construct the following equations as the state probabilities MTTF of the system.

(42) d p 1 ( t ) dt = 2 λ p 1 + μ p 2 + μ p 4 + μ p 7 + μ p 11 ,

(43) d p 2 ( t ) d t = λ p 1 ( 2 λ + μ ) p 2 + μ p 5 ,

(44) d p 3 ( t ) d t = λ p 2 ( 2 λ + μ ) p 3 + μ p 6 + λ p 7 ,

(45) d p 4 ( t ) d t = λ p 1 ( λ + μ ) p 4 ,

(46) d p 5 ( t ) d t = λ p 2 ( λ + μ ) p 5 ,

(47) d p 6 ( t ) d t = λ p 3 ( λ + μ ) p 6 ,

(48) d p 7 ( t ) d t = μ p 3 ( 2 λ + μ ) p 7 + μ p 8 ,

(49) d p 8 ( t ) d t = λ p 7 ( λ + μ ) p 8 ,

(50) d p 9 ( t ) d t = ( 2 λ + μ ) p 9 + μ p 10 ,

(51) d p 10 ( t ) d t = λ p 9 ( λ + μ ) p 10 ,

(52) d p 11 ( t ) d t = μ p 9 ( 2 λ + μ ) p 11 + μ p 12 + μ p 13 ,

(53) d p 12 ( t ) d t = λ p 11 ( λ + μ ) p 12 ,

(54) d p 13 ( t ) d t = λ p 11 ( 2 λ + μ ) p 13 + μ p 14 ,

(55) d p 14 ( t ) d t = λ p 13 ( λ + μ ) p 14 ,

The solution is

K = 8λ 4 + 16λ 3 μ + 13λ 2 μ 2 + 5λμ 3 + μ 4.

So,

(56) p 1 = 4 μ 5 + 11 λ 4 μ + 13 λ 3 μ 2 + 9 λ 2 μ 3 + 4 λ μ 4 + μ 5 λ 2 K ,

(57) p 2 = 4 λ 6 + 15 λ 2 μ + 24 λ 4 μ 2 + 22 λ 3 μ 3 + 13 λ 2 μ 4 + 5 λ μ 5 + μ 6 λ ( 2 λ 2 + 2 λ μ + μ 2 ) K ,

(58) p 3 = λ 3 + 3 λ 2 μ + 3 λ μ 2 + μ 3 K ,

(59) p 4 = 4 λ 4 + 7 λ 3 μ + 6 λ 2 μ 2 + 3 λ μ 3 + μ 4 λ K ,

(60) p 5 = ( λ + μ ) ( 4 λ 4 + 7 λ 3 μ + 6 λ 2 μ 2 + 3 λ μ 3 + μ 4 ) ( 2 λ 2 + 2 λ μ + μ 2 ) K ,

(61) p 6 = λ ( λ + μ ) 2 K ,

(62) p 7 = μ ( λ + μ ) 4 ( 2 λ 2 + 2 λ μ + μ 2 ) K ,

(63) p 8 = λ μ ( λ + μ ) 3 ( 2 λ 2 + 2 λ μ + μ 2 ) K ,

(64) p 9 = p 10 = p 11 = p 12 = p 13 = p 14 = 0 .

4.1 Calculation of the MTTFIM of system

Taking repairs in the states p 1 , p 2 , p 3 , p 4 , p 5 , p 6 , p 7 , p 8 , p 9 , p 10 , p 11 , p 12 , p 13 , and p 14 , the general form to calculate the MTTF of system is

(65) MTTF IM = [ p 1 ( ) + p 2 ( ) + p 3 ( ) + p 4 ( ) + p 5 ( ) + p 6 ( ) + p 7 ( ) + p 8 ( ) + p 9 ( ) + p 10 ( ) + p 11 ( ) + p 12 ( ) + p 13 ( ) + p 14 ( ) ] .

Using equations (56)–(64), equation (65) can be rewritten as follows:

(66) MTTF IM = 4 μ 5 + 11 λ 4 μ + 13 λ 3 μ 2 + 9 λ 2 μ 3 + 4 λ μ 4 + μ 5 λ 2 K + 4 λ 6 + 15 λ 2 μ + 24 λ 4 μ 2 + 22 λ 3 μ 3 + 13 λ 2 μ 4 + 5 λ μ 5 + μ 6 λ ( 2 λ 2 + 2 λ μ + μ 2 ) K + λ 3 + 3 λ 2 μ + 3 λ μ 2 + μ 3 K , + 4 λ 4 + 7 λ 3 μ + 6 λ 2 μ 2 + 3 λ μ 3 + μ 4 λ K + ( λ + μ ) ( 4 λ 4 + 7 λ 3 μ + 6 λ 2 μ 2 + 3 λ μ 3 + μ 4 ) ( 2 λ 2 + 2 λ μ + μ 2 ) K + λ ( λ + μ ) 2 K + μ ( λ + μ ) 4 ( 2 λ 2 + 2 λ μ + μ 2 ) K + λ μ ( λ + μ ) 3 ( 2 λ 2 + 2 λ μ + μ 2 ) K + 0 + 0 + 0 + 0 + 0 + 0 .

So, MTTF IM = 14 λ 5 + 33 λ 4 μ + 33 λ 3 μ 2 + 18 λ 2 μ 3 + 6 λ μ 4 + μ 5 λ 2 K .

5 Numerical and effect results

5.1 Effect of failure rate (λ)

Figure 3 and Table 3 present the calculation and analyses of the effect of the failure rate λ on the availability of 1-out-of-3 cold standby system taking the values of different λ from 0.00 to 1 and when the repair rate is constant, its value is 0.8 and compensated in equation (41).

Figure 3 
                  Effective steady state availability with respective failure rate.
Figure 3

Effective steady state availability with respective failure rate.

Table 3

Calculation of the availability values

Let μ = 0.8
λ values V AAIN values λ values V AAIN values
λ 1 0.00 V AAIN 1 1 λ 11 0.50 V AAIN 11 0.73929
λ 2 0.05 V AAIN 2 0.99629 λ 12 0.55 V AAIN 12 0.70389
λ 3 0.10 V AAIN 3 0.98563 λ 13 0.60 V AAIN 13 0.67005
λ 4 0.15 V AAIN 4 0.96847 λ 14 0.65 V AAIN 14 0.638
λ 5 0.20 V AAIN 5 0.94531 λ 15 0.70 V AAIN 15 0.60788
λ 6 0.25 V AAIN 6 0.91698 λ 16 0.75 V AAIN 16 0.57969
λ 7 0.30 V AAIN 7 0.8846 λ 17 0.80 V AAIN 17 0.5534
λ 8 0.35 V AAIN 8 0.84946 λ 18 0.85 V AAIN 18 0.52892
λ 9 0.40 V AAIN 9 0.81283 λ 19 0.90 V AAIN 19 0.50616
λ 10 0.45 V AAIN 10 0.77582 λ 20 0.95 V AAIN 20 0.48499
λ 21 1 V AAIN 21 0.4653

Figure 3 shows these values.

As for the effect of failure rate (λ) on MTTF,

Figure 4 and Table 4 presents the calculation and analyses of the effect of the failure rate λ on MTTF of the 1-out-of-3 cold standby system taking the values of different λ from 0.05 to 1 and when the repair rate is constant, its value is 0.8 and compensated in equation (66).

Figure 4 
                  Effective MTTF with respect failure rate.
Figure 4

Effective MTTF with respect failure rate.

Table 4

Calculation of MTTF values

Let μ = 0.8
λ values MTTF values λ values MTTF values
λ 1 0.05 MTTF 1 340.262030175877 λ 11 0.55 MTTF 11 5.09986079943651
λ 2 0.10 MTTF 2 90.4380902413431 λ 12 0.60 MTTF 12 4.50931348625346
λ 3 0.15 MTTF 3 42.7730222805851 λ 13 0.65 MTTF 13 4.03523027724139
λ 4 0.20 MTTF 4 25.6191588785047 λ 14 0.70 MTTF 14 3.64726376030491
λ 5 0.25 MTTF 5 17.4573284837716 λ 15 0.75 MTTF 15 3.32454928750521
λ 6 0.30 MTTF 6 12.8975046597436 λ 16 0.80 MTTF 16 3.05232558139535
λ 7 0.35 MTTF 7 10.0676107965943 λ 17 0.85 MTTF 17 2.81988792335951
λ 8 0.40 MTTF 8 8.17567567567567 λ 18 0.90 MTTF 18 2.61930402934919
λ 9 0.45 MTTF 9 6.83870111326861 λ 19 0.95 MTTF 19 2.44458332632915
λ 10 0.50 MTTF 10 5.85251465176503 λ 20 1 MTTF 20 2.29112485041883

The following diagram shows these values.

5.1 Effect of repair rate (μ)

Figure 5 and Table 5 present the calculation and analyses of the effect of the repair rate μ on the availability of 1-out-of-3 cold standby system taking the values of different μ from 0.00 to 1, and when the failure rate λ is constant, its value is 0.8 and compensated in equation (41).

Figure 5 
               The steady state availability with respect to components setting up and repair rate.
Figure 5

The steady state availability with respect to components setting up and repair rate.

Table 5

Calculation of the availability

Let λ = 0.8
μ values V AAIN values μ values V AAIN values
μ 1 0.00 V AAIN 1 0 μ 11 0.50 V AAIN 11 0.37725
μ 2 0.05 V AAIN 2 0.041249 µ 12 0.55 V AAIN 12 0.40981
µ 3 0.10 V AAIN 3 0.081716 µ 13 0.60 V AAIN 13 0.44114
µ 4 0.15 V AAIN 4 0.12145 µ 14 0.65 V AAIN 14 0.47121
µ 5 0.20 V AAIN 5 0.16048 µ 15 0.70 V AAIN 15 0.49995
µ 6 0.25 V AAIN 6 0.19877 µ 16 0.75 V AAIN 16 0.52735
µ 7 0.30 V AAIN 7 0.23629 µ 17 0.80 V AAIN 17 0.5534
µ 8 0.35 V AAIN 8 0.27298 µ 18 0.85 V AAIN 18 0.57809
µ 9 0.40 V AAIN 9 0.30875 µ 19 0.90 V AAIN 19 0.60145
µ 10 0.45 V AAIN 10 0.34354 µ 20 0.95 V AAIN 20 0.62349
µ 21 1 V AAIN 21 0.64426

These values are displayed in Figure 5.

As for the effect of repair rate (μ) on MTTF,

Figure 6 and Table 6 present the calculation and analyses of the effect of the repair rate (μ) on the MTTF of the 1-out-of-3 cold standby system taking the values of different μ from 0.05 to 1, and when the failure rate λ is constant, its value is (0.8) and compensated in equation (66).

Figure 6 
               Effect of MTTF with respect to repair rate.
Figure 6

Effect of MTTF with respect to repair rate.

Table 6

Calculation of MTTF

Let λ = 0.8
µ values MTTF values µ values MTTF values
µ 1 0.05 MTTF 1 2.23650332689685 µ 11 0.55 MTTF 11 2.76131652831583
µ 2 0.10 MTTF 2 2.2859382843688 µ 12 0.60 MTTF 12 2.81800045973992
µ 3 0.15 MTTF 3 2.33590782015804 µ 13 0.65 MTTF 13 2.87545911642228
µ 4 0.20 MTTF 4 2.38649272947592 µ 14 0.70 MTTF 14 2.93367795967374
µ 5 0.25 MTTF 5 2.437755027395 µ 15 0.75 MTTF 15 2.99263983465819
µ 6 0.30 MTTF 6 2.48974086266725 µ 16 0.80 MTTF 16 3.05232558139535
µ 7 0.35 MTTF 7 2.54248303025291 µ 17 0.85 MTTF 17 3.11271454943734
µ 8 0.40 MTTF 8 2.59600313479624 µ 18 0.90 MTTF 18 3.17378502950732
µ 9 0.45 MTTF 9 2.65031345115946 µ 19 0.95 MTTF 19 3.23551461370671
µ 10 0.50 MTTF 10 2.70541852216109 µ 20 1 MTTF 20 3.29788049441683

The following diagram shows these values,

5.2 Effect of Γ

Term (Γ) is defined as the ratio of repair rate to component failure rate and is used to analyze the impact of component capacity partitioning on system availability: Γ = μ/λ

Hence, we will calculate and analyze the effect of component capacity partitioning on system availability1-out-of-3 cold standby system. From equation (41)

(67) V AAIN = Γ + 16 Γ 2 + 16 Γ 3 + 11 Γ 4 + 5 Γ 2 + Γ 6 12 + 26 Γ + 27 Γ 2 + 20 Γ 3 + 12 Γ 4 + 5 Γ 2 + Γ 6 .

Take the values of different Γ from 0.00 to 2 and substitute in equation (67). Table 7 and Figure 7 show the availability values.

Table 7

Calculation of the availability

Γ values V AAIN values Γ values V AAIN values
Γ1 0.00 V AAIN 1 0 Γ21 1.00 V AAIN 21 0.5534
Γ2 0.05 V AAIN 2 0.033064 Γ22 1.05 V AAIN 22 0.5733
Γ3 0.10 V AAIN 3 0.065619 Γ23 1.10 V AAIN 23 0.5923
Γ4 0.15 V AAIN 4 0.097697 Γ24 1.15 V AAIN 24 0.6104
Γ5 0.20 V AAIN 5 0.1293 Γ25 1.20 V AAIN 25 0.6277
Γ6 0.25 V AAIN 6 0.1605 Γ26 1.25 V AAIN 26 0.6443
Γ7 0.30 V AAIN 7 0.1912 Γ27 1.30 V AAIN 27 0.6600
Γ8 0.35 V AAIN 8 0.2214 Γ28 1.35 V AAIN 28 0.6750
Γ9 0.40 V AAIN 9 0.2511 Γ29 1.40 V AAIN 29 0.6892
Γ10 0.45 V AAIN 10 0.2802 Γ30 1.45 V AAIN 30 0.7027
Γ11 0.50 V AAIN 11 0.3088 Γ31 1.50 V AAIN 31 0.7155
Γ12 0.55 V AAIN 12 0.3367 Γ32 1.55 V AAIN 32 0.7277
Γ13 0.60 V AAIN 13 0.3639 Γ33 1.60 V AAIN 33 0.7393
Γ14 0.65 V AAIN 14 0.3904 Γ34 1.65 V AAIN 34 0.7503
Γ15 0.70 V AAIN 15 0.4162 Γ35 1.70 V AAIN 35 0.7607
Γ16 0.75 V AAIN 16 0.4411 Γ36 1.75 V AAIN 36 0.7706
Γ17 0.80 V AAIN 17 0.4653 Γ37 1.80 V AAIN 37 0.7799
Γ18 0.85 V AAIN 18 0.4886 Γ38 1.85 V AAIN 38 0.7888
Γ19 0.90 V AAIN 19 0.5111 Γ39 1.90 V AAIN 39 0.7972
Γ20 0.95 V AAIN 20 0.5327 Γ40 1.95 V AAIN 40 0.8052
Γ41 2 V AAIN 41 0.8128
Figure 7 
               The steady state availability with respect to components setting up and Γ.
Figure 7

The steady state availability with respect to components setting up and Γ.

Figure 7 shows these values.

6 Discussion and conclusion

In the present research, we have evaluated various reliability indices such as availability, MTTF, etc., for the 1-out-of-3 cold standby system considered and studied the MEPN, local electricity generator, and domestic electricity generator, employing Markov process. From the results and analysis of the designed system, one can conclude the following:

  1. Analysis of Table 3 gives us the idea of the availability of the stated system with respect to failure rate λ, when the repair rate μ is constant. Critical examination of corresponding Figure 3 yields that the values of the availability decreases approximately in an even manner with the increment in failure rate λ and the impact of failure rates on the system is greater.

  2. Table 4 displays the MTTF of the mentioned system in relation to different failure rates, with a constant repair rate µ. Upon scrutinizing Figure 4, we observed that MTTF diminishes as failure rates increase, indicating again that the system’s performance is significantly impacted by the changes in failure rates.

  3. Table 5 outlines the system’s availability with respect to the repair rate (µ) while keeping the failure rate (λ) constant. As demonstrated by Figure 5 and Table 5, the system’s availability tends to increase as the repair rate rises.

  4. In Table 6, the MTTF of the specified system is evaluated with respect to various repair rates (µ), with a constant failure rate. A critical examination of Figure 6 shows that the MTTF increases with the increment in repair rate.

  5. Finally, Table 7 and Figure 7 represent the term Γ, defined as the ratio of the repair rate to the component failure rate. It is observable that increasing Γ enhances the effect of component capacity partitioning on the availability of the 1-out-of-3 cold standby system, thereby improving the system’s availability and stability.

  1. Conflict of interest: Authors state no conflict of interest.

  2. Data availability statement: Data sharing does not apply to this article as no datasets were generated or analysed during the current study.

Appendix

MATLAB (R2015a) was used in the current study to calculate and examine the results of all the formulas mentioned above. Moreover, the R2015a software was used to draw the diagrams and representation through the algorithm described below.

Algorithm: To calculate and examine the results of all the formulas mentioned above.

References

[1] Bentley JP. An introduction to reliability and quality engineering. Harlow, Essex, England: Longman Scientific Technical; 1993.Search in Google Scholar

[2] Gnedenko BV, Belyayev YK, Solovyev AD. Mathematical methods of reliability theory. Academic Press; 2014‏.Search in Google Scholar

[3] Asker HK. Reliability models for maintained and non-maintained systems; 2000. (Master thesis). Mustansiriyah University.Search in Google Scholar

[4] Grida M, Zaid A, &Kholief G. Repairable 3-out-of-4: Cold standby system availability. In 2017 Annual Reliability and Maintainability Symposium (RAMS); 2017, January. p. 1–6.10.1109/RAM.2017.7889797Search in Google Scholar

[5] Wang W, Kececioglu DB. Confidence limits on the inherent availability of equipment. In Annual Reliability and Maintainability Symposium. 2000 Proceedings. International Symposium on Product Quality and Integrity (Cat. No. 00CH37055). IEEE; 2000, January. p. 162–8.Search in Google Scholar

[6] Pérez-Ocón R, Montoro-Cazorla D. A multiple system governed by a quasi-birth-and-death process. Reliab Eng Syst Saf. 2004;84(2):187–96.10.1016/j.ress.2003.10.003Search in Google Scholar

[7] Zhang YL, Wang GJ. A deteriorating cold standby repairable system with priority in use. Eur J Oper Res. 2007;183(1):278–95.10.1016/j.ejor.2006.09.075Search in Google Scholar

[8] Zhang YL, Wang GJ. A geometric process repair model for a repairable cold standby system with priority in use and repair. Reliab Eng Syst Saf. 2009;94(11):1782–7.10.1016/j.ress.2009.05.009Search in Google Scholar

[9] Leung KNF, Zhang YL, Lai KK. Analysis for a two-dissimilar-component cold standby repairable system with repair priority. Reliab Eng Syst Saf. 2011;96(11):1542–51.10.1016/j.ress.2011.06.004Search in Google Scholar

[10] Manglik M, Ram M. Reliability analysis of a two unit cold standby system using Markov process. J Reliab Stat Stud. 2013;6(2):65–80.Search in Google Scholar

[11] Jia X, Chen H, Cheng Z, Guo B. A comparison between two switching policies for two-unit standby system. Reliab Eng Syst Saf. 2016;148:109–18.10.1016/j.ress.2015.12.006Search in Google Scholar

[12] Peng D, Zichun N, Bin H. A new analytic method of cold standby system reliability model with priority. In MATEC Web of Conferences. Vol. 175. EDP Sciences; 2018. p. 03060‏.10.1051/matecconf/201817503060Search in Google Scholar

[13] Akhavan Niaki ST, Yaghoubi A. Exact equations for the reliability and mean time to failure of 1-out-of-n cold-standby system with imperfect switching. J Optim Ind Eng. 2021;14(2):197–203.Search in Google Scholar

[14] Danjuma MU, Yusuf B, Ali UA, Ismail AL, Soltani S, Sobhani FM, et al. Analysis of mean time to system failure and availability of a system with cold standby unit. J Ind Eng Int. 2022;18(1):2.Search in Google Scholar

[15] Raghuvanshi L, Gupta R, Chaudhary P. A discrete parametric Markov-chain system model of a two-unit standby system with two types of repair. Reliab: Theory Appl. 2023;18(1(72)):527–38‏.Search in Google Scholar

[16] Kaur K, Bhardwaj RK. Long run performance of a cold standby repairable system with standby failure subject to maximum operation and repair time. Math Stat Eng Appl. 2023;72(1):886–904.Search in Google Scholar

[17] Hindi L, Asker HK. Analyzing the impact of repairable 1-out-of-3 cold standby components on system availability: A capacity analysis. Math Model Eng Probl. 2023;10(3):937.10.18280/mmep.100325Search in Google Scholar

Received: 2023-06-10
Revised: 2023-08-02
Accepted: 2023-08-08
Published Online: 2024-02-28

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. Methodology of automated quality management
  3. Influence of vibratory conveyor design parameters on the trough motion and the self-synchronization of inertial vibrators
  4. Application of finite element method in industrial design, example of an electric motorcycle design project
  5. Correlative evaluation of the corrosion resilience and passivation properties of zinc and aluminum alloys in neutral chloride and acid-chloride solutions
  6. Will COVID “encourage” B2B and data exchange engineering in logistic firms?
  7. Influence of unsupported sleepers on flange climb derailment of two freight wagons
  8. A hybrid detection algorithm for 5G OTFS waveform for 64 and 256 QAM with Rayleigh and Rician channels
  9. Effect of short heat treatment on mechanical properties and shape memory properties of Cu–Al–Ni shape memory alloy
  10. Exploring the potential of ammonia and hydrogen as alternative fuels for transportation
  11. Impact of insulation on energy consumption and CO2 emissions in high-rise commercial buildings at various climate zones
  12. Advanced autopilot design with extremum-seeking control for aircraft control
  13. Adaptive multidimensional trust-based recommendation model for peer to peer applications
  14. Effects of CFRP sheets on the flexural behavior of high-strength concrete beam
  15. Enhancing urban sustainability through industrial synergy: A multidisciplinary framework for integrating sustainable industrial practices within urban settings – The case of Hamadan industrial city
  16. Advanced vibrant controller results of an energetic framework structure
  17. Application of the Taguchi method and RSM for process parameter optimization in AWSJ machining of CFRP composite-based orthopedic implants
  18. Improved correlation of soil modulus with SPT N values
  19. Technologies for high-temperature batch annealing of grain-oriented electrical steel: An overview
  20. Assessing the need for the adoption of digitalization in Indian small and medium enterprises
  21. A non-ideal hybridization issue for vertical TFET-based dielectric-modulated biosensor
  22. Optimizing data retrieval for enhanced data integrity verification in cloud environments
  23. Performance analysis of nonlinear crosstalk of WDM systems using modulation schemes criteria
  24. Nonlinear finite-element analysis of RC beams with various opening near supports
  25. Thermal analysis of Fe3O4–Cu/water over a cone: a fractional Maxwell model
  26. Radial–axial runner blade design using the coordinate slice technique
  27. Theoretical and experimental comparison between straight and curved continuous box girders
  28. Effect of the reinforcement ratio on the mechanical behaviour of textile-reinforced concrete composite: Experiment and numerical modeling
  29. Experimental and numerical investigation on composite beam–column joint connection behavior using different types of connection schemes
  30. Enhanced performance and robustness in anti-lock brake systems using barrier function-based integral sliding mode control
  31. Evaluation of the creep strength of samples produced by fused deposition modeling
  32. A combined feedforward-feedback controller design for nonlinear systems
  33. Effect of adjacent structures on footing settlement for different multi-building arrangements
  34. Analyzing the impact of curved tracks on wheel flange thickness reduction in railway systems
  35. Review Articles
  36. Mechanical and smart properties of cement nanocomposites containing nanomaterials: A brief review
  37. Applications of nanotechnology and nanoproduction techniques
  38. Relationship between indoor environmental quality and guests’ comfort and satisfaction at green hotels: A comprehensive review
  39. Communication
  40. Techniques to mitigate the admission of radon inside buildings
  41. Erratum
  42. Erratum to “Effect of short heat treatment on mechanical properties and shape memory properties of Cu–Al–Ni shape memory alloy”
  43. Special Issue: AESMT-3 - Part II
  44. Integrated fuzzy logic and multicriteria decision model methods for selecting suitable sites for wastewater treatment plant: A case study in the center of Basrah, Iraq
  45. Physical and mechanical response of porous metals composites with nano-natural additives
  46. Special Issue: AESMT-4 - Part II
  47. New recycling method of lubricant oil and the effect on the viscosity and viscous shear as an environmentally friendly
  48. Identify the effect of Fe2O3 nanoparticles on mechanical and microstructural characteristics of aluminum matrix composite produced by powder metallurgy technique
  49. Static behavior of piled raft foundation in clay
  50. Ultra-low-power CMOS ring oscillator with minimum power consumption of 2.9 pW using low-voltage biasing technique
  51. Using ANN for well type identifying and increasing production from Sa’di formation of Halfaya oil field – Iraq
  52. Optimizing the performance of concrete tiles using nano-papyrus and carbon fibers
  53. Special Issue: AESMT-5 - Part II
  54. Comparative the effect of distribution transformer coil shape on electromagnetic forces and their distribution using the FEM
  55. The complex of Weyl module in free characteristic in the event of a partition (7,5,3)
  56. Restrained captive domination number
  57. Experimental study of improving hot mix asphalt reinforced with carbon fibers
  58. Asphalt binder modified with recycled tyre rubber
  59. Thermal performance of radiant floor cooling with phase change material for energy-efficient buildings
  60. Surveying the prediction of risks in cryptocurrency investments using recurrent neural networks
  61. A deep reinforcement learning framework to modify LQR for an active vibration control applied to 2D building models
  62. Evaluation of mechanically stabilized earth retaining walls for different soil–structure interaction methods: A review
  63. Assessment of heat transfer in a triangular duct with different configurations of ribs using computational fluid dynamics
  64. Sulfate removal from wastewater by using waste material as an adsorbent
  65. Experimental investigation on strengthening lap joints subjected to bending in glulam timber beams using CFRP sheets
  66. A study of the vibrations of a rotor bearing suspended by a hybrid spring system of shape memory alloys
  67. Stability analysis of Hub dam under rapid drawdown
  68. Developing ANFIS-FMEA model for assessment and prioritization of potential trouble factors in Iraqi building projects
  69. Numerical and experimental comparison study of piled raft foundation
  70. Effect of asphalt modified with waste engine oil on the durability properties of hot asphalt mixtures with reclaimed asphalt pavement
  71. Hydraulic model for flood inundation in Diyala River Basin using HEC-RAS, PMP, and neural network
  72. Numerical study on discharge capacity of piano key side weir with various ratios of the crest length to the width
  73. The optimal allocation of thyristor-controlled series compensators for enhancement HVAC transmission lines Iraqi super grid by using seeker optimization algorithm
  74. Numerical and experimental study of the impact on aerodynamic characteristics of the NACA0012 airfoil
  75. Effect of nano-TiO2 on physical and rheological properties of asphalt cement
  76. Performance evolution of novel palm leaf powder used for enhancing hot mix asphalt
  77. Performance analysis, evaluation, and improvement of selected unsignalized intersection using SIDRA software – Case study
  78. Flexural behavior of RC beams externally reinforced with CFRP composites using various strategies
  79. Influence of fiber types on the properties of the artificial cold-bonded lightweight aggregates
  80. Experimental investigation of RC beams strengthened with externally bonded BFRP composites
  81. Generalized RKM methods for solving fifth-order quasi-linear fractional partial differential equation
  82. An experimental and numerical study investigating sediment transport position in the bed of sewer pipes in Karbala
  83. Role of individual component failure in the performance of a 1-out-of-3 cold standby system: A Markov model approach
  84. Implementation for the cases (5, 4) and (5, 4)/(2, 0)
  85. Center group actions and related concepts
  86. Experimental investigation of the effect of horizontal construction joints on the behavior of deep beams
  87. Deletion of a vertex in even sum domination
  88. Deep learning techniques in concrete powder mix designing
  89. Effect of loading type in concrete deep beam with strut reinforcement
  90. Studying the effect of using CFRP warping on strength of husk rice concrete columns
  91. Parametric analysis of the influence of climatic factors on the formation of traditional buildings in the city of Al Najaf
  92. Suitability location for landfill using a fuzzy-GIS model: A case study in Hillah, Iraq
  93. Hybrid approach for cost estimation of sustainable building projects using artificial neural networks
  94. Assessment of indirect tensile stress and tensile–strength ratio and creep compliance in HMA mixes with micro-silica and PMB
  95. Density functional theory to study stopping power of proton in water, lung, bladder, and intestine
  96. A review of single flow, flow boiling, and coating microchannel studies
  97. Effect of GFRP bar length on the flexural behavior of hybrid concrete beams strengthened with NSM bars
  98. Exploring the impact of parameters on flow boiling heat transfer in microchannels and coated microtubes: A comprehensive review
  99. Crumb rubber modification for enhanced rutting resistance in asphalt mixtures
  100. Special Issue: AESMT-6
  101. Design of a new sorting colors system based on PLC, TIA portal, and factory I/O programs
  102. Forecasting empirical formula for suspended sediment load prediction at upstream of Al-Kufa barrage, Kufa City, Iraq
  103. Optimization and characterization of sustainable geopolymer mortars based on palygorskite clay, water glass, and sodium hydroxide
  104. Sediment transport modelling upstream of Al Kufa Barrage
  105. Study of energy loss, range, and stopping time for proton in germanium and copper materials
  106. Effect of internal and external recycle ratios on the nutrient removal efficiency of anaerobic/anoxic/oxic (VIP) wastewater treatment plant
  107. Enhancing structural behaviour of polypropylene fibre concrete columns longitudinally reinforced with fibreglass bars
  108. Sustainable road paving: Enhancing concrete paver blocks with zeolite-enhanced cement
  109. Evaluation of the operational performance of Karbala waste water treatment plant under variable flow using GPS-X model
  110. Design and simulation of photonic crystal fiber for highly sensitive chemical sensing applications
  111. Optimization and design of a new column sequencing for crude oil distillation at Basrah refinery
  112. Inductive 3D numerical modelling of the tibia bone using MRI to examine von Mises stress and overall deformation
  113. An image encryption method based on modified elliptic curve Diffie-Hellman key exchange protocol and Hill Cipher
  114. Experimental investigation of generating superheated steam using a parabolic dish with a cylindrical cavity receiver: A case study
  115. Effect of surface roughness on the interface behavior of clayey soils
  116. Investigated of the optical properties for SiO2 by using Lorentz model
  117. Measurements of induced vibrations due to steel pipe pile driving in Al-Fao soil: Effect of partial end closure
  118. Experimental and numerical studies of ballistic resistance of hybrid sandwich composite body armor
  119. Evaluation of clay layer presence on shallow foundation settlement in dry sand under an earthquake
  120. Optimal design of mechanical performances of asphalt mixtures comprising nano-clay additives
  121. Advancing seismic performance: Isolators, TMDs, and multi-level strategies in reinforced concrete buildings
  122. Predicted evaporation in Basrah using artificial neural networks
  123. Energy management system for a small town to enhance quality of life
  124. Numerical study on entropy minimization in pipes with helical airfoil and CuO nanoparticle integration
  125. Equations and methodologies of inlet drainage system discharge coefficients: A review
  126. Thermal buckling analysis for hybrid and composite laminated plate by using new displacement function
  127. Investigation into the mechanical and thermal properties of lightweight mortar using commercial beads or recycled expanded polystyrene
  128. Experimental and theoretical analysis of single-jet column and concrete column using double-jet grouting technique applied at Al-Rashdia site
  129. The impact of incorporating waste materials on the mechanical and physical characteristics of tile adhesive materials
  130. Seismic resilience: Innovations in structural engineering for earthquake-prone areas
  131. Automatic human identification using fingerprint images based on Gabor filter and SIFT features fusion
  132. Performance of GRKM-method for solving classes of ordinary and partial differential equations of sixth-orders
  133. Visible light-boosted photodegradation activity of Ag–AgVO3/Zn0.5Mn0.5Fe2O4 supported heterojunctions for effective degradation of organic contaminates
  134. Production of sustainable concrete with treated cement kiln dust and iron slag waste aggregate
  135. Key effects on the structural behavior of fiber-reinforced lightweight concrete-ribbed slabs: A review
  136. A comparative analysis of the energy dissipation efficiency of various piano key weir types
  137. Special Issue: Transport 2022 - Part II
  138. Variability in road surface temperature in urban road network – A case study making use of mobile measurements
  139. Special Issue: BCEE5-2023
  140. Evaluation of reclaimed asphalt mixtures rejuvenated with waste engine oil to resist rutting deformation
  141. Assessment of potential resistance to moisture damage and fatigue cracks of asphalt mixture modified with ground granulated blast furnace slag
  142. Investigating seismic response in adjacent structures: A study on the impact of buildings’ orientation and distance considering soil–structure interaction
  143. Improvement of porosity of mortar using polyethylene glycol pre-polymer-impregnated mortar
  144. Three-dimensional analysis of steel beam-column bolted connections
  145. Assessment of agricultural drought in Iraq employing Landsat and MODIS imagery
  146. Performance evaluation of grouted porous asphalt concrete
  147. Optimization of local modified metakaolin-based geopolymer concrete by Taguchi method
  148. Effect of waste tire products on some characteristics of roller-compacted concrete
  149. Studying the lateral displacement of retaining wall supporting sandy soil under dynamic loads
  150. Seismic performance evaluation of concrete buttress dram (Dynamic linear analysis)
  151. Behavior of soil reinforced with micropiles
  152. Possibility of production high strength lightweight concrete containing organic waste aggregate and recycled steel fibers
  153. An investigation of self-sensing and mechanical properties of smart engineered cementitious composites reinforced with functional materials
  154. Forecasting changes in precipitation and temperatures of a regional watershed in Northern Iraq using LARS-WG model
  155. Experimental investigation of dynamic soil properties for modeling energy-absorbing layers
  156. Numerical investigation of the effect of longitudinal steel reinforcement ratio on the ductility of concrete beams
  157. An experimental study on the tensile properties of reinforced asphalt pavement
  158. Self-sensing behavior of hot asphalt mixture with steel fiber-based additive
  159. Behavior of ultra-high-performance concrete deep beams reinforced by basalt fibers
  160. Optimizing asphalt binder performance with various PET types
  161. Investigation of the hydraulic characteristics and homogeneity of the microstructure of the air voids in the sustainable rigid pavement
  162. Enhanced biogas production from municipal solid waste via digestion with cow manure: A case study
  163. Special Issue: AESMT-7 - Part I
  164. Preparation and investigation of cobalt nanoparticles by laser ablation: Structure, linear, and nonlinear optical properties
  165. Seismic analysis of RC building with plan irregularity in Baghdad/Iraq to obtain the optimal behavior
  166. The effect of urban environment on large-scale path loss model’s main parameters for mmWave 5G mobile network in Iraq
  167. Formatting a questionnaire for the quality control of river bank roads
  168. Vibration suppression of smart composite beam using model predictive controller
  169. Machine learning-based compressive strength estimation in nanomaterial-modified lightweight concrete
  170. In-depth analysis of critical factors affecting Iraqi construction projects performance
  171. Behavior of container berth structure under the influence of environmental and operational loads
  172. Energy absorption and impact response of ballistic resistance laminate
  173. Effect of water-absorbent polymer balls in internal curing on punching shear behavior of bubble slabs
  174. Effect of surface roughness on interface shear strength parameters of sandy soils
  175. Evaluating the interaction for embedded H-steel section in normal concrete under monotonic and repeated loads
  176. Estimation of the settlement of pile head using ANN and multivariate linear regression based on the results of load transfer method
  177. Enhancing communication: Deep learning for Arabic sign language translation
  178. A review of recent studies of both heat pipe and evaporative cooling in passive heat recovery
  179. Effect of nano-silica on the mechanical properties of LWC
  180. An experimental study of some mechanical properties and absorption for polymer-modified cement mortar modified with superplasticizer
  181. Digital beamforming enhancement with LSTM-based deep learning for millimeter wave transmission
  182. Developing an efficient planning process for heritage buildings maintenance in Iraq
  183. Design and optimization of two-stage controller for three-phase multi-converter/multi-machine electric vehicle
  184. Evaluation of microstructure and mechanical properties of Al1050/Al2O3/Gr composite processed by forming operation ECAP
  185. Calculations of mass stopping power and range of protons in organic compounds (CH3OH, CH2O, and CO2) at energy range of 0.01–1,000 MeV
  186. Investigation of in vitro behavior of composite coating hydroxyapatite-nano silver on 316L stainless steel substrate by electrophoretic technic for biomedical tools
  187. A review: Enhancing tribological properties of journal bearings composite materials
  188. Improvements in the randomness and security of digital currency using the photon sponge hash function through Maiorana–McFarland S-box replacement
  189. Design a new scheme for image security using a deep learning technique of hierarchical parameters
  190. Special Issue: ICES 2023
  191. Comparative geotechnical analysis for ultimate bearing capacity of precast concrete piles using cone resistance measurements
  192. Visualizing sustainable rainwater harvesting: A case study of Karbala Province
  193. Geogrid reinforcement for improving bearing capacity and stability of square foundations
  194. Evaluation of the effluent concentrations of Karbala wastewater treatment plant using reliability analysis
  195. Adsorbent made with inexpensive, local resources
  196. Effect of drain pipes on seepage and slope stability through a zoned earth dam
  197. Sediment accumulation in an 8 inch sewer pipe for a sample of various particles obtained from the streets of Karbala city, Iraq
  198. Special Issue: IETAS 2024 - Part I
  199. Analyzing the impact of transfer learning on explanation accuracy in deep learning-based ECG recognition systems
  200. Effect of scale factor on the dynamic response of frame foundations
  201. Improving multi-object detection and tracking with deep learning, DeepSORT, and frame cancellation techniques
  202. The impact of using prestressed CFRP bars on the development of flexural strength
  203. Assessment of surface hardness and impact strength of denture base resins reinforced with silver–titanium dioxide and silver–zirconium dioxide nanoparticles: In vitro study
  204. A data augmentation approach to enhance breast cancer detection using generative adversarial and artificial neural networks
  205. Modification of the 5D Lorenz chaotic map with fuzzy numbers for video encryption in cloud computing
  206. Special Issue: 51st KKBN - Part I
  207. Evaluation of static bending caused damage of glass-fiber composite structure using terahertz inspection
Downloaded on 25.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/eng-2022-0517/html
Scroll to top button