Exploring the Influence of the Parameters’ Relationship between Reliability and Maintainability for Offshore Wind Farm Engineering

Abstract

The two main research goals of this study are to develop a relationship diagram between the parameters of reliability and maintainability and to investigate the impact of reliability and maintenance on engineering design costs. In this study, we use the theory of reliability and maintainability parameters to derive the relationship between the parameters using block diagrams. Compared with onshore wind farms, offshore wind farms have higher reliability requirements, but the maintenance degree of offshore wind farms is lower due to environmental factors. This study proposes an important concept of reliability and maintenance for value engineering, which can help system design engineers and project engineers integrate reliability concerns in the design phase and operation and maintenance phase.

1. Introduction

Offshore wind power projects focus on engineering design, operation, and maintenance, and various controls are in place to maintain and improve quality. However, quality control alone is insufficient to ensure long-term performance under field operating conditions. The project’s original design may not be sufficient to achieve the goal of long-term failure-free wind farm operation under different area operating conditions. One of the reasons for this is that designers do not have a concern for “reliability” and do not take working conditions, environmental stresses, or operating life into account in the design phase of the product.

The Advisory Group on Reliability of Electronic Equipment (AGREE), established by the U.S. Department of Defense in 1952, defined product reliability based on research on the reliability of electronic equipment as: “Reliability is the probability of a product performing a specified function under given conditions for a specified period without failure” [1,2].

Reliability theory, like statistical quality control, is a field of study based on probability and statistics, and its contents can be broadly summarized into three: “reliability mathematics”, “reliability engineering”, and “reliability management.” “Reliability mathematics” is a tool and language to describe reliability, which is the essence of this paper. “Reliability engineering” is a professional technique to perform reliability design, manufacturing, testing, and verification, e.g., DNV GL. DNV GL was created in 2013 due to a merger between two leading organizations in maritime—Det Norske Veritas (Norway) and Germanischer Lloyd (Germany). It is also the largest technical consultancy and supervisory to the global renewable energy (particularly wind, wave, tidal, and solar) and oil and gas industry. The DNVGL-ST-0145 is one of the DNV GL’s offshore standards and focuses on the offshore substation. DNVGL-ST-0145 describes the reliability of offshore substations as follows [3]:

(a)

Substation reliability is the probability that the offshore substation power system can collect, transform, and deliver the active power produced by the wind turbine generators for the period intended, under the operating conditions encountered.

(b)

The design of the substation performance focuses on optimizing the substation reliability based on the procedures shown in Figure 1.

The power distribution system is composed of many electrical equipment components, and the failure of any element may cause discontinuity in the power supply. If the system is made up of many parts in series, when any system component fails, it causes the whole system to fail [4]. Reliability is most often expressed as the frequency of system interruptions and the expected duration of interruptions over a year, i.e., counting the number of hours of system interruptions over a year under regular operation. By collecting instantaneous and continuous system outage, component failure, and outage rate information, the overall system reliability indices for any node in the system are calculated using commercial reliability software to investigate the sensitivity of these indices to parameter variations. With these results, economy and reliability can be considered to select the best electrical system design [5]. Therefore, by adopting a reliability-centered maintenance approach, all departments can be efficiently integrated to identify the causes of failure, improve efficiency effectively, and serve as a strategic basis for safety, availability, and operational economy at the “reliability management” level so that reliability programs can successfully achieve their goals.

This paper introduces relevant theoretical explanations of important basic parameters in the reliability assessment program [6], including:

• $F\left(t\right)$: The cumulative distribution function of the time to failure
• $f\left(t\right)$: The probability density function of the time to failure
• $\lambda \left(t\right)$: Instantaneous failure rate function
• $R\left(t\right)$: Reliability function
• MTBF: Meantime between failure
• MTTF: Meantime to failure
• MTTR: Meantime to repair
• μ: Corrective maintenance rate
• $M\left(\tau \right)$: Maintainability function
• $m\left(\tau \right)$: Instantaneous maintainability function

The failure time variation is based on the Weibull distribution described by the cumulative distribution function and the probability density function [7]. In the literature [8], the cumulative distribution of the difference in wind speed between two wind turbines rises to 1 very quickly if both turbines operate well, meaning that the two turbines rarely have different wind speeds. Otherwise, if one turbine is affected by a fault, the Weibull cumulative distribution is close to the diagonal or the linear function. IEEE Std 399 describes a quantitative reliability assessment method, namely Failure Modes and Effects Analysis (FMEA), a helpful tool for quantitative assessment of the reliability design [9]. The FMEA method is based on the reliability parameters and system architecture of the constituent components of the distribution system, where the reliability parameters include the annual reliability index failure rate (λ), mean time to repair (MTTR), and mean time between failures (MTBF) for each combination component. When considering a power outage at a load point due to a distribution system incident, FMEA lists the component combinations that would cause the outage for any possible system outage scenario and finally calculates the systemic reliability index for decision making. In addition, the higher the wind speed at sea, the higher the failure rate [10]. Considering the uncertainty of information obtained from weather station sensors, Stawowy et al. [11] proposed a proprietary method to analyze and model the uncertainty of the weather station sensors’ information quality. Dao et al. [12] observed the failure rate and downtime of more than 18,000 wind turbines and studied the variations of wind turbine subassembly reliability data to identify critical subassemblies and to understand possible sources of uncertainty. In view of this, related studies also assessed the impact on the reliability of wind farms in critical infrastructure by targeting electromagnetic interference with other electronic and electrical equipment [13,14].

In terms of wind farm spare parts’ assessment, the contract between the wind turbine and critical equipment manufacturer and the wind farm owner stipulates that the manufacturer should provide spare parts free of charge during the warranty period of the wind farm. However, from a long-term operational point of view, wind farm developers should develop an optimal storage strategy to reduce the impact of the spare parts’ supply chain on contingencies [15]. In other words, the assessment of the overall reliability of the wind farm needs to incorporate the factor of supply chain reliability. The literature [16,17] indicates that supply chain reliability is the probability of delivering at least a certain number of products or services within a specified period, in addition, the time it takes to perform maintenance work, and the logistic delay time, i.e., delays due to weather conditions, transportation, and spare parts availability [18]. Yan et al.’s [19] study was based on a supply chain system for the wind power industry where the supplier is located at the top of the hierarchy, the second level is a central warehouse, the third level is a local warehouse, and at the bottom of the hierarchy is a wind farm site without spare parts inventory. The conditions that may cause logistic delays are considered in the study to explore the impact on the time to perform maintenance work.

In terms of wind farm operation and maintenance (O&M) programs, O&M accounts for 35–38% of the entire life-cycle cost of an offshore wind farm [20]. As wind farms operate for more extended periods, O&M costs have an increasing impact on reliability, and O&M teams need to review preventive and predictive O&M strategies on a rolling basis [21]. A study by Dao et al. [12] illustrated a solid nonlinear relationship between wind farm reliability and O&M expenditures, and annual electricity production. To realize the benefits of such maintenance strategies fully, developers, owners, and operators must be able to identify critical components and their failure modes, design wind energy systems to reduce failures, and monitor the remaining operational life [22].

The authors’ research on offshore wind power has led to an interest in the relationship between the various parameters related to reliability. Although there are professional books on reliability theory, they are often focused solely on reliability, and there is no intuitive way to understand the relationship between reliability and maintenance. This study explains the importance of reliability assessment in the project validation of offshore wind farm design in Section 1, followed by the derivation of theories related to reliability and maintenance in Section 2 and Section 3, respectively. The topology used to represent the relationship between the parameters is proposed in Section 4 as a visualization basis for developing the reliability theory. In addition, the study results propose the intrinsic availability function connecting the reliability and the maintainability domains. The relative relationship between the meantime to repair and maintainability was observed in the study. The saturation property of the maintainability at the extension of repair time was also found. The conclusions are presented in Section 5, which describes future research directions based on the results of this study.

2. Reliability Parameters

Reliability growth models have been developed to track reliability changes over time at different stages of product operation [7]. The same models can be applied to failure data collected from the field to investigate whether the product′s reliability remains constant in the aftermarket or improves or deteriorates over time.

2.1. Cumulative Distribution Function of the Time to Failure

When building failure analysis modules to study the safety characteristics of a system, the index based on the cumulative distribution function can be used to compare the improvements brought by different measures in the design enhancement [23]. The life test is carried out with $n_0$ identical components. After time t, $n_f\left(t\right)$ components fail, and the remaining $n_s\left(t\right)$ remain functional gives:

$$n_0=n_s\left(t\right)+n_f\left(t\right)$$

(1)

This allows the reliability function to be defined as:

$$R\left(t\right)=\frac{n_s\left(t\right)}{n_s\left(t\right)+n_f\left(t\right)}$$

(2)

(1), (2) can be written as:

$$R\left(t\right)=\frac{n_s\left(t\right)}{n_0}$$

(3)

also, because:

$$R\left(t\right)+F\left(t\right)=1$$

(4)

therefore:

$$R\left(t\right)=1-F\left(t\right)$$

(5)

where

$F\left(t\right)$: the cumulative distribution function of the time to failure.

We can substitute the failure probability into (5), combined with (3):

$$F\left(t\right)=1-\frac{n_s\left(t\right)}{n_0}$$

(6)

From (1), (6) can be written as:

$$F\left(t\right)=1-\left[\frac{n_0-n_f\left(t\right)}{n_0}\right]=\frac{n_f\left(t\right)}{n_0}$$

(7)

2.2. Probability Density Function of the Time to Failure

The probability density function is a mathematical model that describes the probability of an event occurring over time, obtaining the probability rates of system failure due to a failure at a specific time interval. In reliability analysis, the probability density function of the time to failure is used to quantify the uncertainty of system reliability [24,25]. Substituting (7) into (5):

$$R\left(t\right)=1-F\left(t\right)=1-\frac{n_f\left(t\right)}{n_0}$$

(8)

Solving the derivative of (8) for t:

$$\frac{dR\left(t\right)}{dt}=-\frac{dF\left(t\right)}{dt}=-\frac{1}{n_0}\frac{d{n}_f\left(t\right)}{dt}$$

(9)

If $t\to 0$, then (9) can be expressed as the probability density function $f\left(t\right)$ of the instantaneous failure time:

$$\underset{t\to 0}{\lim }\frac{1}{n_0}\frac{d{n}_f\left(t\right)}{dt}=f\left(t\right)$$

and then (9) can be written as:

$$f\left(t\right)=\frac{dF\left(t\right)}{dt}$$

(10)

or

$$\frac{dR\left(t\right)}{dt}=-f\left(t\right)$$

(11)

2.3. Instantaneous Failure Rate Function

The instantaneous failure rate function, also known as the “hazard function”, is defined as the failure rate limit when the length of the time interval, during which a failure can cause the system to fail, is close to zero [26]. Using (3), (9) can be expressed as:

$$-\frac{1}{n_0}\frac{d{n}_f\left(t\right)}{dt}=-n_0\frac{dR\left(t\right)}{dt}$$

(12)

Dividing both sides of (12) by $n_s$, gives:

$$\frac{1}{n_s\left(t\right)}\frac{d{n}_f\left(t\right)}{dt}=-\frac{n_0}{n_s\left(t\right)}\frac{dR\left(t\right)}{dt}=\lambda \left(t\right)$$

The instantaneous failure rate function $\lambda \left(t\right)$ can be expressed as:

$$\lambda \left(t\right)=-\frac{1}{R\left(t\right)}\frac{dR\left(t\right)}{dt}=\frac{f\left(t\right)}{R\left(t\right)}$$

(13)

2.4. Reliability Function

Reliability is defined as the probability of performing a predefined function in a specified time under specified conditions [27]. The reliability function can be expressed by (8), and also by (13), and can be rewritten as follows:

$$-dR\left(t\right)/R\left(t\right)=\lambda \left(t\right)dt$$

(14)

The integration of (14) from 0 to t gives:

$$-{{\displaystyle \int }}_1^{R\left(t\right)}\frac{1}{R\left(t\right)}dR\left(t\right)={{\displaystyle \int }}_0^t\lambda \left(t\right)dt$$

(15)

Since $R\left(t\right)=1$ at $t=0$, (15) can be written as:

$$\mathit{ln}R\left(t\right)=-{{\displaystyle \int }}_0^t\lambda \left(t\right)dt$$

(16)

According to (16), the reliability function can be rewritten as:

$$R\left(t\right)=exp\left[-{{\displaystyle \int }}_0^t\lambda \left(t\right)dt\right]$$

(17)

(17) is a general-purpose reliability function that can solve component reliability with any probability of the failure distribution. Assuming that the failure time of a component is an exponential assignment, the failure rate $\lambda \left(t\right)$ is constant $\lambda$.

$$\lambda \left(t\right)=\lambda$$

then the failure’s probability density function $f\left(t\right)$ can be expressed as:

$$f\left(t\right)=\lambda e^{-\lambda t}=\lambda R\left(t\right)$$

(18)

(18) is the most basic mathematical model of reliability, called the exponential distribution. The most frequently used function in reliability engineering is the reliability function, which expresses the probability that a project operates without failures over a certain period [28].

2.5. Meantime between Failures

Mean-time between failures (MTBF) is the average continuous failure-free time during operational use or testing. The MTBF is not a measured value but a theoretical reference value estimated by engineers during the product design phase [29,30]. MTBF is described in DNVGL-ST-0145 as follows [3]:

(a)

MTBF is the mean time between two consecutive failures [31].

(b)

The MTBF comprises all relevant components faults.

The concept of the average expiration time of a product is only applicable to a repairable product repaired when the fault occurs [32]. The meaning of MTBF is similar to the average life of the product (θ), which is expressed as

$$MTBF={{\displaystyle \int }}_0^{\infty }tf\left(t\right)dt={{\displaystyle \int }}_0^{\infty }R\left(t\right)dt=\frac{T}{r}$$

(19)

where:

• $f\left(t\right)$: Probability density function of the time to failure
• T: Total operating time of the product
• r: Total number of failures in time T
• t: Time interval at which the fault occurred
• MTBF: An estimate of the average time between failures of the product.

It should be emphasized here that MTBF only makes sense for repairable products. More importantly, the reliability function of the product can only be achieved under the assumptions of when the product is serviceable and when the failure rate is constant. (17) can be expressed as

$$R\left(t\right)=e^{-\lambda t}\begin{array}{c}=e^{-t/\theta }\end{array}\begin{array}{cc}=e^{-t/MTBF}& t\ge 0\end{array}$$

where:

• $\lambda$: Failure rate
• $\theta$: The average life of the product, $\theta >0$.

2.6. Meantime to Failure

It is generally assumed that the failed system can be repaired when using MTBF. If the failed system cannot be repaired, the mean time to failure (MTTF) is generally used instead to indicate the average time the system successfully operates before failure [33,34]. The expected value of the failure time, E(t), is called the MTTF [6]. For the probability density function of the continuous random variable (t), the expected value is:

$$E\left(t\right)=MTTF={{\displaystyle \int }}_0^{\infty }tf\left(t\right)dt$$

where:

• $f\left(t\right)$: the failure probability density function.

The average product failure time, also known as the average life, is the expected value of the product failure time defined by basic probability theory:

$$MTTF={{\displaystyle \int }}_0^{\infty }tf\left(t\right)dt$$

(20)

Using the integration by parts method:

$$MTTF=-{tR\left(t\right)|}_0^{\infty }+{{\displaystyle \int }}_0^{\infty }R\left(t\right)dt$$

(21)

Since $0\le R\left(t\right)\le 1$ for any time t, the first term on the right side is zero at the lower limit of integration ($t=0$). As for the upper limit of the points:

$$\underset{t\to \infty }{lim}\left[-\frac{t}{R{\left(t\right)}^{-1}}\right]=\underset{t\to \infty }{lim}\left[-\frac{t}{R{\left(t\right)}^{-2}\lambda \left(t\right)R\left(t\right)}\right]=\underset{t\to \infty }{lim}\left[-\frac{R\left(t\right)}{\lambda \left(t\right)}\right]=0$$

(22)

For the existence of (22), $\lambda \left(t\right)$ must satisfy the sufficient condition that when the time t approaches infinity ($t\to \infty$), $\lambda \left(t\right)$ does not approach zero.

If the above conditions are proper, the first term on the right side of (21) is equal to zero, and the following equation can be used to calculate the MTTF of the product.

$$MTTF={{\displaystyle \int }}_0^{\infty }R\left(t\right)dt$$

(23)

The use of (23) simplifies the calculation of many MTTF products. For example, if you know the product’s reliability function $R\left(t\right)$, MTTF can be found through integrating or approximating the value by the graphical method. For available products, MTTF is defined as the time at which the initial failure of the product occurs.

3. Maintainability Parameters

If we only pursue durability for a system or product, it is not very meaningful from a cost perspective. Although a system or product has a short life and is prone to failure, the failure is not fatal to the system, i.e., it can be repaired in an acceptable amount of time without affecting the associated peripheral systems and causing successive failures. In other words, although the system’s or product’s durability is short, it can still be repaired to a serviceable state within a short period.

From this point of view, the second meaning of reliability must be considered maintainability. The probability that the maintenance work will be completed within a specified period is observed by considering the expected failure scenario, the required environmental conditions, or the maintenance of the product under the specified impact conditions [35].

3.1. Mean Time to Repair

MTTR is derived from the average maintenance time in IEC 61508, for which the time required for maintenance must include the time to obtain parts, the response time of the maintenance team, and the time to put the equipment back into operation, in addition to the time required to confirm that a failure has occurred [36]. General repair work can be divided into two types [37]:

(1)

Preventive maintenance

(2)

Corrective maintenance

Corrective maintenance means performing the repair according to the repair method after the fault occurs. The cause is traced, and troubleshooting is completed when the fault is found. Therefore, corrective maintenance affects the operation time, which is usually longer and must be considered when calculating the maintainability. In the literature [38], the failure rate and average maintenance time are also used to assess the impact of the length of wind farm cables on project cost, reliability, and power loss.

The mean time to repair (MTTR) is obtained by recording the repair time required for each failure and averaging it. Similar to the reliability calculation, the first thing to know when calculating the maintainability is allocating the repair time. Experience dictates that the repair time is mostly a logarithmic normal distribution (the time t is represented by log). The cumulative curve of the lognormal distribution is similar to the cumulative curve of the exponential distribution. Therefore, the calculation of maintainability in this study also assumes that the repair time is exponentially distributed [37].

3.2. Corrective Maintenance Rate

Corrective maintenance can be defined as a situation where a wind farm project needs to be restored to a working condition when there is a failure or equipment damage [39]. If the MTTR of a machine or system is known, the corrective maintenance rate μ is the reciprocal of the MTTR,

$$\mu =\frac{1}{MTTR}$$

(24)

In the literature [40], the corrective maintenance rate evaluated the benefits of maintenance costs for lighter vessels and oilfield support vessels. The quantitative results of the analysis indicated that the costs of corrective maintenance are lower for lighter vessels selected for minor repairs.

3.3. Maintainability Function

The maintainability function is defined as “the probability of being repaired or restored to the specified condition within the repair time (τ) duration of maintenance tasks, when maintenance is performed according to the specified procedure [41]”, as in (25):

$$M\left(\tau \right)=1-e^{-\mu \tau }$$

(25)

In the maintenance process, Wang Q. considered incomplete maintenance activities and used the maintainability function to describe the probability distribution of maintenance time [42]. In contrast to the reliability index, the maintainability index of the update process was introduced to describe the probability that the maintenance activity successfully repairs the equipment.

3.4. Instantaneous Maintainability Function

The instantaneous repairability function considers the model of a minimum repairable system, where the time of system failure is a random variable. If the aftermarket repair rate is immediate, i.e., minimal repair time, no periodic maintenance work is taken [43].

Relative to the probability density function of the time to failure, the instantaneous maintainability function can be expressed as:

$$m\left(\tau \right)=\frac{dM\left(\tau \right)}{d\tau }$$

(26)

4. Discussion

4.1. Graphical Representation of Parameter Relationships

In engineering practice, reliability analysis and electrical system analysis engineers cannot effectively communicate reliability consensus, mainly because electrical engineers have insufficient knowledge of reliability. The same problem is reflected in the teaching practice; when electrical system analysts learn reliability theory, they often have difficulty understanding it, due to the overly complicated theory. The theories of the relevant parameters in this study are derived in detail and then successfully used to display the relationships between the parameters in graphical blocks. The graphical relationships facilitate quick understanding and serve as a platform to bridge different research fields to explore the reliability theory.

The cumulative distribution function of the time to failure can be defined as the reliability and probability density function of the time to failure based on the length of the time interval. The reliability function and the probability density function of the time to failure can lead to a standard instantaneous failure rate function. For repairable or non-repairable system or equipment failures, MTTF and MTBF are used to express the MTTF, respectively. In other words, it is generally assumed that the faulty system can be repaired when using MTBF. If the flawed system cannot be repaired, MTTF is usually used. The parameter formulas for the derivation of reliability theory in the subsections of Section 2 can be used to show the interrelationships graphically, as shown in Figure 2.

Based on the expected failure scenario, the required environmental conditions, or the maintenance of the product under the specified impact conditions, the MTTR is observed and expressed as the corrective maintenance rate. Similar to the previous reliability description, the recovery rate is based on the time interval length, which leads to the maintainability function and the instantaneous maintainability function, respectively. Finally, the parametric formulas for deriving the maintainability in the subsections of Section 3 can be used to show the interrelationships graphically, as shown in Figure 3.

4.2. Intrinsic Availability

The correlation diagram in the previous section shows that there is no formula to represent the correlation between reliability and repairability. However, the reliability assessment should intuitively consider further maintainability based on the repairable system or equipment. In this regard, this study uses the intrinsic availability function $A_I\left(t\right)$ as an essential parameter to link reliability and maintainability.

After deducting the wind turbine failure and daily maintenance time when the turbines cannot generate electricity, the calculated percentage of average power generation for the whole year is the availability of the wind farm. The availability calculation is based on evaluating the offshore wind farm’s sea conditions, weather conditions, turbine failure rate, and maintenance capability of the power plant and the development plans of similar offshore wind farms.

The overall operational availability of the wind farm mainly entails the availability of submarine cables and substations, regardless of whether the substation type is onshore or offshore. According to experience, the availability is mostly 99.5% [44].

The availability is generally used to evaluate repairability and durability. Availability is defined in [45] as “the probability that a repair system maintains its function at a specified point in time or maintains its function for a certain time”. The operational availability ($A_O$) shown in Figure 4 is defined in ISO 14224 as (27):

$$A_O\left(t\right)=\frac{MUT}{MUT+MDT}$$

(27)

where:

• MDT: mean downtime
• MUT: mean uptime

In addition, based on the concept of fault occurrence and repair, intrinsic availability $A_I\left(t\right)$ is expressed as (28):

$$A_I\left(t\right)=\frac{MTBF}{MTBF+MTTR}$$

(28)

Use graphics to show the interrelationships, as shown in Figure 5.

Availability is a measure of the efficiency of machine equipment use and an essential indicator of system capacity utilization. The substation’s primary power system availability, as detailed in DNVGL-ST-0145, refers to the state where the offshore power system can collect, convert, and transport the active power generated by the wind turbine. Even if it cannot participate in the required grid rules, the active or reactive power meets the control setting and should be considered usable [3].

The minimum availability, as defined in DNVGL-ST-0145 [3], is the minimum ratio of the active power that the substation can provide under N-1 operating conditions and the nominal active power of the offshore substation, as in (29):

$$A{R}_{\%}=mi{n}_{i=1}^k\frac{{\left(P_{\left(N-1\right)}\right)}_i}{P_n}\times 100$$

(29)

where:

• $A{R}_{\%}$: The minimum availability
• $P_n$: The nominal active power of the offshore substation at the point of common coupling
• $P_{\left(N-1\right)}$: The active power of the offshore substation at a common coupling point under N − 1 operation
• k: The number of substation components, where disabling one would cause a permanent drop in the active power delivered
• $\left(N-1\right)$: $\left(N-1\right)$ is used as a description of the system that maintains normal operation after a fault occurs in any of the N components of the power system (generators, transmission lines, transformers, etc.).

4.3. Based on Practical Maintenance Discussion

The project is committed to evaluating system reliability during the design phase. Engineers use empirical values, or good rate data from various equipment vendors, to perform subsystem, primary system, or entire system reliability assessments to meet the owner’s reliability requirements for the wind farm during commissioning and the warranty period. In general, the reliability of a wind farm during commissioning can meet the specification requirements. However, equipment failures, system abnormalities, or other unexpected conditions are inevitable during the more extended warranty period. In addition to the immediate loss of electricity sales, it is difficult to estimate the loss of the wind farm brand due to the reduced reliability of the wind farm. On the other hand, offshore wind farms require higher reliability but have lower maintenance than onshore wind farms. Because of this, the wind farm project team should conduct more on-site maintenance scenarios for different wind farm environments to improve the maintenance degree further. From (25), the following two points can be observed.

(1)

From (24), the smaller the MTTR, the larger the corrective maintenance rate μ. Therefore, when the repair time τ is constant, the smaller the MTTR and the higher the repair degree M(τ), as shown in Figure 6.

(2)

As shown in Figure 7, if the repair rate $\mu$ is kept fixed, and the repair time $\tau$ increases, the repair degree $M\left(\tau \right)$ increases.

In (25), if the value of $\mu \times \tau$ is assumed to be constant, the O&M team’s maintenance target is set. Therefore, if the time τ of the fault repair is very long due to insufficient material or long procurement time of the equipment, it is necessary to improve the after-treatment repair rate (μ). However, to increase μ, the average repair time MTTR must be reduced, and there must be enough skilled maintenance personnel and spare parts. The required conditions increase the repair cost, so a trade-off method could be introduced in further research to find the most advantageous point between $\mu$ and $\tau$.

In addition, acceptable system performance quality factors (including reliability and cost) were crucial for the project team in exploring the best design when comparing various electrical system design options early in the engineering process. Reliability is the probability that equipment operates normally without failures for a specified period, determined by the equipment’s maintenance requirements and failure rate. The reliability of a power system can be studied in depth through a digital computer program that performs probabilistic and statistical analysis to obtain reference information for selecting the best design.

5. Conclusions

The author has shown considerable interest in the relationship between the relevant parameters in the reliability study. The result of the study is to visualize the relationship between the parameters using a correlation diagram and further propose the intrinsic availability function to strengthen the correlation between reliability and maintainability.

Wind power is one of the most commercially viable renewable energy resources. However, compared to onshore wind farms, offshore wind farms are located in the marine environment, where daily operation and maintenance tasks are more complex and expensive, so a more cost-effective maintenance approach should be adopted. The results discussed in this study show that MTTR can be considered a key performance indicator (KPI) in O&M projects. Therefore, maintenance teams should always strive to improve it. Reduced MTTR means less downtime, which means stable power production, satisfied customers, and lower maintenance costs for the wind farm.

Managing the number of spare parts for wind turbines, offshore substations, and submarine cables is an important issue because it considerably impacts many of the reliability indices, annual production, and overall costs of a wind farm. Having many spare parts guarantees many reliability indices, but it also brings higher costs. Considering both technical and economic aspects is the only way to arrive at the best model for managing the number of spare parts to reduce costs while also maximizing energy production and thus increasing revenues. Based on this study, the author’s future research will explore the saturation characteristics of maintainability at the extension of repair time and use A.I. to assist and predict preventive maintenance. The future study is expected to enable early replacement of failing parts at the optimal time, reduce maintenance frequency, and lower operation and maintenance costs.