Reliability, Availability, and Maintainability Assessment-Based Sustainability-Informed Maintenance Optimization in Power Transmission Networks

Abstract

Reliable and resilient power transmission networks serve as vital for sustainable development and uninterrupted electricity supply. Effective maintenance programs are necessary to comply with reliability and sustainability requirements in the power sector. To that end, RAM (reliability, availability, and maintainability) assessments can provide efficient maintenance services that minimize adverse consequences and increase productivity at the lowest possible cost. We employ a statistical framework to evaluate RAM principles, including data acquisition, homogenization, trend hypothesis validation, and parameter estimation. The RAM evaluation of power transmission networks identifies primary bottlenecks in subsystems based on failure and repair behavior trends, which should be prioritized. To find the optimal maintenance policies for each subsystem, we adapt a Multi-Attribute Utility Theory (MAUT) approach, taking costs, availability, and dependability into account. The results of this approach can help improve the operational performance and sustainability of power transmission networks.

1. Introduction

Electricity technology and its development have led to a wide range of potential hazards associated with electricity for various stakeholders, including technologists, workers involved in electricity production, transmission, and distribution, as well as domestic and industrial consumers [1,2,3]. Power transmission is a vital component of modern society, enabling the uninterrupted supply of electricity to homes, businesses, and industries. The reliable operation of transmission networks is crucial for sustainable development and the continuous provision of electrical power. In this context, effective maintenance strategies are crucial for guaranteeing the reliability and sustainability of transmission networks [4].

1.1. Reliability, Availability, and Maintainability (RAM) Principle and Analysis

RAM analysis of power transmission networks is a crucial factor in meeting the growing demand for electricity and maintaining high service quality standards. To achieve efficient and resilient power transmission networks, the implementation of robust RAM strategies is of paramount importance. These methodologies enable proactive maintenance practices, reducing downtime and optimizing the overall system performance [5]. Within the RAM framework, reliability refers to the ability of transmission systems to perform their intended function without failure over a specified period. This involves assessing the probability of component failures, identifying potential failure modes, and designing systems to mitigate associated risks. Availability, on the other hand, measures the readiness of the system to deliver power when required, accounting for both planned and unplanned downtime. Maintainability is determined by the ability to repair damaged systems or components, with a higher maintainability corresponding to an increased capacity to effectively repair and restore the system [6].

RAM methodologies offer a structured approach to evaluate, optimize, and manage the reliability, availability, and maintainability of power transmission networks. These approaches encompass a range of techniques, including Condition-based Maintenance (CBM), Reliability-Centered Maintenance (RCM), Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Life Cycle Cost (LCC) analysis. RAM analysis serves multi-faceted objectives in operations and safety, with a key aim of identifying the most critical components that have the greatest impact on improving the overall system reliability [7].

1.2. RAM Analysis and Sustainability

Studies have demonstrated that well-designed and implemented maintenance processes can significantly contribute to sustainability efforts [8,9,10]. Optimizing maintenance procedures is crucial for achieving a sustainable future. Efficient and effective maintenance minimizes waste, reduces resource consumption, and optimizes material and energy use [11,12]. By ensuring that equipment and infrastructure are functioning optimally, maintenance activities can prevent unnecessary breakdowns, malfunctions, or inefficiencies that may result in resource waste or increased energy consumption [13]. This, in turn, can lead to cost savings and environmental benefits. A proficient maintenance system profoundly influences the performance of the maintained assets across the TBL—economic, environmental, and social. Given its impact on various sustainability aspects, maintenance is increasingly recognized as a process requiring sustainable management practices [14,15]. Traditionally, maintenance research has primarily focused on economic and technical considerations, overlooking the significant environmental and social implications [15,16,17].

1.3. Motivation and Research Objectives

Most maintenance and repair programs, as well as asset performance analyses in electrical distribution networks, are developed using manufacturer information or operating experience, both of which include uncertainties in determining optimal maintenance and repair policies. To overcome such issues, function-oriented techniques or root-oriented solutions such as RAM analysis could serve as a substantial approach, as pointed out in this research. The primary objective of the current study is to investigate how RAM techniques may efficiently identify and address problems influencing the performance of the distribution network’s power lines. This study intends to suggest strategies and interventions for enhanced performance by analyzing the relationship between RAM metrics and the overall network line performance. Likewise, this study aims to discover critical components, failure patterns, and optimal maintenance practices that can be optimized to improve the network line’s performance by conducting a detailed examination of the network’s RAM characteristics.

This study tackles the challenge of optimizing maintenance programs for power transmission networks. It proposes a novel approach that leverages a multi-stage statistical analysis for RAM assessment. This method surpasses traditional techniques by addressing inherent uncertainties and incorporating data homogenization, trend analysis, and autocorrelation tests. The resulting RAM evaluation identifies critical network components and informs the development of optimal maintenance policies utilizing MAUT. This data-driven approach concurrently considers maximizing RAM indicators and minimizing costs, ultimately leading to enhanced network performance and sustainability.

2. Literature Review

RAM analysis has become an essential aspect of electrical industries, aiming to ensure optimal performance, minimal downtime, and efficient maintenance of power systems. Numerous research papers have explored the methodologies and techniques to assess and improve RAM parameters (a summary of the literature is shown in

Table 1. Literature review on RAM methodologies.

Ref.	Case Study	Objective (s)	Methodology	RAM Model	MP	Main Finding (s)
[7]	Solar panel system	Evaluating a solar panel system’s reliability using parallel solar panel configuration.	PDFs, Weibull distribution	Yes	No	The reliability of each individual solar panel unit is 0.122 or 12.2% and preventive maintenance measures applied to the system were not effective, causing the reliability value to decrease over time.
[19]	Wind turbine systems	Improving the reliability of OWTS and minimize maintenance costs.	Mathematical models	Yes	No	Mathematical models used for structural health monitoring, combined with maintenance technologies, are the most effective approach for improving the reliability of OWTS while minimizing maintenance costs.
[20]	CHP generation systems	Minimizing the overall cost of capital and operating different CHP system designs.	Gradient-based nonlinear models	Yes	No	Integrating RAM parameters into the optimization process for biomass-driven CHP generation can improve system efficiency and maintain economic competitiveness.
[21]	Power plants	Evaluating power plant systems according to RAM principles.	PDFs	Yes	No	With the best possible equipment and maintenance practices, achieving the target availability of 99.9% for the IFMIF-DONES detritiation system is very challenging.
[22]	Power generation machines	RAM analysis for performance power generation machines.	Qualitative reliability model	Yes	No	Finding significant differences in availability between the machines: MPL1 (93.48%), MPL2 (82.19%), and MPL3 (70.55%). Identifying the need for improvement in maintenance performance, particularly availability, for MPL2 and MPL3.
[23]	Brazilian nuclear power plant	Developing an RAP specific to a PWR experimental nuclear installation.	RAP	Yes	No	The RAP applied to identify significant risk SSCs in long-term decay heat removal during a refueling shutdown identified 148 significant risk components from 393 failure modes analyzed.
[24]	Electric power station	Conducting a qualitative reliability model and LCC analysis.	FMECA, LCC analysis	Yes	No	By RAMS in maintenance decision policies, the number of failures can be reduced and their consequences minimized in the Afam electric power station.
[25]	Wind turbine	Developing an RAM analysis model for wind turbine subassemblies.	MOAM, Weibull	Yes	No	The study demonstrates the effectiveness and efficiency of the proposed approach in achieving secure operation and improving the reliability and availability of wind turbine systems.
[26]	Thermal power plants	An RAM analysis framework for a water system in a coal-fired power plant.	RBD FTA, and MBDP, PSO	Yes	No	PSO reportedly achieves an optimal availability of 99.9829% compared to 96.26% using traditional methods.
[27]	Coal-fired thermal power plant	Developing Markov-based availability simulation model in coal-fired thermal power plant.	Markov-based simulation	Yes	No	Focusing on optimizing single-burner mode operation to save up to 7% fuel consumption. The Markov approach was used to evaluate the availability of the BF system, showing that the boiler drum is the most critical equipment.
Current study	Power transmission networks	Identifying key subsystems, assessing RAM elements, and identifying an effective maintenance policy for power transmission networks.	Statistics-based models, key metrics such as MTTF, MTBF, MTTR, EDT	Yes	Yes	Refer to Section 4, “Results and Discussion”.

). Renewable electrical energy sources such as wind and solar power have gained significant popularity in recent years. The intermittent nature of these sources presents a major challenge in ensuring a stable and reliable electricity supply. This is where the importance of RAM study comes into play. A recent study reported by Agbakwuru et al. [18] analyzes SHM and maintenance technologies for OWTS by six indicators, one of which is potential RAM. Their study aims to improve the reliability of offshore wind turbine systems [19]. Another study in this field was conducted by Fitrianingtyas et al. [7]. They want to increase the reliability of a solar panel system by arranging the solar panels in parallel. The results show that arranging the solar panels in parallel increases the system’s reliability, as the failure of one or several solar panels does not affect the overall system performance. Sayed et al. [8] conducted research with the goal of analyzing the reliability and availability of various subassemblies in solar PV systems. The methods used included analyzing the failure rates and probabilities of various components. The results showed that the reliability of the PV module decreased over time, while the inverter subsystem had a very low reliability [8]. Rezaei et al. [20] present an enviro-economic optimization approach for CHP generation systems. The study focuses on the impact of RAM parameters on the system design and operation. The results show that integrating RAM parameters into the optimization analysis keeps biomass-fueled systems competitive economically. Research by Kowal [21] indicates that the availability of the deterioration system in normal operating conditions can exceed 99% if high-quality equipment is used and periodic maintenance reduces the aging effects by at least 80%. Nurcahyo et al. [22] conduct an RAM analysis for the performance evaluation of power generation machines in the banking sector. The main objective of a study by Gomes et al. [23] is to develop an RAP specific to a PWR experimental nuclear installation in Brazil, supported by an RAM model. The RAP, subsidized by an RAM model, will work with logical relationships between each component of the plant and provide a structured way to meet the regulatory requirements for licensing while complementing the plant safety analysis report. Chibu [24] emphasizes the importance of FMEA in minimizing failures and reducing costs. The paper suggests implementing RAM tools and methods to improve the maintenance systems in the Afam electric power station. El-Naggar et al. [25] present a developed technique for the RAM analysis of wind turbine subassemblies using a Weibull distribution. The study demonstrates the effectiveness and efficiency of the proposed approach in improving system reliability and availability. Jagtap et al. [26] in their study present an RAM analysis framework for evaluating the performance of a WCS in a coal-fired power plant. The study uses an RBD, FTA, and Markov birth–death probabilistic approach to assess the performance of the WCS. The results highlight the impact of the failure and repair rates on the system’s availability and propose an optimized maintenance schedule based on criticality levels. The study aims to assist decision-makers in planning maintenance activities and allocating resources effectively [26]. Jagtap et al. [27] conducted research to develop a Markov-based simulation model for analyzing the performance and optimizing the availability of the boiler–furnace system in a coal-fired thermal power plant. The study also applies particle swarm optimization to obtain the optimum availability parameters and suggests a maintenance strategy based on the optimized failure and repair rates [27].

Research Gaps

According to the literature, statistical- and probabilistic-based methods relying on operational data (e.g., failure, repair, outage, maintenance, cost, breakdown, etc.) are employed to examine and evaluate RAM indicators in power network systems. In that direction, a specific distribution function (such as Weibull or lognormal) is performed to fit RAM indices, which may result in some uncertainties throughout their calculations. To tackle such issues, a developed model based on data homogeneity tests, trend tests, and autocorrelation tests is adopted for evaluating RAM indicators in power network systems. On the other hand, few studies have taken advantage of the RAM technique’s results to develop an optimal maintenance policy in power systems, which serves as one of the study’s novelties. In other words, current power system maintenance and repair programs rely on manufacturer information or operational experiences, while employing RAM analysis methods in conjunction with existing methods, which may assist in optimizing and improving maintenance and repair programs in power network systems. As a result, it is expected that optimizing maintenance programs in power systems would play a significant role in lowering costs, minimizing risky incidents and breakdowns, and enhancing network availability and sustainability. In this study, MAUT is applied to establish an optimal maintenance policy by maximizing RAM indicators while minimizing costs.

In a nutshell, the primary objectives and contributions of the current research are as follows:

• Performance evaluation of power transmission networks

To successfully implement performance evaluation programs such as Total Productive Maintenance (TPM), Business Continuity Management (BCM), and so on, engineering tools in particular RAM principles can play an important role. RAM analysis leads to the identification of significant bottlenecks and optimization of maintenance for power transmission networks.

• Addressing Uncertainties in Classical Methods

While existing research utilizes classical statistical and probabilistic methods based on operational data for RAM evaluation in power transmission networks, these approaches can introduce uncertainties. This is often due to fitting specific distribution functions (e.g., Weibull or lognormal) to RAM evaluation.

Multi-Stage Statistical Approach-Based RAM Analysis

To overcome classical methods’ limitations, this study presents a data-driven framework (replace with classical statistical and probabilistic methods). This framework leverages a multi-stage statistical approach-based RAM analysis of power transmission networks that incorporates:

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Data homogenization tests: These tests ensure the data used for analysis are consistent and comparable. This minimizes the influence of external factors and improves the accuracy of RAM calculations.

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Trend tests: by identifying potential degradation or improvement trends in equipment performance, these tests enable proactive maintenance strategies that target components most susceptible to failure.

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Autocorrelation tests: these tests account for potential dependencies within the data, leading to more reliable RAM estimations.

• Optimizing Maintenance Beyond RAM Analysis

This research goes beyond adapting a multi-stage statistical approach-based RAM analysis by integrating the obtained results with maintenance optimization. Unlike existing maintenance programs for power transmission networks that rely solely on manufacturer information or operational experience, this study proposes an RAM-based maintenance policy optimization approach utilizing MAUT. This approach allows for the following:

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Balancing Multiple Objectives: the MAUT framework considers various factors simultaneously, such as maximizing RAM indicators, while minimizing maintenance costs.

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Data-driven Decision Making: by incorporating RAM analysis results, this approach creates a more informed and data-driven basis for maintenance planning, leading to improved resource allocation and cost-effectiveness within power transmission networks.

3. RAM Methodology

The proposed framework, as shown in Figure 1, consists of three main steps: system description, statistical analysis, and maintenance optimization. The first step, system description, involves identifying the critical components. To evaluate RAM, this step depends on obtaining the necessary data, such as failure and repair data, maintenance cost data, and so on. In the reliability analysis process, important tests such as homogeneity and trend tests are conducted to determine the appropriate statistical model. The second step involves statistical analysis, which is essential for understanding the RAM characteristics of the system. The final step is maintenance policy optimization, which utilizes MAUT to balance various performance criteria simultaneously. This allows for the development of an optimal maintenance strategy that considers the trade-offs between different objectives. Below, we provide a detailed explanation of each stage of the proposed framework.

3.1. System Description

In power transmission networks, the primary function is the reliable conveyance of electrical power from the high-voltage transmission systems to the medium-voltage distribution networks. This process involves the transfer of electricity over medium-voltage networks, typically ranging from 63 kV to 132 kV, playing a crucial role in ensuring the reliable and continuous supply of power to the end consumers. The key components of this network include conductors, towers, insulators, and associated protection systems. Conductors, typically made of aluminum or copper, carry the electrical current from the power generation source to the end users. Electrical towers are reticular steel structures that function as aerial supports for the transmission and distribution of electrical power, with their shape and size varying based on the voltage of the distributed energy. Insulators physically and electrically separate the power lines from the ground, maintaining the necessary air gap between the energized, bare conductor and ground to prevent electrical shorts and flashovers.

The reliable operation of these critical components is essential for the continuous and efficient transmission of electricity from the high-voltage networks to the medium-voltage distribution systems, ultimately ensuring a reliable and uninterrupted power supply to the end consumers. Protective relays are used to monitor the transmission system and detect any abnormal operating conditions or faults. They act as sensors and provide signals to the protective devices to initiate protective actions, such as tripping circuit breakers or activating alarms. The configuration of the transmission system is designed to ensure redundancy and reliability. Multiple parallel circuits are often employed to minimize the impact of failures or maintenance activities on the overall system. This redundancy allows for the continuous delivery of power even if one circuit or component experiences a failure. Figure 2 shows the schematic of a power transmission network process.

3.2. Statistical Framework-Based RAM Analysis

This investigation employs a statistical framework to evaluate RAM characteristics. The framework entails a three-stage sequential process:

3.2.1. Data Collection and Homogeneity

The initial stage encompasses two critical processes in RAM analysis: data acquisition and homogenization. The required data pertain to operational details, including TBFs and TTRs, along with various maintenance cost categories such as corrective and preventive maintenance. Following data acquisition and classification, a minimum threshold for operational data suitable for RAM analysis is established. In instances where a unit or equipment possesses data below this threshold, statistical approaches like mixture or Bayesian models may be recommended for analysis [28,29].

Subsequently, homogeneous groups are formed based on a risk analysis checklist adapted from a well-regarded source, such as the NASA Manager’s Handbook [28]. Units within each group should share identical characteristics and experience comparable operational and environmental stresses [30]. This study considered various factors that might influence data homogeneity, including the unit’s location, environment, manufacturer, installation, and design characteristics, as well as the software and procedures used. If the data exhibit heterogeneity (variability), we can address this in two ways: segmentation or covariate adjustment. Segmentation involves dividing the data into smaller, more homogeneous subsets based on these factors. Alternatively, covariate-based models can be employed to statistically account for the influence of these external variables while analyzing the entire dataset [31].

3.2.2. Trend and Dependency Analysis

The significance of trend tests in evaluating asset degradation or improvement is well documented in the literature [30,31,32,33]. To evaluate the hypothesis of the trend nature of repair and failure datasets, a range of tests are utilized [34,35,36]. The primary trends observed in each unit can be categorized as concavity (downward curvature), convexity (upward curvature), or linearity (straight line), which can be identified using either graphical or statistical trend tests [28]. Mann–Kendall, Laplace, AD Military Handbook (MIL-HDBK-781), and graphical tests like the Total Time on Test (TTT) plot are examples of prevalent tests [28].

The following hypotheses are part of the statistical hypothesis testing framework used in this study to determine whether trends are present in the data:

H0. 

The data are not trending (non-monotonic).

H1. 

The data show a trend, a monotonic trend.

The Military Handbook and Laplace tests are first applied by the trend analysis node of the decision framework. The test statistic U, which has a chi-square distribution with 2(n − 1) degrees of freedom (df), is used in the Military Handbook test, where n is the sample size [34]. The following judgment criteria are then applied when comparing the trend test findings to the statistical parameter U:

$$\mathrm{U}=2\sum _{\mathrm{i}=1}^{\mathrm{n}-1} \ln \left(\frac{{\mathrm{T}}_{\mathrm{n}}}{{\mathrm{T}}_{\mathrm{i}}}\right)$$

(1)

where n is the total failures, T_n is the latest time failure, and T_i is the ith time failure. The U statistic is computed based on the empirical data, while the critical value $X_a^2$, df can be obtained from the chi-square distribution using the df. If the calculated statistic is less than or equal to $X_a^2$, df, the null hypothesis (H0) is considered plausible. Conversely, if the statistic exceeds $X_a^2$, df, the null hypothesis is rejected, and the alternative hypothesis (H1) is considered plausible.

Like the test found in the military manual, the Laplace test relies on the null hypothesis (H0₂) of “no-trend in data” and the alternative hypothesis of “trend in data”. These theories are computed using the subsequent procedure.

$$\mathrm{L}\mathrm{A} \left(\mathrm{Laplace}\right)=\sqrt{12.N\left(t_k\right)}\left(\frac{\sum _{i=1}^k t_i}{\tau \cdot N\left(t_k\right)}-\frac{1}{2}\right)2_i \mathrm{where} \left\{k=n-1,\tau =t_n\right\}$$

(2)

The null hypothesis H0₂ is rejected in the Laplace test when the absolute value of |U| > Za/2 is at the significance level of a%. The Laplace trend test is more appropriate for a log-linear intensity function, whereas the Military Handbook test is effective for NHPP power law intensity values. Even if the data show a Renewal Process (RP), which indicates that there is no trend, these tests typically reject the null hypothesis of no trend. This highlights how incorrectly traditional trend tests can detect patterns in specific types of data.

If the initial trend tests (H0₁ and H0₂) reject the null hypothesis, the next step is to apply the Mann–Kendall test (H0₃) to determine whether the failure data follow a Random Process (RP) or an NHPP model. Rejection of the null hypothesis (RP) in the Mann–Kendall test indicates the presence of a trend in the data, which can be further characterized.

$${\mathrm{M}}_{\mathrm{M}\mathrm{a}\mathrm{n}\mathrm{n}}=\frac{\mathrm{M}-\mathrm{n}(\mathrm{n}-1)/4}{\sqrt{\left(2{\mathrm{n}}^3+3{\mathrm{n}}^2-5\mathrm{n}\right)}/72}$$

(3)

At the percentage level (5%), the null hypothesis (H0₃) is rejected if |M_Mann| > Z_a/2.

When the initial trend tests (Laplace or Military Handbook) fail to reject the null hypothesis, the next step is to apply the AD trend test or graphical techniques like the TTT plot. The AD test can be estimated using the scale parameter, shape parameter, and running time (t), with the cumulative failure function defined accordingly. These alternative approaches are appropriate for situations where the previous trend tests did not detect a significant trend in the data:

$$\mathrm{A}\mathrm{D}=-\frac{1}{n}\left[{\sum }_{i=1}^n (2i-1)\left(\mathrm{l}\mathrm{n}\left(\frac{T_i-T_0}{T-T_0}\right)+\mathrm{l}\mathrm{n}\left(1-\frac{T_{n+1-i}-T_0}{T-T_0}\right)\right)\right]-n$$

(4)

At the percentage level (5%), the null hypothesis (H0₃) is rejected if |D| > 2.492.

When the data exhibit a pattern in failure occurrences, using statistical distributions for RAM analysis may not be appropriate. In such cases, a non-stationary model based on the PLP, such as the NHPP, can be more suitable.

$$\rho (t)=\frac{\beta }{\alpha }(\frac{t}{\alpha }{)}^{\beta -1}\alpha ,\beta >0$$

(5)

The cumulative failure function for the NHPP model is defined based on the PLP parameters. Specifically, the scale parameter is represented by λ, the shape parameter is represented by β, and the running time is denoted as t:

$$H(\mathrm{t})={\left(\frac{t}{\alpha }\right)}^{\beta }$$

(6)

3.2.3. Parameter Estimation

The final stage of the framework involves parameter estimation to select the appropriate reliability model, such as the HPP, NHPP, or Random Process (RP). This study focuses on the PLP model, a type of NHPP.

To estimate the scale (λ) and shape (β) parameters of the PLP model, the Maximum Likelihood Estimation (MLE) function is employed, leveraging the total running time (tn) and the number of failure events (n).

$$\beta =\frac{n}{\sum _{i=1}^n ln\left(\frac{t_n}{t_i}\right)}$$

(7)

$$\lambda =\frac{t_n}{n^{\frac{1}{\beta }}}$$

(8)

Additionally, confidence intervals (upper and lower bounds) for the estimated scale (λ) and shape (β) parameters can be calculated using Equations (7) and (8). Analyzing the shape parameter (β) provides valuable insights—a value less than 1 indicates a decreasing failure rate, while a value greater than 1 suggests an increasing failure rate. When the true value of β is unknown, appropriate asymptotic confidence intervals can be used for estimation purposes, as described in the referenced literature [37,38]. RAM analysis is carried out using Minitab statistical software (version 20.2).

3.3. Maintenance Policy Optimization

The proposed maintenance optimization model in this study employs MAUT as the decision-making framework. MAUT was selected due to its capability to effectively structure management scenarios and its strong theoretical basis in expected utility theory, as discussed in the work of Garmabaki et al. [39]. In the present case, the objective function aims to minimize costs while maximizing reliability and availability. The general form of the MAUT function is presented, which captures these competing objectives in a comprehensive manner. Generally, MAUT is defined as follows:

$$\begin{array}{cc}U\left(x_1,x_2,x_3,\dots ,x_n\right)\hfill & =f\left[u_1\left(x_1\right),u_2\left(x_2\right),\dots ,u_n\left(x_n\right)\right]\hfill \\ & =\sum _{i=1}^n w_i\cdot u_i\left(x_i\right)\hfill \\ & {\displaystyle \sum _{i=1}^n} w_i=1\hfill \end{array}$$

(9)

where U represents the overall MAUT function. This function aggregates the individual utility functions (u_i) associated with each considered criterion (e.g., reliability, availability, cost) into a single, composite value. The summation symbol (∑) denotes the calculation of this overall utility by summing the contributions from each individual criterion (i). These individual contributions are captured by the terms w_i * ui(xi). Here, w_i represents the weight assigned to a specific criterion “i”. The relative significance of each criterion in the decision-making process is reflected in these weights. A higher weight might be assigned to reliability (wi) compared to cost, reflecting a prioritization of equipment uptime. Finally, ui(xi) represents the individual utility function for criterion “i” evaluated at level “xi.” In simpler terms, ui(xi) denotes the “utility,” or the perceived value, associated with a specific level of performance (xi) for a particular criterion (i). For example, ui(xi) could represent the utility of a specific level of reliability (xi). By maximizing the overall MAUT function (U), we can identify the maintenance strategy that provides the optimal balance between availability, dependability, and cost for our specific needs.

4. Results

4.1. Characteristic Statistics

Table 2. Failure and repair descriptive statistics.

Operational Data	Subsystem	Mean (h.)	StDev	CoefVar	Min.	Max.	Skewness	Kurtosis
TBF dataset	Cables	16,179	7489	46.29	7800	26,544	0.38	−1.35
	Insulators	1386	2535	182.83	24	10,824	2.36	5.12
	Joints	3997	3490	87.33	24	7920	−0.11	−2.26
	Jumpers	31,078	17,139	55.15	7152	51,972	−0.16	−1.56
	Relays	2895	2611	90.18	456	6648	0.68	−1.57
	Wires	6473	3290	50.82	1176	12,792	0.28	0.03
	Transient connections	3044	1991	65.40	576	8592	1.01	1.95
TTR dataset	Cables	12.71	2.81	22.11	9.00	17.00	0.22	−0.83
	Insulators	4.429	3.329	75.16	1.000	12.000	0.98	−0.28
	Joints	5.33	2.94	55.20	2.00	10.00	0.64	−0.30
	Jumpers	10.13	6.60	65.18	3.00	23.00	1.18	0.91
	Relays	0.6857	0.2410	35.15	0.3000	1.0000	−0.37	−0.50
	Wires	4.727	2.936	62.10	1.000	8.000	−0.08	−1.96
	Transient connections	0.6358	0.3458	54.39	0.1000	2.0000	1.11	3.37

provides the descriptive statistics of failure or TBFs data pertaining to the operation of power transmission networks. The following are the primary observations:

(a)

For cables, insulators, joints, jumpers, relays, wires, and transient connections, the corresponding mean TBFs were estimated at 16179, 1386, 3997, 31078, 2895, 6473, and 3044 h.

(b)

Approximately 120 h was the coefficient of variation (CoefVar) for the entire process. Standard deviations (StDevs) were highest for the separators.

(c)

Transient connections and relays had the shortest repair times, at 0.1 and 0.3 h, respectively. Jumpers assessed their maximal failure times to be 23 h.

(d)

The values in the repair distributions have a positive skew. This suggests that the tail on the right side is longer than the tail on the left.

The cumulative behavior of the various power transmission network components’ failures is depicted in Figure 3. Insulators and relays have a higher failure rate in the initial stages of operation. Furthermore, there is a growing pattern of failures that center on jumpers’ time interval ends. The behavior of the other components is nearly stable, suggesting a steady state that is not subject to significant fluctuations over time.

4.2. Analysis of Trends and Correlations

The findings presented in

Table 3. The failure data’s trend test.

Subsystem	TBF Dataset					Final Decision
	MIL-Hdbk −189 Test (H01)	Laplace’s Test (H02)	Decision of H01 and H02 at the 5% Significant Level	Mann–Kendall Test (H03)	AD Test/TTT Plot (H04)
Cables	8.31 (0.48)	0.38 (0.70)	-	-	-	Not rejected
Insulators	309.46 (0.000)	−8.72 (0.000)	AD test/TTT plot	-	72.02 (0.000)	Rejected
Joints	25.31 (0.027)	−0.66 (0.508)	AD test/TTT plot	-	2.16 (0.075)	Not rejected
Jumpers	8.79 (0.31)	1.24 (0.216)	-	-	-	Not rejected
Relays	17.93 (0.236)	−1.35 (0.178)	-	-	-	Not rejected
Wires	18.48 (0.889)	−0.48 (0.634)	-	-	-	Not rejected
Transient connections	48.94 (0.147)	−2.67 (0.008)	AD test/TTT plot	-	4.13 (0.008)	Rejected

The trend test statistics’ p-values are displayed by the values in the brackets.

summarize the trend and correlation tests conducted to investigate the “Independent and Identically Distributed (IID)” hypothesis for the power transmission network subsystems. The failure trends were identified using well-established tests, including the AD test or TTT plot (H0₄), which was found to be significant at the 5% level, Laplace’s test (H0₂), Mann–Kendall test (H0₃), and the MIL-Hdbk-189 test (H0₁). The results presented in Table 3 indicate that for most of the power transmission network subsystems, the null hypothesis (H0) of independence and identical distribution (IID) was “Not rejected” based on the Laplace (H0₂) and MIL-Hdbk-189 (H0₁) tests. This suggests these subsystems can be considered IIDs, allowing the use of Random Process (RP) models and distributions to assess reliability under the independence assumption. However, for the turbine subsystem, the final decision rejected the null hypothesis (H0), despite the MIL-Hdbk-189 (H0₁) and Laplace’s (H0₂) tests indicating “Not rejected.” A similar situation was observed for the transient connections and insulators, where additional trend tests like the AD or TTT plot were required to make the ultimate decision. Interestingly, the null hypothesis (H0) was “Not rejected” for the joints subsystem under the AD test. These findings suggest that while most subsystems can be considered IIDs, some require more comprehensive trend analysis, such as the AD or TTT tests, to make a definitive conclusion about the validity of the IID assumption.

The autocorrelation tests are used for key subsystems of power transmission networks, as shown in Figure 4a–g. Considering that the t-test results fall within the confidence level range (−1.96 < 95% confidence level < +1.96), it may be inferred that there is no correlation between the failure data and the plausibility of the null hypothesis. Additionally, for different lags, the same findings as the graphical method can be found. In other words, for different lags, e.g., 1, 2, 3, etc., the failure data for Figure 4a–g are within the acceptable range of the correlation values (−0.4 to +0.4). As a result, the failure data pursue the “IID” assumption with a 5% significance level. Additionally, when evaluating the reliability of other statistical models, such as HPP, NHPP, and BPP, in power transmission networks, the RP model may be particularly helpful.

4.3. Best-Fit Model

The analysis of the best-fit models for estimating the failure rates and reliability of critical power transmission network subsystems was conducted using Random Process (RP) distributions. To determine the best-fit model, the AD test was used, with a smaller statistical value indicating a better model fit. The MLE technique was then employed to estimate the parameters of the selected models, as shown in

Table 4. The best-fit model for failure data.

Operational Data	Unit	MLE Method	AD Test	Model Parameters
TBF data	Cables	IID—RP—3P-Weibull	1.97 *	Shape = 2.33, Scale = 16,857.2
	Insulators	No IID-NHPP	-	Shape = 0.77, Scale = 476.97
	Joints	IID—RP—3P-Weibull	2.183 *	Shape = 2.736, Scale = 8867.99
	Jumpers	IID—RP—Weibull	2.034	Shape = 2.47, Scale = 7278
	Relays	IID—RP—Weibull	1.991	Shape = 1.14, Scale = 3042.91
	Wires	IID—RP—Weibull	1.291	Shape = 2.16, Scale = 7296.52
	Transient connections	No IID-NHPP	-	Shape = 0.63, Scale = 1238.75

* indicates the lowest value.

. The results indicate that the two- and three-parameter Weibull distributions were found to be the best-fit models for cables, joints, jumpers, relays, and wires. In contrast, the NHPP model was identified as the best-fit model for insulators and transient connections, exhibiting the lowest AD test value. Furthermore, the analysis of the TTR data revealed that the lognormal model had the best fit, with the lowest AD test value, for the power transmission network subsystems. These best-fit models and their associated parameter estimates were then utilized in the subsequent failure rate and reliability analyses for the critical power transmission network components.

The analysis of the best-fit distributions for failure and reliability assessment included evaluating various potential models, such as normal, lognormal, logistic, Weibull, exponential, and smallest extreme value, as illustrated in Figure 5a–e. The results indicate that the three-parameter Weibull (3P-Weibull) distribution provided the best fit for cables, joints, jumpers, relays, and wires, as shown in the respective figures. This comprehensive evaluation of the various distribution models allowed for the identification of the most appropriate statistical representations for the failure and reliability characteristics of these critical power transmission network subsystems.

4.4. The Results of RAM Analysis

Figure 6 depicts the reliability and maintainability functions of subsystems within power transmission networks, modeled using the NHPP and Weibull distributions. The reliability functions for insulators, transient connections, and relays exhibit a sharp decline, approaching zero within 3000, 6500, and 8500 h of operation, respectively. Similarly, the reliability of other subsystems, such as cables, joints, insulators, jumpers, and wires, often reaches a zero value around 9000 operating hours. Notably, due to the series configuration of the entire system, the overall reliability value decreases to zero within 4000 h of operation, emphasizing the necessity of increased attention and focus on the critical units within the system.

The electromechanical components’ maintainability index in the power transmission networks was evaluated using the repair rate results. Maintainability basically illustrates the period needed to return the system to operational status in each percentage of its overall failures. For instance, the TTR values for subsystems such as cables, jumpers, wire joints, insulators, transient connections, and relays from Figure 7 are approximately 14, 13, 7, 7, 1, and 1 h, respectively, to estimate the maintainability more than 80%. Consequently, the drive should be restarted with the mean TTRs lowered. Establishing efficient repair scheduling is one strategy to reduce repair times. Effective repair scheduling requires the consideration of several key factors, including worker expertise, advanced inventory planning, and well-designed logistics. The prescribed maintenance procedures encompass not only the specific repair methods but also the availability of essential maintenance resources, such as personnel, spare parts, tools, and manuals. Additionally, the preventive maintenance program, skill levels of the maintenance crew, and the size of the crew itself must all be considered when planning and executing repairs.

Figure 8 displays the plot of the average availability of the seven subsystems that make up power transmission networks. The MTTR and MTBF were included as the primary downtime parameters for availability estimation for this reason. It is evident that these components are calculated to be more than 99% available.

4.5. Maintenance Policy Optimization

To validate the RAM analysis, the results are adapted to various maintenance policy scenarios in power transmission networks. In fact, through MAUT decision techniques, the various RAM and cost scenarios are projected by defining a sensitivity of actual values of the “Best value” and “Worst value” for RAM and cost in a power transmission network, and then utility (U) for each maintenance policy are applied based on the assigned weights and value ranges for each criterion to find the optimal maintenance policy. Let us consider an example where we have a range of values for cost, reliability, and availability for insulators in power transmission networks to determine the optimal maintenance policy. According to experts’ perspectives about insulators, the following ranges are assumed, with each criterion such as reliability (R), availability (A), and cost (C) specified as follows:

C: Best value = $300, worst value = $1500;

R: Best value = 0.9 (on a scale of 0–1), worst value = 0.6;

A: Best value = 0.95 (on a scale of 0–1), worst value = 0.8.

We assign weights to each criterion as follows: C: 0.3, R: 0.4, and A: 0.3.

Now, we calculate the utility values for each policy based on the assigned weights and the value ranges for each criterion.

Now, let us consider three maintenance policies: maintenance policy (I), maintenance policy (II), and maintenance policy (III).

I: C: $600, R: 0.8, and A: 0.9;

II: C: $900, R: 0.7, and A: 0.85;

III: C: $1200, R: 0.6, and A: 0.8.

We can now calculate the overall utility values for each policy based on the assigned weights and the utility functions for each criterion:

-

Based on maintenance policy I, we have

U total = (0.3 × U(C)) + (0.4 × U(R)) + (0.3 × U(A)).

For C:

U(C) = (C worst − C)/(C worst − C best);

U(C) = (1500 − 600)/(1500 − 300) = 0.571.

For R:

U(R) = (R − R worst)/(R best − R worst);

U(R) = (0.8 − 0.6)/(0.9 − 0.6) = 0.667.

For A:

U(A) = (A − A worst)/(R best − A worst);

U(A) = (0.9 − 0.8)/(0.95 − 0.8) = 0.625.

Utility = (0.3 * 0.571) + (0.4 * 0.667) + (0.3 * 0.625) = 0.628.

For maintenance policy II and III, follow a similar calculation process to determine their utility values.

Based on these calculations, we can compare the overall utility values for each policy. The policy with the highest utility value represents the optimal maintenance policy. Performing the calculations, the following results were obtained:

For maintenance policy I: U total = 0.628;

For maintenance policy II: U total = 0.590;

For maintenance policy III: U total = 0.555.

In this case, it can be seen that maintenance policy (I) has the highest overall utility value of 0.628. Therefore, this maintenance policy represents the optimal policy based on the assigned weights and the utility functions for cost, reliability, and availability. Likewise, the chosen maintenance policy for each subsystem of power transmission networks was weighed against the results from the current maintenance programs and policies. The overarching discussion and investigations based on the available documents, the results of the current research, and the opinions of power experts revealed that the implemented policies can have a significant impact on maintenance programs in power transmission networks in the medium to long term.

5. Conclusions

Electricity transmission is a critical section in the transition of networks towards sustainable energy sources. One of the primary steps in applying sustainability principles to power transmission protection is to assess the performance of the equipment. In this work, the performance of a power transmission network is evaluated using RAM principles. A systematic decision framework utilizing a statistical approach is employed to evaluate the reliability and maintainability parameters. The RAM evaluation of the power transmission network identified the primary bottlenecks based on subsystem failure and repair behavior trends, which should be prioritized. To select the optimal maintenance policy, an MAUT is utilized, considering reliability, availability, and costs. Furthermore, various levels of reliability focusing on the transmission network policy are examined to suggest the appropriate maintenance intervals.

5.1. Limitations of the Study

This study demonstrates the value of RAM analysis and MAUT for optimizing maintenance in power transmission networks. However, some limitations require consideration.

The accuracy of the maintenance optimization model relies heavily on the representativeness of the cost data used. Future research should explore more robust methods for estimating and incorporating different maintenance cost categories.

Additionally, the current study applies the framework to a specific context. Further research applying the framework to diverse transmission network configurations would broaden the generalizability of the findings. This would allow for a more comprehensive understanding of the framework’s effectiveness across various network types.

5.2. Implications of the Work

The proposed framework offers significant advantages for power transmission network maintenance. By analyzing data to optimize maintenance plans, utilities can prioritize activities, reduce costs, and improve overall network reliability and availability. The framework’s ability to identify critical components and failure patterns allows for targeted asset management strategies, focusing resources on the most vulnerable equipment. This leads to reduced downtime from unplanned outages, enhancing efficiency and customer satisfaction. Furthermore, the framework’s potential to incorporate environmental factors into the decision-making process contributes to sustainable operations. This is achieved by improving reliability, reducing maintenance costs, and promoting environmentally friendly practices. Finally, standardization and global adoption of the framework can lead to more consistent and effective maintenance practices across the entire power transmission industry. Key implications and engineering applications for the power transmission industry include implementing performance evaluation programs like TPM and BCM using RAM-based analysis, identifying critical components and failure patterns for maintenance optimization, upgrading and optimizing current maintenance plans and policies based on cost and RAM analysis, enhancing sustainability through improved RAM, reduced costs, and environmental considerations, and providing practical standardizations and regulations for consistent maintenance practices.

5.3. Future Research Directions

This study successfully applied RAM analysis and MAUT for power transmission network maintenance. Several promising avenues exist for further exploration.

One future direction involves expanding the MAUT model. Currently, it considers cost, reliability, and availability. Future research can integrate additional factors such as safety, environmental impact, and social impact. Assigning weights to these factors will necessitate careful consideration of stakeholder preferences.

Another promising direction lies in dynamic optimization. This study assumes fixed reliability and cost values for maintenance policies. Future research can explore dynamic models that account for how these values change over time. Factors like aging infrastructure, environmental variations, and technological advancements can all influence these values. By creating dynamic models, we can enable more adaptable maintenance strategies.

Finally, the integration of machine learning algorithms presents a valuable opportunity. These algorithms can be incorporated to predict future failures and optimize maintenance scheduling based on real-time data. Anomaly detection can also be employed to identify early signs of equipment degradation.