This section contains an analysis to find out when to split the insertion policy. The goal is to make a framework in which future products can be assessed whether splitting the test insertion will be financially viable. This analysis simplifies the input parameters in order to find the critical area in which it will be beneficial to split the insertion policy instead of keeping the test policy on a single insertion.
Input parameters
There are a lot of input parameters that are product specific. This makes a thorough analysis hard. However several input parameters influence each other, so this means that they can be simplified and merged into fewer parameters. Table 7.19 shows the complete set of input parameters.
Table 7.19: The parameters that influence the insertion policy Parameters
The number of parameters can be decreased by making several assumptions. The hot and the cold test times are similar, so in this analysis, they are assumed to be the same. To convert a single insertion strategy to a split insertion strategy, a fraction is needed which states how much of single insertion full pin test can be tested at a higher parallelism. For this analysis, this fraction will be called full/min pin fraction. This fraction is similar for both the hot and cold tests, so in this analysis, they are also assumed to be the same. The full pin test is tested with a parallelism of 8 and the min pin test is tested on a parallelism of 32. The test time per insertion and the lot size is combined to a single parameter: test time of the full pin test. With these assump-tions, the input test times can be generated for the scheduling algorithm. The area of interest will a comparison between the costs of the single insertions policy versus the split insertions policy.
With these assumptions, the input parameters can be defined. The scheduled jobs for the split
insertion policy will be based on the min/full pin fraction, the test time of the full pin on a single insertion, and the test parallelism. So if for example, the product has a single insertion full pin test time of 5 hours and a min/full pin fraction of 0.6, the conversion to the split insertion test times would be as follows:
Tmin pin split= 5h · 0.6 · 8
32 (7.2)
For the full pin test on the split insertion policy it would be:
Tf ull pin split= 5h · (1 − 0.6) (7.3)
With this conversion, the split insertion policy can be compared with the single insertion policy.
The changeover times between the different test programs are not different from the previous analysis, so those values are kept the same. The costs that are used for the objective function are based on the hardware costs from section 7.1. Both Calypso 3M and the Panther product are tested on a parallelism of 8 during a full pin test and a parallelism of 32 during a full pin test, so these values are also used for this analysis. Table 7.20 shows hardware costs values for this analysis.
Table 7.20: The hardware costs of the two load boards
Tester UP1600 UP1600
Handler Matrix Matrix
Parallelism 8 32
Lb cost [$] per Set 20,000 29,000
Contactor Kit cost [$] per Set 12,853 46,867 Conversion Kit cost [$] per Set 17,000 17,000 cost of Maintenance- Pogo Pin [$] Monthly 953 3,360 Cost of Maintenance-Handler PM
/Spare Per Handler [$] Monthly 3,067 3,067
Tester cost [$] 1,021,386 1,021,386
Handler Cost [$] 470,000 470,000
The hardware has a depreciation time of approximately five years. The cost values are translated to a cost per time unit and used for the objective function.
Results
This section contains the results of the viability analysis. The results are visualized in contour that shows an area in which splitting the insertion is financially viable and an area in which it is not. The input parameters of the contour plots are the fraction between in which the test can be tested on min pin and the test time of the single insert full pin test. The comparison is done based on a tester capacity. Four different tester capacities are assessed. Figure 7.6 show the four contour plots of the assessed tester capacities. Each of the contour plots shows two colored areas. The purple area means that the single insertion policy costs less than the split insertion policy and the yellow area means that the split insertion policy costs less than the single insertion policy.
NXP Graduation thesis Results
Figure 7.6: The contour plots that show when splitting the insertion policy is financially viable based on the tester capacity. The purple area means that the split insertion strategy is not financially viable
and the yellow area means that it is financially viable.
The four plots show a very similar trend, the switch point is very clear when splitting the insertion policy is financially viable. With the increase of tester capacity the slope moves to the left in the figures. This means that when the tester capacity increases or an increase in demand for the product requires more testers, the split insertion policy might become the more viable option in some cases. For example, if a product has a full pin test time of 5 hours and 60% of that 5 hours can be tested on a min pin test. If the tester capacity for this product is only one then this product would be tested on a single insert policy however, when the tester capacity would grow to three or four testers then splitting the insertion policy would be the better option.
The plots also show that in every case the limit of the fraction that can be tested on min pin is around 0.25. Below this threshold, splitting the insertion policy is not a viable option.
For a new product, the insertion policy needs to be determined. After analysis by a test engineer, the fraction is found on which the product can be tested on min pin and the test times per test program. With these two parameters, the lot sizes and the tester capacity, the engineer can look up in the contour plots to determine the insertion policy of the product.
For example, if a new product has a min pin/ full pin fraction of 0.4 and a single product has a test time of 20 seconds. Now with a tester capacity of three, lot sizes determine if this product should be tested on a split policy or single policy. According to figure ?? a product with a min
pin/ full pin fraction of 0.6, the min pin test at a single insert needs to be at least 6 hours. This means that in this case, the lot size should at least be 1080 products to be financially viable on the split insertion policy.
The contour plots can also be used to evaluate new/future products when the demands increase over the years. For example, engineers are evaluating two new products. Product A in which 60 % of the full pin test can be tested on min pin and the average full pin test has a duration of six hours. For this product, the demand increases in four years so that each year another tester is needed to comply with this demand. The second product, product B can 40 % of the full pin test be tested on min pin and the average full pin test has a duration of 7 hours. The demand increases so that the tester capacity is increased from one to two testers in two years.
After the second year, the lot sizes are doubled for product B. Figure 7.7 show the effect of these demand changes on the insertion policy choice. The red dots are product A and the green dots are product B.
Figure 7.7: The contour plots with the hypothetical cases shown as dots. The purple area means that the split insertion strategy is not financially viable and the yellow area means that it is financially viable.
The figure shows that product A should stay on a single insertion policy in years one and two.
After year two it should switch to a split insertion policy due to the increase in tester capacity.
Product B should also stay on the split insertion policy in years one and two. In year three the lot sizes are doubled which doubles the test time of the full pin test. This causes the split insertion policy to be less expensive than the single insertion strategy.
NXP Graduation thesis Results
Conclusion
Several analyses can be done to evaluate new or future products on its insertion strategy. With the right input parameters, a good estimation can be made to see if which of the insertion strategy would be less or more expensive. The contour plots show that the split insertion policy becomes more viable with the increase of tester capacity. The minimum fraction to make the split insertion policy viable is 0.25. Below that fraction, it will be less costly to use the single insertion policy than the split insertion policy.
8 Conclusion and recommendations
8.1 Conclusion
The problem this thesis tackled is a scheduling problem at the final test of a semiconductor production line. An evaluation was made between two different test insertion policies. The first policy dictated that the products are only tested once per test program with all the connections pins connected to the tester, which meant that it could only be tested on a low test parallelism.
The other policy would split that single test into two tests per test program. The split policy tests one test with all the connection pins connected on a low test parallelism and the second test with only a subset of the connection pins connected which increases the test parallelism.
The problem is defined as a scheduling problem and the two insertion policies are evaluated on several parameters when they are on their optimal test schedule.
The thesis tackled this problem with an optimal scheduling model. The model scheduled a fixed set of test lots on both test insertion policies to evaluate important performance parameters.
Scheduling models are often NP-hard problems, this means that the solution space grows expo-nentially relative to the problem size. Three modeling methods are evaluated to optimize the test schedule: a mixed-integer linear problem, a basic genetic algorithm, and a hybrid genetic algorithm with local search algorithms. The mixed-integer linear problem is an exact method and the basic genetic algorithm and the hybrid genetic algorithm with local search algorithms are heuristic methods. The mixed-integer linear program gave very accurate results but due to the nature of the scheduling problem, the computing times were very long. This was solved with a basic genetic algorithm, which gets near-optimal solutions with a significantly lower computing time. However, the basic genetic algorithm could not give consistently accurate results with more difficult problem sizes. The modeling method that was most promising is the hybrid genetic algorithm with local search algorithm. The performance of this method proved to be a sweet spot between accuracy and computing time.
With the hybrid genetic algorithm model, several analyses have been done to evaluate the different insertion policies in final test. The first analysis compared several actual products on the different insertion policies when they have the same tester capacity and similar throughput. The conclusion from this analysis, the split insertion policy decreases the total test time from the Matterhorn sig-nificantly this results in a significant hardware decrease when comparing the policies on a similar throughput. The trade-off however is at a lower tester capacity, the changeovers between different test programs increase significantly. The reason for this significant decrease in total test time is that the Matterhorn product can test a high percent of its tests on min pin. The full pin test can only be tested on a parallelism of six and thus giving the split insertion policy a great advantage in test parallelism which results in a decrease in total test time. The Calypso 3M product shows an increase in total test times on the split insertion policy. When comparing the insertion policies on the same throughput, the single insertion policy needs less hardware. The reason for this result is that the Calypso 3M product can be tested on a higher test parallelism during the min pin test of the single insertion policy than the split insertion test. The min pin parallelism on the single insertion test is 16 and on the split insertion test only eight. If the full pin test on the split insertion policy also on that higher parallelism can be set the results would probably favor the split insertion tests. The last product that is evaluated, is the Panther product. This product shows a decrease in total test time on the split insertion policy. When comparing the policies on a similar throughput, the single insertion needs more hardware. The split insertion does need a lot more changeovers between different test programs compared to the single insertion policy. The changeovers between different test programs could cause several problems on the test floor and are preferably avoided. The Panther should probably only be tested on the split insertion policy if the
NXP Graduation thesis Conclusion and recommendations
tester capacity is high enough to prevent an excess of changeovers between different test programs.
The second analysis simplified the input parameters in order to evaluate the effect of the changing properties of a new product. This analysis looked at the effect of the fraction that can be tested on the min pin test and the test time of the full pin tests as input parameters. This analysis showed that there is a clear switch point from when splitting the insertion becomes financially viable. The analysis showed also that when increasing the tester capacity this switch points shifts in the direction in which it will be more financially viable to do a four insertion policy on a lower min pin/ full pin fraction and shorter test times. Finally, the analysis shows that the lower bound of the min pin/ full pin fraction is 0.25. This means that all the cases in which only 25%
of the full pin test can be done on a min pin test, will not be financially viable and should be avoided.