Optimisation of Preventive Maintenance Regime Based on Failure Mode System Modelling Considering Reliability

Complex production systems need to be run continuously and have minimal periods of downtime [9‐11]. To ensure the continuity output of a system, its reliability and requirements should be considered when planning preventive maintenance. Essentially, reliability is the probability of all the system components functioning correctly at all times. System reliability is an important consideration in complex engineering applications with multiple components or multiple failure mechanisms [12]. The performance of the overall system is influenced by each component in some way. In the event of a failure of any system component, the overall performance of the system will be affected partially, or the system will be shut down entirely. To achieve adequate reliability levels for a complex system, it is essential to consider the preventive maintenance intervals for components [13].

The reliability of components needs to be estimated for maintenance optimisation. Several published papers have focused on group preventive maintenance strategies tailored to the reliability of multi-component systems; however, maintenance activities such as repairs or replacements require the whole system to be shut down. The researchers have chosen Weibull distribution for describing failure rates. For example, by using three models, Tam et al. [14] determined the optimal maintenance intervals for multi-identical component systems. Under regular downtime conditions, maintenance can be performed given a minimum acceptable level of reliability and at a minimum total cost. In this research, cost and reliability are considered simultaneously for multi-component series systems. In complex systems, Hou et al. [15] presented the relationship between component reliability and system performance. A model for determining the optimal timing and cost of preventive maintenance was developed for series and parallel systems. A preventive, corrective, and opportunistic maintenance approach has been proposed by [16] to address multi-identical components with high production losses and economic dependence. A conditional information-based search method was proposed concerning reliability analysis for components. In the authors' study, however, when one component fails, the entire system, which is made up of several components connected in series, fails. Another study based on series–parallel systems and their reliability [17] developed a preventive maintenance decision model that evaluated the restriction of system reliability on maintenance considerations. For multi-identical component systems subject to multiple dependent and competing failure processes, Song et al. [18] designed a reliability model and maintenance policy for an identical-component system. A fixed inspection interval and an age replacement policy were both considered in the research. During their study, the system failed when a minimum of one parallel subsystem failed. In another study for the optimisation of multi-component maintenance strategies, Guo et al. [19] designed a numerical analysis method. Each different component was estimated to have a different maintenance time, cost, and failure rate. The authors considered a series–parallel structure for a system with only four components. Under different system reliability conditions, the cost rate and availability of the maintenance system are optimised. Moreover, by using statistical analysis, Fallahnezhad et al. [20] presented a method for identifying the best preventive maintenance strategy for parallel, series, and single-item replacement systems. A balance between total cost and reliability is used to determine the values of decision variables. Their system is based on a specific number of equipment items, and as they deteriorate in terms of their function, the system will fail. For multi-component systems with serially connected subsystems that are subject to reliability requirements, Shi et al. [21] developed a condition-based maintenance decision framework. The authors assumed that the maintenance process needed to be performed by shutting down the system during the maintenance of any identical component over a finite planning horizon to minimise the overall maintenance cost while ensuring the reliability of the system complies with the predefined requirement. In a multi-level approach incorporating structural and economic dependencies, Dinh et al. [22] proposed opportunistic predictive maintenance for multi-identical component systems. The replacement of components can be opportunistic if their predicted reliability dips below the threshold for opportunistic maintenance. The system can be caused to shut down by a component failure or a preventive maintenance procedure, as all of its components are integrated in hierarchical series. For production system availability, an optimisation model based on a preventive maintenance policy was presented by [23] for flexible scheduling of a flow-shop in a series–parallel production system of disposable appliances.

Some of the literature considered a reliability-analysis-based maintenance policy for multi-non-identical component systems. For instance, Shen et al. [24] dealt with the reliability of a multi-non-identical component system involving components that are subjected to continuous degradation processes and categorised shocks. Based on their recursive analysis, the authors developed a simulation method to approximate the failure time of k-out-of-n systems. If at least k components fail, the system fails. Using reliability analysis, Martinod et al. [25] developed an optimisation strategy to optimise the cost of preventative and corrective maintenance for complex multi-component systems. The authors studied complex systems based on non-identical components, where the failure of any one component would affect the performance of the system. Recently, Kamel et al. [26] presented a model for maintenance that minimises total maintenance costs for series–parallel systems consisting of nonidentical components under the consideration of reliability constraints. Based on the grouping maintenance approach, Vu et al. [27] developed a method for managing systems composed of multiple non-identical components. The method can be used to consider a variety of maintenance opportunities when making a decision about maintenance. In their research, they presented the reliability block diagram of a power plant system formed from six main components connected in a redundant configuration. The authors emphasised that the system must be shut down in order to maintain critical components in the proposed models. In order to minimise maintenance costs for a series of multi-component systems, Wang et al. [28] developed opportunistic maintenance models for each component based on the optimal reliability threshold. The replacement of the component can only be implemented when the component's reliability meets the PM reliability threshold. Failure distributions between the components obey a two-parameter Weibull distribution and the failure of any component in the series multi-nonidentical component system leads to system failure.

A variety of scheduling approaches have been stated in the previously mentioned studies for achieving the specific target of system performance. When a system fails, most approaches do not consider the underlying causes. The effect of failures, e.g. the severity of the machine faults was regarded as trivial, and able to be resolved with ‘normal’ maintenance schemes. When complex engineering systems are involved, this assumption is not always true.

Identification of potential failure modes is important during the analysis process. Failure modes can have various effects on a system, however not all will lead to a complete system failure. Whether a failure mode produces one or more failures depends on the configuration of the system. Therefore, to identify risks associated with a potential failure mode and understand what happens to a system when a failure mode occurs, identifying the effects of failure modes and understanding dependency maps between components are important steps in the FMEA process. In this way, preventive maintenance of components can be planned more effectively to ensure that the system does not have to shut down completely during maintenance. The literature review shows that most studies used the development of the FMEA concept to support planning and provide recommendations for maintenance actions in accordance with the risk priority number (RPN), which is a fundamental component of any FMEA.

For example, using a reliability model to test the reliability of PM planning, Cicek et al. [30] proposed a flexibility interval between maintenance interventions based on failure analysis. To attain the highest safety standards at the lowest cost, the authors analysed failures and accidents. Feedback, brainstorming, and expert judgement were used in the FMEA to generate PM plans that increased system reliability. Puthillath et al. [31] evaluated a preventive maintenance schedule that would reduce downtime and improve performance using the FMEA method. Based on reliability information for aircraft indicators, Guo et al. [32] improved preventive maintenance intervals through the optimisation of the long-term cost of operation. FMEA reports from two suppliers were used to identify the major failure modes in two applications of the indicator. Saleem et al. [33] employed the FMEA method to identify the causes of failures in tyre-curing presses to increase efficiency by implementing the priority risk number RPN, and reduce maintenance and downtime costs. Moreover, Piechowski et al. [34] used the FMEA method to analyse failures, scheduling, and planning processes. According to the concept of sustainable production, they evaluated failure based on different perspectives, such as operator safety and environmental impact.

In other recent studies, the FMEA method has also been used to identify failure types and to recommend preventative maintenance of some components of a machine so that they can function as expected and minimise the impact of failures [35]. Using the FMEA approach, Rahmania et al. [36] reduced potential failure opportunities, thus enabling resources to be directed to components with multiple or more critical failures. Sudadiyo et al. [37] proposed a classification method for the first group of centrifugal pump subcomponents using FMEA to determine maintenance level criteria. As part of a preventive maintenance strategy, Palei et al. [38] analysed failure-mode effects with real-world operational data. At the earliest mean time to failure (MTTF) in their study, reliability-centred maintenance was implemented on a cluster of critical-failure components. In an attempt to evaluate the failure potential of aircraft wings, Gholizadeh et al. [39] proposed an analysis based on failure modes and failure analysis in criticality. An optimal design can be achieved when reliability, maintenance, and repair factors are considered in a risk assessment model. A method for preventing unplanned downtime incidents was described by [40]. Using FMEA, they made maintenance schedules that reduced unexpected downtime by predicting the conditions of each component in the production line. The system takes a break if one of its components or parts fails or is undergoing maintenance. Moreover, a maintenance planning and production scheduling tool was developed by [41] using FMEA analysis. In this study, a machine was considered with matching components, however, if one component failed, the entire machine might also fail, therefore halting production.

For system reliability analysis, there are different structures available in the literature that can be used to analyse reliability and maintenance, for example, a fault tree structure. It is used for analysing failures caused by various factors based on their representation in the form of a tree [42]. The fault tree structure is used to measure a system's reliability, where a top-down approach is used to identify the root causes of any system failure [43‐45]. Fault Maintenance Trees (FMTs) are discussed in reference [46, 47] as structures that allow managers to manage total maintenance costs and reliability while maintaining the availability of a system. While the fault tree is commonly used for the analysis of systems failure modes, it is a complicated process and the data flow is not represented.

Another structure to assess the reliability of continuous systems under fatigue and corrosion failure conditions [48] used structural health monitoring data. In their study, A Bayesian inference method was applied to determine the structural reliability. The concept of graph structure was used by [49] to develop new models and algorithms for assessing the reliability of a system composed of multiple components. By using the Hasse diagram, these developments exploit a graphic representation of the order relation between the states of the system components. Despite using graphical representations of functional requirements, this approach does not use them for safety analysis because they are not detailed.

Although all these methods are a good, readily available structure to evaluate the reliability and maintenance of complex systems, the continuity of system outputs is not taken into account. Thus, to refine the approach that has been previously proposed, this paper uses the FMEA structure.

The FMEA method for failure analysis has been used in the previously mentioned studies. However, the studies have not used the FMEA block-based PM concept to maintain the continuity of the system outputs. Furthermore, the procedure used in the system analysis is not effective for understanding how the system works, or the impact of failure on the whole system. For example, the work safety risk analysis is carried out and recommendations of ideal maintenance actions to be taken are detailed in a report to control the risks identified during the failure process observation in the production system, which is completely different to our approach in this paper. In other words, they did not consider the FMEA block concept to keep the system's output continuous during maintenance activities. This concept is to model and identify the components that have the same failure effect and then group them into blocks based on failure modes and the impact of these failure modes on the rest of the components. Through this technique, we can avoid the replacement of unnecessary components, which may affect the other components in the system, causing production system stoppages, lost production costs, and high total maintenance costs.

Given the above discussions, an interesting avenue for the current study is to maintain production outputs even partially during maintenance activities with a high level of reliability. Focusing on failure mode modelling of the production system, Alamri et al. [50] have proposed a method to determine the preventive replacement intervals using the meantime-to-failure values for groups of components as blocks in the complete system to prevent frequent breakdown failures. Based on the FMEA block concept, the proposed method was shown to arrive at a satisfactory solution where continuous production outputs are maintained and the system maintenance costs are optimised. This is achieved by exponential failure distribution, which also enables further investigations with more reliability-oriented distribution functions instead of the exponential failure function.

In this paper, we propose failure-modes-based preventive maintenance scheduling using the FMEA method. The objective is to maintain continuity of the complete production system while optimising maintenance costs and achieving a maximum level of system reliability.

The novelty and contributions of this work can be summarised as follows:

The general block replacement strategies for a single component and identical components have been widely detailed in literature [52]. The model assumes that replacement of components will take place at regular intervals of time with failure replacements performed as necessary. The component becomes as good as new after each replacement. Whenever a failure occurs during a cycle, it is immediately replaced. The goal is to minimise the total replacement cost per unit of time by optimising the interval between the replacements. With system complexity, the replacement policy for a single component is insufficient to support complex systems maintenance. In this research, the mathematical model is used as a group replacement strategy. The cost of replacing a group of non-identical components under preventive replacement conditions is assumed to be lower than replacement costs under failure conditions. The matrix model considers an optimal interval which minimises the average cost rate and guarantees reliability by controlling the failure rate to a certain extent within acceptable limits. By considering the above two goals, we aim to calculate the replacement for the FMEA blocks based on system failure modes, where \(T^{x}\) is the optimal time interval between group replacements in preventive maintenance events.

In this model, preventive replacement means that components in one FMEA block are replaced simultaneously at the end of each maintenance cycle length T. Thus, the expected replacement cost is given by:

The optimal preventive maintenance interval \(T^{x}\) is reached when the breakdown costs are more costly than the cost for planned replacement for all group components with an increasing failure rate. In order to achieve the most economic balance between replacement costs and failure costs, the optimal preventive maintenance interval is determined.

A preventive maintenance cost is computed by using the first expression PM during the interval \(T^{ }\), so that components are returned to a good-as-new state. Downtime costs of PM are incurred when components need to be replaced as a preventative measure. It includes the number of labourers needed \({\mathbf{PN}}\), cost, and a required time to replace components \(PR_{time}\). Thus, the matrix can be represented as follows:where \({\mathbf{PC}}\) denotes person cost per hour and is defined as a matrix of column \(n \times 1\). \({\text{PN}}\) and \({\text{PR}}_{{{\text{time}}}}\) are defined as a constant value.

For the second expression, F(T) represents the expected failure time during interval (0, T) at the assumption of Weibull distribution, and can be given by diagonal matrix:CM is the cost of a failure replacement including spare parts, labour cost, downtime cost and shutdown cost, and is expressed as Eq. (11):The maintenance model is based on the assumption that spare parts are available at all times. In order to define the spare parts variable, we must acknowledge that spare parts have various costs, and that storage and delivery are not additional costs. Thus, \({\mathbf{S}}\) as \(n \times 1\) column matrix can be represented as follows:System components fail unexpectedly after they begin operating at T > 0. A component must be replaced when it fails. The failure will have a significant impact on other components in the same line. When a failure occurs, downtime is shown as DTC, including replacement time, labour cost LC, and cost of lost production PLs (n × 1). Calculating the cost of labour and downtime can be done by using the following formulas:where C is the hourly cost of a person (constant) and P is the number of workers in (n × 1) column matrix. Then,In some cases, the shutdown may affect some system components due to their dependency. Whenever one component in a series configuration fails, for example, all other components in the same arrangement are shut down.

In this model the Q matrix components are those that are affected by the failure of another component. Components are defined by the rows of the matrix. For example, row-1 is component A, row-2 is component B, and so on. These columns represent the influence one component's failure has on the other components in the system. It takes the value 1 if the failure of one component affects the functioning of another, otherwise it takes the value 0 and can be obtained as:Since all components of the matrix \({\varvec{w}}\) are unaffected by their own failure, all the diagonal elements are zero. If ith component failure affects qth component, the matrix elements will contain value 1, otherwise the matrix elements will contain value 0. Thus:where the sum of lost production for qth component is represented by \({\mathbf{PLr}}^{}\) per hour, and \({\mathbf{SH}}\) denotes the shutdown cost of rest components. Once \({\mathbf{PLr}}\) is computed, SH can be calculated as:Therefore, maintenance costs are evaluated for each FMEA block, and all costs are given in AUD. Based on the configuration of the production system and the previously formulated equations, the optimisation matrix model with the total maintenance costs can be presented as:To find the optimal maintenance time, it is necessary to minimise the expected cost per time unit.

Identify: \(T^{x}\).

minimising: \({\mathbf{T}}_{{{\mathbf{cost}}}} \left( T \right)\).

subject to: \( R_{{{\text{sys}}}} \left( T \right) \ge RR { } { }\).

According to the two equations for maintenance cost and system reliability, there is an optimal maintenance replacement interval, \(T^{x}\), that meets the objective of preventive maintenance subject to reliability. The total cost of the system is calculated by adding up all the cost components, and the overall reliability is determined by the reliability of individual blocks.

\({\mathbf{T}}_{{{\mathbf{cost}}}} \left( T \right)\) is a function of a single variable T, therefore the algorithm following the exhaustive search method has been developed to determine an optimal preventive maintenance interval for each FMEA block. This method searches the entire design space and the minimum value of objective function obtained among these evaluations is declared as the minimum of the function [53]. In a degradation case when \(\beta > 1\), the preventive term decreases while the corrective term increases. This results in a convex cost function. An illustration of the procedures appears in Fig. 1. Details are described below.

Step 1 Give the preventive replacement cost PC, PN and \(PR_{{{\text{time}}}}\) as well as the breakdown replacement cost S, P, C, \(CR_{{{\text{time}}}}\), Q, and PLs for every component in system. Allocate the η and β parameters of the Weibull distribution for each component.

Step 2 Determine FMEA block z. In this step we define the FMEA block to be examined in the simulation model.

Step 3 \({\text{Calculate}}\;{\text{ the}}\;{\text{ expected }}\;{\text{total }}\;{\text{cost }}\) \({\mathbf{T}}_{{{\mathbf{cost}}}} \left( T \right)\). Based on the FMEA block, Eq. (18) is applied to calculate the total PM cost for components. At this point, the iteration process is used to optimise the time for a block by computing the total cost of several different preventive maintenance schedules at every time value during the specific period time t. Then, the maintenance interval of the block of components is optimised based on the sum of maintenance cost.

Step 5 Calculate overall system reliability \(R_{{{\text{sys}}}} \left( T \right)\) from Eq. (6). In this step, reliability is calculated based on individual FMEA blocks. It depends on the arrangement of the components in the production line, for example, series or series parallel.

Step 6 Determine an optimal interval \(T^{x}\).

Step 7 Find the annual total maintenance cost for the block. Where \(T^{x}\) is the optimal maintenance interval, let f be the total number of preventive replacements during the planning period t, which can be obtained as following:Thus, the annual total maintenance cost for each FMEA block is:

Step 8 Update z = z + 1 and repeat steps (2)–(9) until z = Z.

Step 9 Calculate the total maintenance cost of system. Using Eq. (23), the total maintenance cost of the system is calculated based on the sum of annual maintenance costs for number of blocks z as follows:

By minimising the total expected replacement cost per unit of time, the optimal preventive replacements interval is determined using Eq. (19). In Fig. 7 the curve graphs illustrate how PM and reliability have changed over time. The rate of cost decreases as time increases until the minimum cost of $18.20 per hour at \(T^{x}\) = 619 h with reliability of 90%, where the rate then increases again. Preventive replacement occurs for this group of components every 688 h during the given period of 2000 h (one year), which means that the components are replaced twice. Thus, by using Eq. (21) the \(A_{{{\text{cost}}}}\) is $54.59. The reliability of this block starts to drop significantly after optimal time. This means that replacing the components as a group once at the specified optimum time will contribute to maintaining the reliability of the block at an acceptably high level.

By using Eq. (19), Fig. 9 illustrates the optimum replacement time for block 2 components at \(T^{x}\) = 608 h with minimum cost of $37.77 per hour. Based on \(T^{x}\), the reliability of this block is 91.2%. Preventive replacement occurs for this group of components every 608 h during the given period of 2000 h (one year), which means that the components are replaced twice. Thus, by using Eq. (21) the \(A_{cost}\) is $113.31. After the optimal time, the reliability of this block starts to decline significantly. Therefore, replacing all components in this block at the specified optimum time will increase the block's reliability.

Based on FMEA block 3, it can be seen that stopping to carry out maintenance will not affect the rest of the components in the system, so it will not affect the overall system’s operation. It will continue to operate, and the outcome will not be affected by the reduction in operational capacity. Figure 11 shows a rapid decline in the cost rate at the beginning. At this point, it has reached the minimum cost value of $59.29 per hour at the optimal interval of \(T^{x}\) = 542 h. As time passes, cost values gradually increase and approach a certain number. The annual cost for this block is $177.87, while the reliability based on \(T^{x}\) is 91.2%.

Based on the reliability in this block, it is reasonable to replace the components as a group simultaneously. In this case, the other machines will continue working but the system capacity will be lower than before. The tendency in Fig. 13 is the same as Fig. 11, with the minimum cost value of $56.53 per hour and with reliability of 92.4% at optimal \(T^{x}\) = 901 h. The replacement of this block takes place twice annually at a cost of $169.58.

In Fig. 15, the optimal time for a replacement of group of components in this block is 740 h with minimum cost of $15.24 per hour, while at the same time the reliability is 90%. According to this optimal time and period of operation t = 2000, the annual cost is $30.48, assuming replacement occurs twice a year.