input places. The input places have arcs with weights 1 and 2, respectively. Currently, there are no tokens in the output place; however, a transition will be enabled when the number of tokens contained in every input place is equal to or more than the corresponding arc weights. Given this is true for the net shown in Fig. 1, the transition is enabled and the number of tokens equivalent to the output arc number are transferred to the output place; in this instance, one token appears in the output place. The number of tokens moved to the output place is dependent on the corresponding arc weight, hence if the arc weight is ‘n’, then n more tokens will appear in the output place after the transition fires

Petri nets for system representations are built up using these same components. Research has shown the application of these nets to systems that undertake phased missions, where a net is generated for the system and an additional net is developed for the phase, known as a system and phase net, respectively. Extensions for more complex systems have included using three distinct PNs, i.e. phase PN, component PN and master PN. These three kinds of

PNs are linked together and interact with each other. Such an extended approach is adopted in this paper to assess the reliability of AGV systems.

3 Application AGV system and mission

A typical AGV transport system used in a warehouse for material distribution is chosen for analysis in this research. As shown in Fig. 2, the AGV system consists of various subsystems, where the software control system is central to the AGV’s operation. This subsystem is responsible for processing and interpreting the information received from both the laser navigation system and safety system, and sends either motion or operation orders. Linked to this subsystem, there are a number of inputs and outputs. The laser navigation system and the safety system both feed into the control unit. The laser navigation system, like that developed by MacLeod [26], is in essence a position measurement system that is responsible for locating the AGV. The safety system is a collision/avoidance system designed to avoid obstacles that could appear on the pathway with the aid of a laser detection system installed on the AGV. In order to perform its tasks, the AGV has a number of output systems: the drive unit, the brake system, the steering system and the attachments (for lifting, etc.). In terms of the motion or operation orders, these are executed by the drive unit, the brake system and/or the steering system. The drive unit is typically a brushless DC electric motor which is responsible for providing power for the motion and operation of the AGV, the braking system is responsible for slowing down or stopping the AGV and is always applied when the AGV is stationary. The steering system is responsible for manoeuvring the AGV. Attachments refer to additional components that are used to assist moving and carrying of items. All functions require a power system, which is typically lead–acid battery which is responsible for supplying power to the whole AGV system.

In terms of the mission of the AGV, this can be broken up into distinct tasks. First of all, the AGV has to optimise the routes for completing the whole mission, given its assignment. Once in motion, the AGV will travel to the material collection port along the optimised route to pick up the materials. After the AGV is loaded with the materials, it will travel to the destination and unload the materials. After successfully distributing the materials, the AGV will travel back to its original parking position. Therefore, the whole mission can be pided into six phases in total, namely (1) mission allocation and route optimisation, (2) dispatch to station, (3) loading of item, (4) travelling to storage, (5) unloading and (6) travelling back to base. The mission can

be regarded as successful only when the AGV is able to operate successfully throughout all these six phases without any break due to component and/or subsystem failures and maintenance. Such a period is named as a maintenance-free operational period (MFOP).