6.4: The Case Study for Detractors

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The simulation process is restarted to analyze the effect on lead time of each detractor separately.

6.4.1 Define the Issues and Solution Objective

The effect of random downtimes on part lead time for parts processed by the workstation is to be assessed. As discussed in the previous section, the time between breakdowns is modeled as exponentially distributed with a mean of 40 hours and the time to repair is modeled as uniformly distributed between 30 and 120 minutes.

The effect of defective parts on part lead time at the workstation is to be assessed. Five percent of completed parts are found to be effective and must be reworked. The time for reworking is the same as the original processing time.

The effect of setup and batching on part lead time at the workstation is to be assessed. For a target utilization of 95%, the batch size was determined to be 42 parts.

6.4.2 Build Models

The modeling of random downtimes was discussed in chapter 2 and will not be repeated here. To summarize, recall a distinct process is created which models an ongoing cycle of breakdowns and repairs. After the time between breakdowns, the resource representing the workstation enters the broken state from the idle state. After the time for repair, the resource enters the idle state to be ready to process another part.

The model in section 6.3.2 is modified as follows to include defective parts. After a part has completed processing, it is identified as needing rework with probability 5%. If rework is needed, the part is sent back to start the workstation process over again. Parts now arrive to Process Arrive where the arrival time is set. This avoids resetting the arrival time for defective parts.

	// Workstation model with defective parts
Define Arrivals:\ \(\ \quad\quad\) Time of first arrival: \(\ \quad\quad\) Time between arrivals: Number of arrivals:	// mean must equal takt time 0 Exponentially distributed with a mean of 6 minutes Exponential (6) minutes Infinite // Note: The average number of arrivals is 1680
Define Resources: \(\ \quad\quad\) WS/1 with states (Busy, Idle)
Define Entity Attributes: \(\ \quad\quad\) ArrivalTime	// part tagged with its arrival time; each part has its own tag
Define State Variable \(\ \quad\quad\) PercentDefective = 0.05	// Percent of defective parts
Process Arrive Begin \(\ \quad\quad\) Set ArrivalTime = Clock \(\ \quad\quad\) Send to Process Workstation End	// record time part arrives on tag // start processing
Process Workstation Begin \(\ \quad\quad\) Wait until WS/1 is Idle in Queue QWS \(\ \quad\quad\) Make WS/1 Busy \(\ \quad\quad\) Wait for Triangular (3, 4, 8) minutes \(\ \quad\quad\) Make WS/1 Idle \(\ \quad\quad\) If (Uniform(0,1) < 0.05) then \(\ \quad\quad\) Send to Process Workstation \(\ \quad\quad\) Tabulate (Clock-ArrivalTime) in LeadTime End	// part waits for its turn on the machine // part starts turn on machine; machine is busy // part is processed // part is finished; machine is idle //part is defective rework // keep track of part time on machine

The model in section 6.3.2 is modified as follows to include batching and setup. Entities in the workstation process now represent batches. Thus, an entity is not sent from the arrival process to the workstation process until a batch is formed. In the arrival process, the first 41 entities in the batch wait on a list. The 42^nd entity is sent to the workstation process. The time delay in the workstation process is now the setup time plus 42 different samples of the processing time. After the batch is processed, all 42 entities go to the depart process so that each lead time can be recorded.

	// Workstation model with batching and setup
Define Arrivals: \(\ \quad\quad\) Time of first arrival: \(\ \quad\quad\) Time between arrivals: \(\ \quad\quad\) Number of arrivals:	// mean must equal takt time 0 Exponentially distributed with a mean of 6 minutes Exponential (6) minutes Infinite // Note: The average number of arrivals is 1680
Define Resources: \(\ \quad\quad\) WS/1 with states (Busy, Idle)
Define Entity Attributes: \(\ \quad\quad\) ArrivalTime	// part tagged with its arrival time; each part has its own tag
Define State Variable \(\ \quad\quad\) BatchSize = 42 \(\ \quad\quad\) SetupTime = 30 \(\ \quad\quad\) Processed	// Percent of defective parts // Setup time // Number of parts processed
Define List \(\ \quad\quad\) BatchList	// List of parts waiting for batching
Process Arrive Begin \(\ \quad\quad\)Set ArrivalTime = Clock \(\ \quad\quad\)If TotalArrivals(Arrive) % BatchSize ! = 0 then \(\ \quad\quad\quad\quad\)Add entity to list BatchList \(\ \quad\quad\)Send to Process Workstation End	// record time part arrives on tag // stop entity processing for now // start processing
Process Workstation // An entity in this process represents a batch Begin \(\ \quad\quad\) Wait until WS/1 is Idle in Queue QWS \(\ \quad\quad\) Make WS/1 Busy \(\ \quad\quad\) Wait for SetupTime \(\ \quad\quad\) // Processing time for batch as sum of processing times for each part \(\ \quad\quad\) Processed = 0 \(\ \quad\quad\) do while Processed < Batchsize \(\ \quad\quad\) Begin \(\ \quad\quad\quad\quad\) Wait for Triangular (3, 4, 8) minutes \(\ \quad\quad\quad\quad\) Processed++ \(\ \quad\quad\) End \(\ \quad\quad\) Make WS/1 Idle \(\ \quad\quad\) // Send all entities in batch to record lead time \(\ \quad\quad\) Send Batchsize – 1 from BatchList to Process Depart \(\ \quad\quad\) Send to Process Depart End Process Depart \(\ \quad\quad\) Tabulate (Clock-ArrivalTime) in LeadTime End	// batch waits for its turn on the machine // part starts turn on machine; machine is busy // Setup machine // part is processed // part is finished; machine is idle // keep track of part time on machine

6.4.3 Assessment of the Impact of the Detractors on Part Lead Time

The experimental design shown in Table 6-2 can be used with additions as follows:

For the case of breakdowns, add two random streams: one for the time between breakdowns and the other for the time till repair.
For the case of defective parts, add a random stream for determining whether or not parts are defective.
For setup and batching, no additions are needed.

Table 6-5 shows the simulation results assessing the effect on lead time of breakdowns.

Table 6-5: Simulation Results for Breakdown Experiment
Replicate	Average Number at Station	Average Lead Time	Maximum Lead Time	Utilization
1	4.33	25.41	94.28	0.86
2	5.28	32.03	186.20	0.83
3	3.49	20.90	83.38	0.83
4	8.48	48.58	270.39	0.87
5	3.91	24.29	138.08	0.80
6	3.67	22.36	116.80	0.82
7	3.89	23.15	141.18	0.84
8	3.51	21.39	121.25	0.82
9	6.07	35.46	124.02	0.86
10	5.40	32.74	164.23	0.83
11	4.30	25.06	149.75	0.86
12	14.79	85.83	264.19	0.86
13	3.57	21.78	91.78	0.82
14	4.52	28.31	134.16	0.80
15	4.14	24.25	148.00	0.86
16	2.76	16.71	90.52	0.82
17	7.06	42.84	213.73	0.83
18	3.41	21.14	128.25	0.80
19	10.59	60.52	218.28	0.88
20	7.17	41.47	221.30	0.86
Average	5.52	32.71	154.99	0.84
Std. Dev.	2.94	16.68	56.37	0.02
Lower Bound	3.64	22.04	118.93	0.82
Upper Bound	7.40	43.38	191.05	0.85

Note that there is an operational significant increase in the average number at the station, the average lead time, and the maximum lead time versus the base experiment. Notice the increase in the standard deviation of these quantities as well.

This statistical significance of this difference is confirmed for the average lead time using the paired-t test shown in Table 6-6.

Table 6-6: Paired-t test for Difference in Average Lead Time
	Average Lead Time
Replicate	Base	Breakdowns	Increase
1	18.80	25.41	6.62
2	18.11	32.03	13.92
3	20.36	20.90	0.54
4	21.15	48.58	27.42
5	14.13	24.29	10.15
6	16.79	22.36	5.56
7	20.17	23.15	2.98
8	15.66	21.39	5.73
9	18.52	35.46	16.94
10	20.34	32.74	12.40
11	16.99	25.06	8.0
12	26.07	85.83	59.76
13	18.97	21.78	2.81
14	16.46	28.31	11.85
15	18.89	24.25	5.36
16	16.62	16.71	0.09
17	15.49	42.84	27.36
18	15.66	21.14	5.48
19	31.55	60.52	28.97
20	25.75	41.47	15.71
Average	19.32	32.71	13.39
Std. Dev.	4.24	16.68	13.96
Lower Bound	16.61	22.04	4.46
Upper Bound	22.03	43.38	22.31

The application of the paired-t test to the other simulation results is left as an exercise for the reader.

Table 6-7 shows the simulation results for the case of defective parts.

Table 6-7: Simulation Results for Defects Experiment
Replicate	Average Number at Station	Average Lead Time	Max Lead Time	Utilization
1	4.42	25.96	92.01	0.90
2	3.93	23.78	109.29	0.86
3	4.95	29.68	115.86	0.89
4	6.25	35.80	116.02	0.92
5	2.76	17.08	57.05	0.83
6	3.71	22.61	89.94	0.87
7	4.34	25.81	86.87	0.88
8	3.23	19.67	69.43	0.86
9	4.56	26.64	96.35	0.90
10	4.46	27.02	105.34	0.87
11	3.51	20.49	70.55	0.89
12	6.45	37.28	151.03	0.91
13	4.59	27.99	120.01	0.87
14	3.77	23.62	110.85	0.84
15	5.55	32.52	97.14	0.91
16	3.44	20.82	109.64	0.87
17	4.22	25.56	107.08	0.87
18	3.08	19.13	74.60	0.84
19	9.26	52.91	210.05	0.92
20	7.47	43.21	202.32	0.91
Average	4.70	27.88	109.57	0.88
Std. Dev.	1.61	8.83	39.26	0.03
Lower Bound	3.67	22.23	84.46	0.86
Upper Bound	5.73	33.53	134.69	0.90

The average and maximum lead times have increased noticeably. The utilization has increased as would be expected as has the average number at the station. Recall from the VUT equation that average time in the buffer increases in a highly non-linear fashion as the utilization increases.

Table 6-8 shows the simulation results for the case of setting up the machine and batching parts.

Table 6-8: Simulation Results for the Batching and Setup Experiment
Replicate	Average Number at Station	Average Lead Time	Max Lead Time	Utilization
1	1.07	385.04	569.01	0.95
2	1.04	396.15	600.01	0.92
3	1.02	387.67	574.46	0.92
4	1.34	447.70	725.87	0.96
5	0.92	372.75	576.90	0.89
6	1.02	388.70	601.50	0.92
7	1.07	394.96	584.17	0.94
8	0.99	380.84	570.58	0.92
9	1.07	388.28	610.56	0.96
10	1.05	396.50	587.92	0.92
11	1.19	416.94	610.85	0.95
12	1.29	443.08	720.79	0.96
13	1.01	387.51	609.96	0.90
14	0.96	385.28	576.22	0.89
15	1.22	429.32	685.80	0.95
16	0.98	380.15	591.23	0.92
17	0.99	385.66	581.59	0.92
18	0.98	391.68	586.99	0.89
19	1.86	579.34	950.53	0.97
20	1.24	425.28	696.60	0.97
Average	1.12	408.14	630.58	0.93
Std. Dev.	0.21	45.65	90.67	0.03
Lower Bound	0.98	378.94	572.58	0.91
Upper Bound	1.25	437.35	688.58	0.95

The following effects of setup and batching can be noted in table 6-8.

The average number at the station now represents batches instead of individual parts. The average value of 1.12 indicates that on the average a new batch forms in a shorter time than it takes to process the preceding batch.
The average and maximum lead times of a part increase greatly versus the case with no detractors reflecting the time to form a batch and setup time.
The utilization is consistent with that specified to find the best batch size, 95%.