Warship Mission Reliability Modeling and Simulation from the Perspective of Equipment Support Resource

Abstract

To address the complex role of equipment support resource allocation on mission reliability during warship missions, this study establishes a warship mission reliability simulation system by using agent-based modeling to simulate warship task flow, equipment reliability structures, fault rules, and equipment support resource allocation schemes. The simulation system has the characteristics of multielement, modular, flexible configuration and easy operation. The key metrics relevant to different task conditions, such as the mission reliability of multistage and multistate systems, and the number of recommended allocations of equipment support resources, can be calculated by the system. In addition, sensitivity analyses of task parameters, equipment reliability structure, and the number of spare parts is carried out, and the effects on task reliability are discussed. The influencing factors considered in the modeling and calculation of mission reliability are expanded in this study, which can provide technical support for the optimal allocation of shipboard equipment support resources during the use phase of a warship, and the supportability design of warship equipment during the development phase.

1. Introduction

To guarantee the success of military missions, warships need to plan for on-board equipment support resources before carrying out their missions. However, due to the complex structure of warship equipment, diverse missions, and maintenance activities, it is very difficult to model and calculate the mission reliability of warships considering equipment support resources, and designers usually only estimate the number of equipment support resources allocated to typical mission profiles in the equipment development phase, which makes the planning of equipment support resources under conditions of diversified tasks reliant only on the users’ experience for estimation. This situation may ultimately lead to the reduction of mission reliability due to a lack of equipment support resources in the actual missions, or a waste of resources due to over allocation of some equipment support resources.

To solve the above problems, this paper introduces an agent-based modeling (ABM) approach to model and calculate the system reliability considering equipment support resources under multistage and multistate conditions, which can effectively improve the combat effectiveness evaluation capability under the background of actual missions. The main contributions of this paper are summarized as follows:

(a)

A model for the warship mission reliability considering equipment support resources is proposed to be compatible with the calculation of complex mission reliability such as multistage missions and multistate correlation effects.

(b)

A warship mission reliability simulation system that is easy to operate and configure is designed to facilitate the configuration of task flow, equipment structure, and resource list, which are conducive to the operation, use, and analysis by engineering technicians.

(c)

A method for calculating the number of equipment support resources to be carried on shipboard with the objective of satisfaction rate is developed to ensure that the equipment support resources to be carried are configured according to the different mission requirements.

The remainder of this paper is organized as follows. Section 2 reviews previous research related to this study. Section 3 presents the key problem to be addressed and the related definitions. Section 4 describes the simulation system developed based on the agent-based modeling technology. The main computational results and sensitive analysis of warship mission reliability are presented and discussed in Section 5, and the validity of the designed simulation system is verified. Finally, conclusions and insights are presented in Section 6.

2. Literature Review

Because of the complex structure of warship equipment and the diversity of tasks and maintenance activities, it is very difficult to model and calculate the warship mission reliability considering the equipment support resources. There are two common types of reliability assessment methods: analytical methods and simulation methods. Analytic methods mainly include combinatorial model methods and state space methods [1]. Reliability block diagram and fault tree analysis are classical combinatorial model methods, while Petri net [2,3] and the Markov process [4,5,6,7] are common state space methods. The deficiencies of these methods lie in computational explosion, stringent requirements for failure rules, inadequate consideration of equipment support resources, and neglect of the impact of operating status on failure rates. The applicability of the methods is low, and the credibility and accuracy of the calculation results are insufficient, which makes these methods difficult to support the work requirements. In contrast, the simulation methods, which are based on the Monte Carlo method, are the methods for simulating the state and behavior of a system using stochastic tests and assessing the mission reliability in a computer, which to some extent solves the problem of calculating reliability under complex action laws.

For example, Chang [8] developed a multistate network to study reliability estimation methods. Xiong et al. [9] used simulation methods to introduce the virtual ship for fault prediction of complex task systems and propose dynamic optimization of the remaining task processes but did not take into account the impact of support resources. Chiacchio et al. [10] proposed a stochastic hybrid fault tree automaton to solve the reliability assessment problem associated with operating conditions. Yu et al. [11] introduced the mission reliability evaluation model based on an extended object-oriented Petri net, which to some extent solved the problem of modular computation of reliability.

The warship mission reliability evaluation considering equipment support resources needs to address issues such as the influence of fault propagation on system reliability and the impact of support resources on equipment status. To solve related problems, Li et al. [12] designed a method based on a smart agent communication to evaluate the reliability of integrated energy systems. Considering the significant impact of fault propagation in multistate systems on the reliability and safety of systems, Guo et al. [13] proposed an agent-based dynamic reliability modeling method. Similarly, Shukla and Arul [14] proposed a smart component methodology to analyze the reliability of a dynamic system, which can be used as a method for developing a general software for dynamic reliability. These are the applications of ABM in the field of reliability.

Of course, there are also applications of ABM in other related fields. Junhai et al. [15] analyzed the army’s complex equipment maintenance plan, maintenance support mode, human resource configuration, and maintenance process flow by introducing discrete events and constructed a simulation model for a complex equipment maintenance workshop. Feng et al. [16] developed a multiagent technology to investigate the collaborative control of ship electromechanical equipment. Diallo et al. [17] applied the agent-based mode in the Ballistic Missile Defense System (BMDS) to identify emergent behaviors. Tajalli et al. [18] optimized power scheduling for shipboard power systems by using a multiagent-based system. Lynch et al. [19] presented an approach to begin addressing this need by applying heat maps and spatial plots to visually observe unexpected behaviors within ABM. Hilton et al. [20] proposed a software planning tool to develop a complicated plan.

Regarding the verification of ABM, Diallo et al. [21] proposed an approach to formally verify and rigorously validate a simulation system against the specification of the real system in a verification and validation calculator tool. Gore et al. [22] used the Verification and Validation mechanism to gain insight into unexpected and potentially invalid output.

In summary, all the above studies abstract the relevant objects as agents and define simulation logic based on real systems, which proves the value of ABM theory applications and reflects the outstanding advantages of ABM in dealing with complex logical behaviors and influence relations. It shows that ABM can be used to solve the problem of system reliability modeling under complex conditions. However, existing studies have ignored the role of equipment support resources, such as spare parts, maintenance equipment, and support personnel, which is not applicable to mission reliability assessment of warship equipment with long service cycles, long mission times, and difficult material availability. Therefore, it is necessary to conduct targeted research on the mission reliability evaluation methods of warships considering equipment support resources.

3. Problem Description

The problem can be described as the calculation of overall mission reliability $R_U\left(T\right)$ for a given number of equipment support resources $\left\{N_{M_1},N_{M_2},\dots ,N_{M_L}\right\}$, the rule of fault generation $L{T}_{E_k}$, maintenance times $M{T}_{E_k}$, reliability structures $R{S}_{S_j}$, and the linkages between the unit task and the system $U{S}_i$. The definitions and relevant assumptions of some specialized vocabularies involved in this study are as follows:

(a)

Unit task $U_i$: a minimum process unit in which the system performs the specified function within a defined time with a fixed reliability structure.

(b)

Unit task reliability $R_{U_i}\left(t_i\right)=p\left(r{t}_{{}_{U_i}}^{\prime }<t_{{}_{U_i}}^{\prime }\right)$: the success of a unit task is judged by the fact that the delay time $r{t}_i^{\prime }$ caused by the maintenance support is less than the allowed delay time $t_i^{\prime }$.

(c)

Mission profile: the chronological description of the events and environment experienced by the equipment during the time it takes to complete a specified task. In this study, the mission profile is suitably simplified by assuming that the unit tasks are executed sequentially; the sequence of $I$ unit tasks required to complete the specified task is $U=\left\{U_1,U_2,\dots ,U_I\right\}$.

(d)

Overall mission reliability $R_U\left(T\right)$: probability of the equipment completing the task flow $U$ within the specified time $T$. It is assumed that if a unit task fails, the overall mission will fail, as calculated by Equations (1) and (2):

$$R_U\left(T\right)={\displaystyle \prod _{i=1}^n{R}_{U_i}\left(t_i\right)}$$

(1)

$$T={\displaystyle \sum _{i=1}^n{t}_i}$$

(2)

(e)

System availability $A_{s_j}={\mathsf{\Phi }}_j\left(A_{e_1},A_{e_2},\dots ,A_{e_{m_J}}\right)$: due to the influence of the equipment reliability structure, the availability of the system $S_j$ is simultaneously related to the availability of each component.

According to the definition of the unit task reliability, this value is influenced by the linkages $U{S}_i$ between the equipment function and the mission and is related to the system availability to be worked on, which can be expressed as:

$$R_{U_i}\left(t_i\right)=U{S}_i\left(A_{S_1},A_{S_2},\dots ,A_{S_J}\right)$$

(3)

The system availability $A_{s_j}$ is related to the availability of its components (including subsystems and equipment) and is influenced by the reliability structure $R{S}_{S_j}$:

$$A_{S_j}=R{S}_i\left(A_{S_1},A_{S_2},\dots ,A_{S_J},A_{E_1},A_{E_2},\dots ,A_{E_K}\right)$$

(4)

(f)

The fault interval $L{T}_{E_k}$ of the equipment $E_k$ follows a Weibull distribution [23,24]: ${\mathsf{\Gamma }}_{E_k}(t)=\frac{m_{E_k}}{{\eta }_{E_k}}{t}^{(m_{E_k}-1)}{e}^{(-\frac{t^{m_{E_k}}}{{\eta }_{E_k}})}$.

(g)

The maintenance time $M{T}_{E_k}$ of the equipment $E_k$ follows a normal distribution [25]: ${\mathrm{H}}_{E_k}(t)=\frac{1}{\sqrt{2\pi }}{e}^{-{(t-{\theta }_{E_k})}^2/(2{\sigma }_{E_k}{}^2)}$.

(h)

The availability of equipment $E_k$ is represented by $A_{E_k}$. $S{R}_{E_k}=\left\{“\mathrm{Health}”,\hspace{0.17em}“\mathrm{Waiting} \mathrm{for} \mathrm{Repair}”,\hspace{0.17em}“\mathrm{in} \mathrm{Maintenance}”\right\}$ indicates that the health state of $E_k$ consists of three states, and $S{G}_{E_k}=\left\{“\mathrm{Stand} \mathrm{by}”,“\mathrm{Working}”\right\}$ indicates that the working state of $E_k$ consists of two states.

(i)

There is a total of $L$ equipment support resources, where $M=\left\{M_1,M_2,\dots ,M_L\right\}$. The initial allocation quantity of equipment support resource $M_l$ is $N_{M_l}$. Equipment support resources are divided into occupied resources (such as maintenance and support personnel, maintenance, and support apparatuses and equipment) and consumable resources (such as repair pieces and spare parts). The difference between the two types of resources is that occupied resources will be restored after use, while consumable resources will be reduced after use.

(j)

The status change and indicator statistics rules for equipment $E_k$:

When $S{R}_{E_k}=\left\{“\mathrm{Health}”\right\}$, equipment $E_k$ is in an available state. When $S{R}_{E_k}=\left\{“\mathrm{Waiting} \mathrm{for} \mathrm{Repair}”,\hspace{0.17em}“\mathrm{in} \mathrm{Maintenance}”\right\}$, equipment $E_k$ is in an unavailable state. The health state of the equipment affects the value of $A_{E_k}$.

When $S{R}_{E_k}=\left\{“\mathrm{Health}”\right\}$ and $S{G}_{E_k}=\left\{“\mathrm{Working}”\right\}$, the fault interval $L{T}_{E_k}$ is reduced, and the $L{T}_{E_k}$ remains unchanged when the equipment $E_k$ is not in use.

When $L{T}_{E_k}=0$, $S{R}_{E_k}=\left\{“\mathrm{Waiting} \mathrm{for} \mathrm{Repair}”\right\}$.

When the required quantity $\left\{n_{M_{1_k}},n_{M_{2_k}},\dots ,n_{M_{L_k}}\right\}$ is not greater than the available quantity $\left\{r{n}_{M_{1_k}},r{n}_{M_{2_k}},\dots ,r{n}_{M_{L_k}}\right\}$, $S{R}_{E_k}=\left\{“\mathrm{in} \mathrm{Maintenance}”\right\}$.

The working state $S{G}_{E_k}$ of the equipment $E_k$ is influenced by the system to which it belongs and the performance of associated unit tasks.

In the above assumptions, it is impossible to calculate complex state transfer rules using analytical methods. The state transfer rules of equipment are the most difficult to express due to the impact of support resources, systems, unit tasks, and other aspects. Therefore, considering the complex changes in the health and working states and the frequent interaction between objects, it is appropriate to use the state diagram technique and communication technique in ABM [12,26] to simulate them.

4. Simulation Design

Anylogic [27] combines a variety of modeling and simulation methods including agent-based modeling, system dynamics, and discrete events. In this platform, the state chart and communication technology can quickly and effectively simulate the various elements in the mission and equipment system and realize the visual modeling and simulation scheme. The following are the advantages of using ABM:

(a)

It can quickly adapt to changes in the maintenance logic of the actual system with a high degree of scalability.

(b)

It has visual editing capability and can better reflect the status of each element.

Therefore, the Anylogic platform was chosen for modeling in this paper. The mission profile, the function and structure of the warship equipment, and the support plan are modeled by Anylogic, and these factors are abstracted into four types of agents: unit task, system, equipment, and support resource. The interaction behavior between different agents is constructed to output various indicators such as overall mission reliability, unit task reliability, equipment task reliability, support resource satisfaction rate, support resource utilization rate, and recommended number of support resource configurations.

A warship mission reliability simulation and evaluation system by using agent-based modeling is constructed, and the framework design of the system is shown in Figure 1.

As shown in Figure 1, the system should be able to use four types of simulation modules to build a simulation structure, and the four simulation modules correspond to the four types of agents to be constructed. The functional design of the agents is shown in

Table 1. Functional design of the agents.

Agent	Function
Unit task	The mission profile is formed by this agent. The agent can flexibly build task flow and communicate with the system agent.
System	Simulates the state of each level system and calculates the mission reliability of different types and levels of systems by simulating the reliability structure $R{S}_{S_j}$ of the equipment.
Equipment	Simulates the state and behavior of equipment. The fault is generated according to the remaining fault interval $L{T}_{E_k}$, and the status transfer is performed according to the equipment support resources.
Support resource	Simulates the state and behavior of equipment support resources.

.

Several influence relationships and elements can be simulated through these kinds of agents, such as task flow, equipment usage, equipment reliability structure, and maintenance support activity. The key to the calculation of mission reliability lies in using communication techniques to affect the internal state of the agents. The communication techniques and agents involved in these elements are shown in

Table 2. Element simulation scheme.

Element	Communication Technique	Agent	Explain
Task flow	Port communication	Unit task	The order of the unit task is used to build the task flow.
Equipment usage	Port communication	Unit task, system	Port communication is used between unit tasks and the system to pass task status information and equipment health information.
Equipment reliability structure	Port communication	System, equipment	Port communication is used to pass task status information and equipment health information.
Maintenance support activity	Hybrid communication	Equipment, support resource	Hybrid communication is used to communicate the status of support resources and equipment maintenance requirements.

.

4.1. Unit Task Agent and Mission Profile

The designs of icon and statechart for unit task agent are shown in Figure 2 and Figure 3.

The statechart of the unit task agent adopts the design of a hierarchical state machine [28]. This design allows the unit task agent to function in two ways:

(a)

Horizontal simulation for the working state of each unit task is in the mission profile. The port communication is required to enable state migration between the unit task agents and to enable visualization of mission profile. It enables flexible configuration of task order and structure.

(b)

Longitudinal simulation for the effect of each associated system agent state on the unit task agent. The agent bottom port is used to communicate system agent. It includes the equipment health state, which in turn triggers a condition transition of $G$ and $F$ to achieve task suspension or continuation (the number of system agents working as required by the unit task is at or below the specified number). In addition, the port can reversely transmit the task state information of the unit task agent, which helps to play the role of the task state on the equipment working state.

4.2. System Agent and Reliability Structure

The design of icon and statechart for system agent are shown in Figure 4 and Figure 5.

The design of the system agent separates the health state $S{R}_{E_k}$ and working state $S{G}_{E_k}$, which allows a smoother transfer of the health state $S{R}_{E_k}$ to the unit task or higher-level system and the working state $S{G}_{E_k}$ to the lower-level component or system. This design requires the $out$ and $in$ ports of the agent to be exposed through a normalized communication protocol to simulate a multilevel equipment reliability structure. $S{R}_{E_k}$ uses message transition to convey the global impact of the working state. $S{G}_{E_k}$ uses the condition transition to simulate different reliability structures (including series, parallel, and k/n(G) systems) using the difference between the number of working redundancies and the number of subsystems.

The simulation of equipment reliability structure utilizes the idea of fault tree analysis [29,30]. According to the form of the equipment catalog structure, the equipment is divided into hierarchical structures. The port communication between the system agent and equipment agent is used to visualize the equipment reliability structure and realize the real-time output of the state and task availability of each system and equipment.

Table 3. Several types of equipment reliability structures.

Type of Reliability Structure	Reliability Block Diagram	Connection Mode of Agents	Design Highlight
Series system			These systems are simulated by setting different redundancy numbers (the number of equipment that can be faulted) in the system agent.
Parallel system
k/n(G) system
Hybrid system			The hybrid system is simulated by a normalized design of port communication protocols to be compatible with communication messages of different agent types and to implement a multilevel connection structure.
Equipment with different reliability structures for different unit tasks			The same equipment is used for different tasks, but its reliability structure may be different. The same equipment agents are connected by different connections instead of recreating new agents, which allows for more realistic and accurate calculation results.

displays the classification of the equipment reliability structures simulated using port communication.

4.3. Equipment Agent and Fault Rule

The designs of the icon and statechart for the equipment agent are shown in Figure 6 and Figure 7.

The statechart of the equipment agent is designed with reference to the system agent. The health state, working state, and maintenance support request of the equipment agent are transmitted via port communication as well as global communication. The most important part in the equipment agent is the simulation of fault occurrence rules and maintenance time. The state transition rules are designed as follows:

(a)

$C$ transition: the condition transition is introduced to simulate the fault interval $L{T}_{E_k}$ affected by the working state. When $S{R}_{E_k}=\left\{“\mathrm{Health}”\right\}$ and $S{G}_{E_k}=\left\{“\mathrm{Working}”\right\}$, $L{T}_{E_k}$ will be reduced, otherwise unchanged.

(b)

$E$ transition: the timeout transition is introduced to simulate the maintenance time $M{T}_{E_k}$.

The mean time between failure (MTBF) based on Weibull distribution and mean time to repair (MTTR) based on Weibull distribution are designed in the equipment agent. The MTBF and MTTR of diesel engines and other equipment agents are entered.

4.4. Support Resource Agent and Maintenance Support Activity

The designs of the icon and state diagram for the support resource agent are shown in Figure 8 and Figure 9.

The design of the support resource agent simulates both consumable and occupied resources. For the received maintenance support requests, the principle of “first request, first allocation” is adopted to respond and allocate support resources.

Only the repair by the ship crew is considered in the simulation. The key to simulating maintenance assurance activities is to simulate the behaviors of fault equipment, such as requesting resources, sending resources, and returning resources. The simulation of these behaviors is achieved through the design of the communication logic between the equipment agent and support resource agent. The communication between the two agents adopts a mixed communication mode of global communication and point-to-point communication. The communication logic is shown in Figure 10.

As shown in Figure 10, the equipment agents send a list of required support resources to all support resource agents in the event of a fault, and the support resource agents respond according to the list. If the number of occupied resources meets the list requirements, the resources will be allocated in real-time, otherwise, they will go into the queue of resources to be allocated and will be judged again when the next equipment returns the resources. If the number of consumable resources meets the list requirements, the resources will be allocated in real-time, otherwise, the information that the support resources do not meet the requirements in this simulation will be recorded. The equipment agents continuously monitor whether all support resources have been obtained after receiving the support resources. The maintenance begins once support resources are fully secured. After the maintenance is completed, the acquired occupied resources are returned, and the acquired consumable resources are used.

5. Case Study

Figure 11 depicts a task flow of a warship, and the parameters for the unit tasks are shown in

Table 4. Unit task parameter list.

Unit Task	Time (h)	Allowed Delay Time (h)
Shipping	160	8
Main-gun attack	1	0
Evacuation	10	2
Shipping (return)	130	8

.

The simulation structures shown in Figure 12 and Figure 13 and

Table 5. Support resource in the simulation system.

Type	Name	Initial Number
Spare parts	synchronous capacitor	4
	sealing ring	5
	gasket	5
	bolt	5
	pressure sensor	4
	temperature sensor	4
	diode	5
	circuit breaker	5
	relay	5
	supercharger	2
	desuperheater	2
Spare parts	button	12
	pilot lamp	10
	rectifier	3
	check valve	2
	fuse	5
	gear	3
	liquid level sensor	4
Maintenance personnel	mechanical repair	2
	electrical repair	2
Maintenance tool	maintenance tool	2

are obtained based on the reliability structure, reliability parameters, maintenance parameters, and the configuration scheme of the support resources of the relevant equipment in each unit task.

The success of a unit task in the simulation is based on the allowed delay time. When the delay time of the unit task due to maintenance is less than or equal to the allowed delay time, the unit task is considered successful, otherwise the unit task fails. A mission is considered to have failed as soon as one of the unit tasks in the entire task flow fails. The simulation was run 3000 times, resulting in 2798 successes and 202 failures for the entire task flow, with overall mission reliability of 0.933. The task flow has a reliability of 0.990 for the shipping unit task, 0.980 for the main-gun attack unit task, 0.965 for the evacuation unit task, and 0.995 for the shipping (return) unit task. The variation curves of the overall mission reliability and the mission reliability of each unit task during the simulation are shown in Figure 14 and Figure 15, respectively.

Figure 15 shows that the reliability of the attack unit task and the evacuation unit task in the task flow is low and needs to be focused. The following two types of work could be considered to reduce the impact: (1) Tasks are planned in the way that the proportion of execution time spent on the relevant unit tasks is reduced without compromising the quality of the tasks; (2) The equipment monitoring frequency and the amount of personnel are increased to improve maintenance speed during the execution of the relevant unit tasks.

In addition, the simulation results for the equipment with a high percentage of fault time are shown in

Table 6. The proportion of equipment fault time.

Name	Total Fault Downtime (h)	Required Work Time (h)	Proportion
Diesel generator	2609.7	877,449.5	0.00297
Diesel engine	1732.8	877,449.5	0.00197
Auxiliary system	1442	877,449.5	0.00164
Communication system	1428	877,449.5	0.00162
Radar	1345.6	877,449.5	0.00153
Recognition systems	1335.5	877,449.5	0.00152
Velocity radar	4.5	2969.3	0.00151
Photoelectric tracker	4.3	2969.3	0.00145

. Table 6 indicates that the percentage of fault time of the diesel generator and diesel engine is relatively high, which needs to be focused on during the mission. The following three types of work can be considered to reduce the proportion of fault time for the related equipment: (1) The equipment is technically inspected or maintained in preparation for a mission to ensure that it is in optimal condition; (2) The influencing factors such as maintenance process and personnel allocation for the equipment should be analyzed to reduce maintenance time; (3) Sufficient maintenance support resources need to be prepared for the equipment to avoid the inability to maintain equipment due to lack of support resources.

The requirement for analyzing support resources lies in outputting the number of support resources that the warship should be allocated before the mission starts so that the maintenance support request can reach a certain satisfaction rate $\theta$. Where the calculation process is for the recommended number of consumable resources in the support resources is as follows:

Step 1: Record the used number of support resources in $n$ simulations.

$$N=\left[\begin{array}{cccc}R{N}_{1,M_1}& R{N}_{1,M_2}& \dots & R{N}_{1,M_L}\\ R{N}_{2,M_1}& R{N}_{2,M_2}& \dots & R{N}_{2,M_L}\\ \dots & \dots & \dots & \dots \\ R{N}_{n,M_1}& R{N}_{n,M_2}& \dots & R{N}_{n,M_L}\end{array}\right]$$

(5)

Step 2: Rank the used number of support resource $M_l$ in $n$ simulations in ascending order.

$$N_{sort,M_l}=\left[R{N}_{{\partial }_1,M_l},R{N}_{{\partial }_2,M_l},\dots ,R{N}_{{\partial }_n,M_l}\right]$$

(6)

Step 3: Obtain the recommended number of support resource $M_l$.

$$N_{\mathrm{recommended},M_l}=R{N}_{{\partial }_{\lceil n\theta \rceil },M_l}$$

(7)

Under the condition of the initial quantity, the satisfaction rate, utilization rate, and recommended quantity of various consumable resources are obtained through multiple simulations, as shown in

Table 7. The satisfaction rate and recommended quantity of support resource.

Name	Initial Quantity	Satisfaction Rate	Utilization Rate	Recommended Quantity
				$\mathit{\theta }=0.9$	$\mathit{\theta }=0.8$
Synchronous capacitor	4	99.4%	28.4%	3	2
Sealing ring	5	99.9%	23.8%	3	2
Gasket	5	99.9%	23.8%	3	2
Bolt	5	99.9%	23.8%	3	2
Pressure sensor	4	98.8%	34.3%	4	2
Temperature sensor	4	99.6%	26.2%	2	2
Diode	5	99.8%	25.3%	3	2
Circuit breaker	5	99.9%	23.4%	3	2
Relay	5	99.9%	23.4%	3	2
Supercharger	2	98.5%	14%	1	1
Desuperheater	2	99.3%	11%	1	1
Button	12	100%	31.1%	6	5
Pilot lamp	10	99.9%	33.5%	6	5
Rectifier	3	98.7%	22.4%	2	1
Check valve	2	99.7%	5.3%	1	1
Fuse	5	99.9%	24.5%	3	2
Gear	3	99.6%	14.2%	1	1
Liquid level sensor	4	99.8%	21%	2	2

.

For occupied resources, the simulation results show an occupancy rate of 1.2% for mechanical maintenance personnel, 1.5% for electrical maintenance personnel, and 1.3% for maintenance tools. These results can be used as effective guidance for reasonable arrangement of maintenance personnel, number of maintenance tools, and personnel scheduling.

This case is used for sensitivity analysis, including research on task parameters, reliability structure, and allocation of support resources.

For task parameters, this study considers the impact of task time and allowed delay time in a unit task on task reliability. Taking the shipping unit task as an example, constant factors include:

(a)

The structure between the unit mission and equipment.

(b)

The equipment reliability structure.

(c)

The scheme of support resources.

The task time is set from 20 to 1000, the allowed delay time is 10, and a 300,000 h parameter comparison experiment is fulfilled. The change of mission reliability with task time is shown in Figure 16.

Considering the scenario where the task time and allowed delay time are allowed to change simultaneously, the task time is set from 20 to 1000, and the allowed delay time is set from 1 to 10. The 3D curve graph is shown in Figure 17.

For equipment reliability structure, the power system uses difference reliability structure in the two unit tasks.

(a)

The engines in the shipping unit task are a parallel system that consists of two subsystems; the subsystems are a series system consisting of two engines.

(b)

The engines in the evacuation unit task are a series system that consists of four engines.

The task time of the two unit tasks is set as 200 h, and the simulation time is set as 300,000 h under the condition of varying the allowed delay time. The change of mission reliability is shown in Figure 18.

As you can see from the Figure 18, equipment reliability structure has great influence on mission reliability, we need to pay attention to the design of equipment reliability structure and the way the equipment is used.

Other types of reliability structures need to be further analyzed by changing the structure of the simulation model according to the reliability structure of specific equipment.

For the equipment support resource allocation scheme, the number of indicators is selected as the change parameter. The number of indicators is set from 1 to 5, the task time is set as 400 h, and the allowed delay time is set as 10 h. Each round is simulated for 300,000 h, and the variation of mission reliability with the number of spare parts is shown in Figure 19.

As can be seen from Figure 19, the configuration of the spare parts’ quantity has little influence on the short-time task, and the primary influence factors are the task time and allowed delay time.

Mission time is extended to 10,000 h, and the allowed delay time is 100 h. The number of other spare parts is set to be very sufficient, the number of indicators is set from 1 to 15, and the simulation time is set as 500,000 h. The change in mission reliability with the number of spare parts of the indicator is shown in Figure 20.

Therefore, for a long-time mission, the biggest limit affecting mission reliability is the allowed delay time in the mission parameters, but it is also necessary to pay attention to the configuration scheme of the number of spare parts. In addition, the simulation reveals that the number of maintenance tool configurations has little effect on the shipping unit task, so the detailed chart is not listed here.

6. Conclusions

This paper solves the problem of evaluating warship mission reliability under the condition of equipment support resources by agent-based modeling and simulation technology and proposes a modeling paradigm for the application of agent technology in the field of warship mission reliability calculation. The influence of support resources on equipment state is introduced into the modeling of warship mission reliability, which expands the influencing factors considered in mission reliability modeling and improves the accuracy of reliability calculation. This study provides technical support for the calculation of system reliability models with more complex influence relationships. Moreover, the proposed method combines Markov processes and Petri nets at the theoretical level and has preferable expansibility, which can conduce to build a general, accurate, and compatible equipment reliability analysis model.

Based on the calculation of mission reliability, this paper also calculates the quantity of various equipment support resources that the warship should carry before the start of a mission with satisfaction rate as the objective. Applying the calculation results can ensure that the overall mission reliability of the warship meets the predetermined target and can effectively improve the utilization efficiency of equipment support resources and avoid the waste of resources and funds caused by excessive allocation of equipment support resources. In addition, the sensitivity analysis of the system shows the actual use of the system, which can provide reference for decision makers.

The configuration and calculation process of the designed simulation system adopts a visual editing method to enable real-time observation of the state of tasks, equipment, and support resources in the system. The simulation system has the advantages of matching actual engineering application scenarios, easy editing of the simulation structure by engineers and technicians, and a low threshold for use. Low threshold for use means that the operator can analyze only by dragging operations and entering parameters, and it does not require high coding ability. In addition, various analysis indicators (i.e., global mission reliability, unit task mission reliability, system reliability, equipment reliability, recommended quantity of equipment support resources, and utilization rate of equipment support resources under the default configuration scheme) can be exported through the simulation system to facilitate further data analysis by the researchers.

In general, the application of agent-based technology in warship mission reliability evaluation considering equipment support resources plays a significant role in the whole process of equipment management. First, in the process of equipment development, convenient and fast reliability design methods and equipment development tools are provided for developers, which improve the efficiency and quality of supportability analysis in the development stage and then improve the quality of equipment design. Second, in the process of equipment use, dynamic and accurate reliability data are provided for the scientific use of equipment, rather than static and typical reliability design data, which works as an effective data guarantee for the effective evaluation of the equipment system and mission reliability analysis with complex mission conditions and then provide support for mission decision-making.

The agent-based modeling paradigm for warship mission reliability considering equipment support resources developed in this paper can be used as a valid reference for reliability modeling with complex influencing factors. However, for different fault rules, fault propagation, and environmental impacts of actual equipment, it is necessary to carry out further research on the parameters, transition, and communication rules involved in the model.