*Second Experiment*

A more detailed model of the FMS system was developed taking into account the quality, availability and reliability of AGVs and battery charging.

AGVs have very advanced design and are considered very reliable, but there are certainly few publications about AGV reliability, compared to publications about machine reliability including [48,49]. With the use of fault tree analysis, a reliability block diagram and a hazard decision tree of AGV components, reliability evaluation of the failure rate λ [1/h] was estimated to be 0.003 [48] and 0.0014 [49]. That can also be described with the Mean Time Between Failures (MTBF) as reciprocal of the failure rate λ. Basing on the λ values, we have the range of MTBF = 300 ÷ 700 h and we have assumed an average of MTBFagv = 500 h for modelling the reliability of AGV. We have also assumed Mean Time To Repair (MTTRagv) = 8 h. The reliability of CNC machine tools was omitted because its reliability should be much better than that of AGVs, and we will concentrate on the failure e ffect of the AGVs. The machines are working parallelly; therefore, the e ffect of machine failures would be very small. On the other hand, another random factor could hinder the analysis of results.

The AGV can work 24 h per day but sometimes battery loading is required. We have assumed a working schedule for 6 AGVs with a 4 h pause for battery loading. It means that AGVs charge the batteries alternately, and in each moment 5 AGVs are working and one is charging the battery. In the case of malfunction, the AGV is automatically moving to the parking place for maintenance or should be manually removed to prevent blockage.

The scenario includes continuous work of the FMS for 3 shifts per day and 5 days per week. As a result of the long-time effect of AGVs failures, long-time simulations were performed, including work for 24, 120, 500 and 1500 h. The experiment's results without and with reliability parameters of AGVs are presented in Tables 2 and 3, respectively. (The raw data are included in the Supplementary Materials).

**Table 2.** The results of simulation experiments (Average production completed Pavg, in [pieces] for 6 AGVs with battery charging, without failures, 30 simulation runs in each experiment, 95% confidence level).


**Table 3.** The results of simulation experiments (Average production completed Pavg, in [pieces] for 6 AGVs with battery charging, with AGVs failures, MTBF = 500 h, MTTR = 8 h, 30 simulation runs in each experiment, 95% confidence level).


An analysis of the previous model showed that blockage of the machines sometimes occurs; therefore, small loading/unloading buffers with a capacity of one piece were added to machines in order to improve the production flow. Quality parameters were defined as 99.9% of good products according to the OEE quality factor.

Comparing the results from Tables 2 and 3, a small but significant effect of AGVs failures on production can be seen (a decrease of about 0.7%). For a more detailed analysis, the OFE metrics can be used. Since the model was built based on the OEE components and contains parameters of availability, performance and quality, the production value from the simulation Pavg can be directly used to calculate the OFE indicator [25,41].

$$\text{OFE} = \frac{\text{P}\_{\text{avg}}}{\text{P}\_{\text{limit}}} \tag{9}$$

The value Plimit represents the theoretically available maximal production in ideal conditions. For the average machining time of tm = 530 s, the limit is equal to 6.79 pc./hour for one machine and 652 pc./24 h for the whole machining system (Plimit = 27.17 pc./hour).

The juxtaposition of the OFE indexes is included in Table 4.

The differences between OFE2 and OFE3 are related to the warmup of the system in a short time and to the effect of AGV failures in a long time. This result is consistent with assumed reliability parameters and inherent availability (Equation (3)) of AGV and parallel system. As there is a small

probability of simultaneous failure of all AGVs, the effect is connected with the loss of performance including loss of speed during loading/unloading, waiting for transport and blocking.


**Table 4.** The Overall Factory Effectiveness (OFE) metrics for model of 6 AGVs without failures OFE2 and with failures OFE3 and OFE1 from the previous experiment.
