Keywords

1 Introduction

Maintenance tasks are an important way to ensure the normal operation of the product. Essentially, maintenance is also a kind of typical human-computer interaction activity, which is changed by the interaction between human and machine. In order to analyze the relationship of human and machine in maintenance activities, the modeling of maintenance activities is the first step in the study of maintenance. The whole process of the maintenance task and the object properties involved are analyzed.

As a conventional method of maintenance modeling, Petri net is used to construct the relationship of human and object in the interaction activity [1,2,3]. In fact, in order to more systematically research on the complex activities, it is important to bring a multi-hierarchy and multi-granularity analysis method [4]. Moreover, maintenance activities have hierarchical structure. In the research of maintenance activities, maintenance activities are usually divided with bottom-up approach into several levels [5]. therbligs are the lowest level of maintenance activities [6].

The interaction between human and machine in maintenance activities shows up as the sequential and timing relationship among therbligs. Petri net is better to describe the discrete event system which is multistage, concurrent and asynchronous, but it is difficult to characterize the hierarchical structure and time sequence characteristics of system. In addition, “human” activities change state of “machine” in the maintenance activities, In other words, that change the relationship of human-computer interaction.

However, model based on Petri network is so poor in reusability that a new model of maintenance activities is constructed. Therefore, it is very necessary to propose a flexible and multi-granularity method to describe the interaction between human and machine in the maintenance activities.

Formalization description is a method to describe the properties of the system by the mathematical theory and form [7]. As a standard language describing the characteristics of system, it is standard that can describe the time characteristics, the internal structure, behavior characteristics of the system by the strict rules and definitions. As an effective method to establish the system model, it is integrated that provides a complete and unified framework to describe, establish and validate system [8]. Formalization description can not only describe the characteristics and structure of maintenance activities more accurately, but also make up for the deficiency of Petri Network.

According to the hierarchical structure of the maintenance activities, as the lowest level of maintenance activities, therbligs can model all hierarchy of maintenance activities from the bottom to the top. In this paper, Based on the extension theory of the description of the relationship between things, as the bottom of maintenance task, maintenance therbligs are redefined. Based on Agent theory of the concepts of state, action, activity and behavior [9], the formalization representation of the therblig is defined, and the definition of maintenance activity is transformed into a description of multiple variables. The validity of the method is verified by examples.

2 Decomposition and Definitions of Maintenance Activities

The decomposition of maintenance is to decompose the complex task to the basic task, so as to show the man-machine relationship and the “human” property in the maintenance task. Based on the analytic hierarchy process, this paper establishes the decomposition rule of the maintenance task, which is defined according to the external constraints such as the maintenance target and the environment. Specific rules are as follows.

  1. (1)

    the top level includes the maintenance objectives, environmental conditions, and the associated objects and operations.

  2. (2)

    for maintenance, first of all, it is necessary to maintain the target and the environment and other external constraints to the first level. The complex tasks are divided into the basic tasks according to the sub objectives and constraints.

  3. (3)

    The sub objective is composed of several functional points, according to which the next level is divided.

  4. (4)

    the lowest level is the smallest human-computer interaction system.

The maintenance is divided into four levels, which are maintenance work, Maintenance activity, elementary maintenance and therblig.

Agent is a behavioral entity that has the characteristics of autonomy, interactivity, responsiveness and initiative [10]. According to the Agent theory of the concepts of state, action, activity and behavior, not only the four hierarchies of maintenance activities are defined and described, but also the interactive relationship between human and machine is explained [11, 12]. Specific definitions are as follows.

Definition 1.

Therblig is the smallest operation unit in the maintenance activities.

Definition 2.

Elementary Maintenance Activity consists of a series of therbigs by sequence and time. The relationship of therbligs is the “order”, “and” and “or”.

Definition 3.

Maintenance activity consists of a series of elementary maintenance activities on the condition.

Definition 4.

Maintenance work consists of a series of maintenance activities on the condition.

3 Formalization Modeling of Maintenance

3.1 Description of Therbligs

Essentially, the execution of the therbligs is a process that changes not only themselves but also the relationship of human and machine in maintenance activities. The change is the process where one state transforms into another. In order to describe this process, this paper introduces basic element of extension theory to describe maintenance therbligs as agent.

In the extension theory, basic element is to describe the world of an atomic element, can be expressed as

$$ {\text{B}} = \left( {{\text{O}},{\text{c}},{\text{v}}} \right) $$

Where O denotes the object; c is feature; V is representation attribute value When an object has n characteristic attributes, the basic element is represented by an n-dimensional. According to the different objects, the basic element can be divided into matter element, Affair element and relation element. Matter element, Affair element and relation element can further describe the problem comprehensively.

Thus, the maintenance therbligs can be composed of “human” matter element and “machine” matter element and “interactive action” affair element. Expressed as:

$$ \begin{aligned} {\text{Act}} & = \left[ {{\text{H}},{\text{I}},{\text{M}}} \right] \\ {\text{H}} & = \{ {\text{c}}_{\text{h1}} ,{\text{c}}_{\text{h2}} , \ldots ,{\text{c}}_{\text{hn}} \} \\ {\text{I}} & = {\text{TR}}({\text{c}}_{\text{i1}} ,{\text{c}}_{\text{i2}} , \ldots ,{\text{c}}_{\text{in}} ) \\ {\text{M}} & = \{ {\text{c}}_{\text{m1}} ,{\text{c}}_{\text{m2}} , \ldots ,{\text{c}}_{\text{mn}} \} \\ \end{aligned} $$

Where Act is the maintenance therbligs; H is “human” as matter element; M is “machine” as matter element; I is “interactive action” as affair element; cH, ci and cm represent feature attributes.

Attribute values are static and dynamic. Dynamic attribute values can change themselves over time, while static attribute values are fixed. The attribute values of H and M are static attribute values. The attribute values of I is a dynamic attribute value. In order to definite the complete and independent concepts of all therbligs, our static properties of the H and M values are put forward.

$$ {\text{H}} = \left\{ {{\text{HA}},{\text{HS}},{\text{HM}},{\text{HD}},{\text{HP}},{\text{HT}}} \right\} $$

Where HA is Human actuator; HS is Human actuator shape; HM is Human force method; HD is Human force direction; HP is Human posture; HT is Human tool;

$$ {\text{M}} = \{ {\text{MS}},{\text{MM}},{\text{MP}},{\text{MG}},{\text{MR}}\} $$

Where MS is Machine size; MM is Machine modeling; MP is Machine position; MG is Machine operation guide; MR is Machine operating restriction.

All the maintenance therbligs can be represented by this method, and the formal description of each maintenance therblig is unique.

3.2 Description of Elementary Maintenance Activity

Elementary Maintenance Activity consists of a series of therbigs by sequence and time. The relationship of therbligs is the “order”, “and” and “or”. These relations can be represented by a relation element. Elementary Maintenance Activity (acts) can be expressed as:

$$ \begin{aligned} {\text{Acts}} & = \left[ {{\text{A}},{\text{R}}} \right] \\ {\text{R}} & = \left( {{\text{T}},{\text{L}}} \right) \\ \end{aligned} $$

Where: A- the collection of therbligs; R- the timing and logical formula of therbligs, indicating the timing relationship “T” is the “before” and “after”. Logical relationship “L” between the therbligs is the “order”, “and” and “or”.

3.3 Description of Maintenance Activity

Maintenance activity consists of a series of elementary maintenance activities on the condition. Maintenance Activity (Atv) can be expressed as:

$$ {\text{Atv}} = \, < {\text{I}},{\text{C}}, {\text{Acts}} > $$

Where: I - the purpose and intent of the maintenance operation; C - the collection of conditions or environmental factors, representing the condition or environment to stimulate the maintenance operations. the impact of stimulation divides into three kinds. The first one is its own factors, such as the difficulty of operation, operation time, complexity and so on. The second kind of individual factors is the impact of individual’s operation ability and cognitive level. The third kind of environmental factors is the spatial size of the working environment, lighting, noise, and climate and so on. The first two belong to their own influence, the latter one is outside the impact; Acts - elementary maintenance activities, Acts ∈ As, As - the collection of all elementary maintenance activities.

For example, Maintenance activity (Atv) can be showed as:

3.4 Description of Maintenance Work

Maintenance work consists of a series of maintenance activities on the condition. Maintenance work (W) can be expressed as:

$$ {\text{W}} = \, < {\text{G}}, {\text{C}}, {\text{A}}, {\text{Atvs}} > $$

Where G is the set of all the purposes in the maintenance; C is the set of all factors that affect the maintenance activities; A is the set of all motivations in the maintenance. Atvs is the set of all Maintenance activities. Maintenance work represents the process of human-machine interaction by the triple in this formula.

4 Verification

In order to verify the validity of the formalization modeling method based on agent, we take an activity (W0), which is adapted from the literature [11, 12]. This method and Petri net are respectively used to model W0.

First of all, using this method, it can be formalized as follows:

Similarly, the active W0 can be modeled based on Petri net, as shown in Fig. 1.

$$ \begin{aligned} {\text{P}} & = \{ {\text{p}}_{ 1} ,{\text{p}}_{ 2} ,{\text{p}}_{ 3} ,{\text{p}}_{ 4} , \ldots ,{\text{p}}_{ 1 1} ,{\text{p}}_{ 1 2} \} \\ {\text{T}} & = \{ {\text{t}}_{ 1} ,{\text{t}}_{ 2} ,{\text{t}}_{ 3} ,{\text{t}}_{ 4} , \ldots ,{\text{t}}_{ 9} \} \\ \end{aligned} $$
Fig. 1.
figure 1

Petri’s expression of W0

Full size image

Where: P is a set of finite places based on Petri nets; T is a set of finite transitions based on Petri nets.

It can be seen that the Petri net model is consistent with the method of this paper in dealing with the distribution and concurrency. The validity of the method is verified by examples.

5 Conclusion

In the future, on-orbit maintenance activities are complex and varied, and the operating procedures are diverse [13]. Therefore, it is necessary to study on-orbit maintenance activities in a more systematic way.

In order to study and analyze the maintenance activities more systematically, according to Agent theory and the formal definition of therbligs, this paper defines and describes elementary maintenance activities, maintenance activities and maintenance works. The effectiveness of the method is verified by practical application. The method of multi-granularity formalization solves the problems of the expression of complex hierarchical and sequential-timing relationship in the modeling process of maintenance activities. This paper will further study the method of automated modeling process of maintenance activities.