It is important to validate the implemented model in order to find out if the model is working accordingly. The objective function consists of the minimization of four parts: the makespan, the load board used, the changeovers, and the lead time/net process time fraction. To validate the model, each part of the objective function will be validated individually with a simple case that has a known optimum. The optimum of the simple cases can be calculated by hand or are self-evident.
Makespan minimization
In order to validate the makespan optimization, a case has to be defined in which the optimum is known. In this case, the process times of all the scheduled jobs are the same and the changeover times between different test programs and testers are set to zero. If a single lot has four test programs and the number of testers is set to an even number, the optimal makespan will be the sum of all the scheduled jobs divided by the number of testers.
A case with 15 lots and each test program has a duration of 10 time units on four testers. This means there are 60 jobs to be scheduled with a total time of 600 time units. The absolute minimum time it takes to schedule all the test jobs is the total test time divided by the number of testers. In this case, the optimum makespan will be 150 time units. Figure 6.9 show that the optimum can be found.
Figure 6.9: The optimal solution of the test case validating the makepan minimization
Another case with 50 lots and each test program has a duration of 10 time units on four testers.
This means there are 200 jobs to be scheduled with a total time of 2000 time units. The problem size is a lot bigger so the computing time will longer. Again the lowest possible test it takes to complete all the test jobs is the total test time divided by the number of testers. The optimum makespan will be 500 time units. Figure 6.10 shows that even a problem size that is a lot bigger is not a problem for the genetic algorithm.
Figure 6.10: The optimal solution of the second test case validating the makepan minimization
Changeovers between different test programs
A part of the objective function minimizes the number of changeovers between different test programs. To validate this part of the objective function, a case can be optimized in which the changeovers will be penalized and the other parts of the objective function will not be used. The hypothetical case has 15 lots, with each lot having four test programs and there are four testers
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available for scheduling. If the algorithm works properly, each tester should have only one test program and there should be zero changeovers between different test programs due to the fact that they are scheduled on other testers.
Figure 6.11: The optimal solution of the test case that minimizes the number of changeovers
Figure 6.11 shows exactly the predicted outcome. Each test program is being tested on a different tester. Note that there are large gaps between several lots, this is due to the fact that this schedule is only optimized for changeovers between different test programs, it will not minimize the makespan. These gaps a result of a tester waiting until a lot has finished its previous test program.
Load board minimization
The next part of the objective function is the load board minimization. The load board type is dependent on the test parallelism. The insertion policy problem has a maximum of four test programs: the min pin and full pin setting on both hot and cold temperature tests. The min pin tests are tested with a higher test parallelism than the full pin tests. This means that the min pin tests are tested on a different load board than the full pin tests. The optimal amount of load boards can also be found with an example case with a known optimal amount of used load boards. This example case schedules 15 lots on two testers. The lots will be tested on four test programs: cold min pin, hot min pin, cold, full pin and hot full pin. The full pin tests and the min pin tests use different load boards due to their difference in test parallelism. The optimal schedule, in this case, would be that the min pin tests are scheduled on one tester and the full pin tests on the other and thus using only two load boards.
Figure 6.12: The optimal solution of the test case that minimizes the of number of used load boards
Figure 6.12 show the optimal result of the load board validation case. The Figure shows the expected result of the test programs with the same parallelism being tested on different testers.
Note that in order to make a clear image, also the changeovers were minimized.
Lead time minimization
The last part of the objective function is the minimization of the lead/net process time fraction.
The goal of this part of the objective function is to decrease the lead time of each lot in the system, this has resulted in a decrease in WIP. To validate if this part is working correctly another case problem with a known optimum is feed into the algorithm. This case consists of 10 lots that will be tested on two testers. Each lot will be tested on two test programs (cold and hot full pint tests). This case will not have any changeover times. The expected optimum will be that each lot will test its test programs right after each other. In that case, the lead time would be equal to the net process time. The lead time can not be lower than the net process time without breaking the non-overlapping constraint.
Figure 6.13: The optimal solution of the test case that minimizes the fraction of the lead time relative to the net process time
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Figure 6.13 shows that the expected optimum is indeed reached by the algorithm. This result is the shortest time each lot can be in the system.
7 Results
This section contains the results of the test insertion study. The section is divided into two subsections: the first subsection consists of an analysis of several current products that NXP is currently running in Kuala Lumpur. The second section is an analysis of the parameters that influence the insertion policy.
7.1 Actual products
This section compares three products on the different insertion policies. The first part is a detailed data analysis that results in the input variables of the scheduling analysis.
Input parameters: test jobs
One of the main input values of the scheduling algorithm is the test jobs that need to be scheduled.
The test jobs are being generated with several input variables.
• Lot size
• Test parallelism
• Test time per insertion
• Handler time per insertion
The lots vary in size for each of the products. The lot size and the test parallelism determine the number of insertions per lot. If for example a lot has a size of 604 and the test is being done with a parallelism of six, the number of test insertions will be 101 for that particular lot. The test time per insertion determines the time that is needed to test those six units and the handler time per insertion determines the time that is needed to insert the units into the load board.
For the insertion policy comparison, a total of 50,000 units of integrated circuits will be used for each evaluated product. The machine-level data of each of the three evaluated products will be analyzed and the lot sizes of the last year will be fitted on a histogram. The figures below show the empirical lot sizes of the three evaluated products.
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Figure 7.1: The empirical lot sizes of the evaluated products
The empirical data does not show the trend of a known probability function. This means that the lot sizes need to picked with empirical distribution from the available data.
The other values of the needed input parameters can be found in Table 7.1. This table is composed of planning data and input from test engineers. The table shows imported test information sorted on product and insertion policy.
Table 7.1: The input data needed to compose the jobs for scheduling Product name Insertionpolicy Insert Pinconfiguration Test
Program Test time [s]
per insertion Handler time [s]
per insertion Parallelism
Matterhorn Single 1 Full pin Cold 180 1.1 6
2 Full pin Hot 180 1.1 6
Matterhorn Split 1 Min pin Cold 1 135 4.3 32
2 Min pin Hot 1 157 4.3 32
3 Full pin Cold 2 14 1.1 6
4 Full pin Hot 2 16 1.1 6
Calypso 3M Single 1 Full pin Cold 63.6 1.8 16
2 Full pin Hot 82.2 1.8 16
Calypso 3M Split 1 Min pin Cold 1 65 4.3 32
2 Min pin Hot 1 87 4.3 32
3 Full pin Cold 2 10 1.1 8
4 Full pin Hot 2 16 1.1 8
Panther Single 1 Full pin Cold 56.6 1.1 8
2 Full pin Hot 68.5 1.1 8
Panther Split 1 Min pin Cold 1 76.5 4.3 32
2 Min pin Hot 1 83.1 4.3 32
3 Full pin Cold 2 14.9 1.1 8
4 Full pin Hot 2 14.9 1.1 8
Table 7.1 shows the test and handler time per insertion for each of the insertion policies of the different products. The test jobs can be generated with these times, test parallelism, and the picked lot sizes. To calculate a test job the following formula is used:
Ji,o= LSi Po
· (To+ Ho) (7.1)
The formula states that test job (J) from lot i on test program o is calculated by rounding up the fraction of lot size of lot i (LSi) and the test parallelism of test program o (Po), and multiply that rounded figure by the sum of the test and handling time per insertion (To and Ho). The number of total test jobs is the number of unique lots multiplied by the number of test programs of that lot.
In order to reflect continuous production, the job list has to be modified. In reality, the test jobs will never be scheduled into an empty system, so the list of test jobs needs to be changed to accommodate unfinished lots on the test floor. If for example, a week’s worth of test jobs needs to be scheduled, the unfinished lots at the start of the week and the unfinished lots at the end of the week need to be considered as well. Table 7.2 shows how an example job list with six complete lots on two test programs is modified to reflect a continuous production. The first three lots on the first test program are moved to the end of the schedule. The new job list more realistic in a continuous production setting.
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Table 7.2: An example of a job list conversion in a two test insertion policy Table 7.3: The original job list
Lot Test time on testprogram 1 [h] Test time on test program 2 [h]
Lot Test time on testprogram 1 [h] Test time on test program 2 [h]
Tables 7.5 and 7.6 shows the conversion to continuous production in a split test insertion policy scenario. The tables show that test jobs from the first lots are moved to the end of the schedule.
This modification incorporates the uncompleted lots in the beginning and the end of a schedule.
This reflects a continuous production setting. To make sure the split insertion policy can be compared with the single insertion, the number of lots per test program needs to be the same.
Table 7.5: An example of the original test jobs Lot Test time ontest program 1 [h] Test time on
test program 2 [h] Test time on
test program 3 [h] Test time on test program 4 [h]
Table 7.6: The modified job list that reflects a continuous production
Lot Test time ontest program 1 [h] Test time on
test program 2 [h] Test time on
test program 3 [h] Test time on test program 4 [h]
Input parameters: changeover times
The changeover times between the different test programs are important input parameters for the scheduling algorithm. The split insertion policy has four test programs: cold and hot min pin test and cold and hot full pin test. This means that on this policy there are 16 possible changeovers with 16 different changeover times. Within those 16 possibles, there are three types of changeovers. The first type is a changeover in which the next test program is the same as the current test program. This changeover takes the shortest amount of time because nothing has to change on the tester. The second type is a temperature changeover on the same load board, for example, a cold min pin to hot min pin. This changeover takes longer due to the temperature change of the tester. Depending on the current test program and the next test program, the tester needs to cool down or warm-up. The final type is a changeover in which the load board needs to be changed. This happens when a switch is being made from a min pin test to a full pin test or vice versa. This type of changeover has the longest duration of all the changeovers.
To find all the changeover times, two years of data from 20 UP1600 testers have been analyzed and all the changeovers have been ordered and plotted in histograms. Figure 7.2 shows the empirical data of two changeovers. The graphs show that some extreme outliers heavily influence the mean of the data. In order to get a representative value of the changeover times, the median is taken of each data set.
(a) The empirical data of the changeover from cold full pin to hot min pin
(b) The empirical data of the changeover from cold full pin to cold min pin
Figure 7.2: The empirical data of two changeovers between different test programs
The other 14 histogram plots with the empirical data of the other changeovers can be found in Appendix B. The median values of all the changeover data have been collected and can be found in table 7.7.
Table 7.7: The median value of all the 16 changeovers of the split insertion policy
Current program \Next program Cold min pin Hot min pin Cold full pin Hot full pin
Cold min pin 0.59 h 1.47 h 3.54 h 2.88 h
Hot min pin 1.62 h 0.51 h 2.87 h 2.23 h
Cold full pin 5.02 h 3.45 h 0.52 h 1.59 h
Hot full pin 2.92 h 2.80 h 1.96 h 0.43 h
The changeover times in hours of the single insertion policy are included in the 16 changeover times of the split insertion policy. The single insert policy only has four changeovers which are
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only changeovers between the same test program and changeovers between temperature tests.
No load boards need to be changed when testing on the single insertion test policy. Table 7.8 shows the changeover times of the single insertion policy.
Table 7.8: The changeover times in hours of the four changeovers in the single insertion policy Current program \Next program Cold full pin Hot full pin
Cold full pin 0.52 h 1.59 h
Hot full pin 1.96 h 0.43 h
Input parameters: objective function
The objective function consists of the minimization of four parts: the makespan, the load boards, the changeovers, and the fraction of the lead time and the processing time. The makespan and the load boards can be based on the actual costs of the hardware. The changeovers and the lead time process time fraction are penalty costs that are user input values. In the case of the three actual products that are being evaluated, the hardware costs are listed in table 7.9. With this table, the costs of running a tester can be calculated. With the assumption that the average lifetime of a load board is five years, the load board running costs can be calculated as well. An extra constraint is set on the amounts of load boards that can be used in the split insertion policy, which is one more than the number of available testers.
Table 7.9: An overview of all the hardware and maintenance costs
Product name Matterhorn Matterhorn Calypso 3M Calypso 3M Calypso 3M Panther Panther
Tester UP1600 UP1600 UP1600 UP1600 UP1600 UP1600 UP1600
Handler Matrix Matrix Matrix Matrix Matrix Matrix Matrix
Parallelism 6 32 8 16 32 8 32
Lb cost [$] per Set 26,000 29,000 22,000 24,000 29,000 20,000 29,000
Contactor Kit cost [$] per Set 11,000 50,000 12,321 18,481 46,867 12,853 46,867 Conversion Kit cost [$] per Set 17,000 17,000 17,000 17,000 17,000 17,000 17,000 cost of Maintenance- Pogo Pin [$] Monthly 2,824 5,136 953 1,554 3,360 953 3,360 Cost of Maintenance-Handler PM
/Spare Per Handler [$] Monthly 3,067 3,067 3,067 3,067 3,067 3,067 3,067
Tester cost [$] 1,021,386 1,021,386 1,021,386 1,021,386 1,021,386 1,021,386 1,021,386
Handler Cost [$] 470,000 470,000 470,000 470,000 470,000 470,000 470,000
The other two parts of the objective function that minimizes the changeovers between different test programs and the lead time of an individual are set with penalty costs. The penalty costs are set in a manner that the algorithm minimizes the changeovers but keeps the WIP constant.
Results: the same tester capacity
Three products that are currently running in the test and assembly plant in Kuala Lumpur will be assessed on their insertion policy. The products are called Matterhorn, Calypso 3M, and Panther. These products are used in the automotive industry.
The first analysis compares the three products on a tester capacity level. The insertion policies are compared on an equal number of testers. The goal of this comparison is to find the effect on the makespan of all the tested lots and the changeovers between different test programs. The number of testers is increased from two to five to look at the effects of tester availability on the makespan and number of changeovers.
Table 7.10 shows the results for the Matterhorn product. The results show a significant decrease in makespan on each tester capacity when Matterhorn is tested on a split insertion policy compared to the single insertion policy. The drawback is that at lower tester capacity the number of changeovers between different test programs increases significantly. The higher number of changeovers increases the man-hours needed to perform those changeovers and decreases the tester’s efficiency.
Table 7.10: Matterhorn insertions policy comparison with the same tester capacity Tester
Table 7.11 show the results for the Calypso 3M product. The results show that in this case, the single insertion policy is performing better in every aspect. The process times are lower than the split insertion policy and the number of changeovers is less.
Table 7.11: Calypso 3M insertions policy comparison with the same tester capacity Tester
The last table shows the results for the Panther product. The processing time decreasing when using the split insertion policy. However, the number of changeovers increases a lot at a tester capacity of two and three.
Table 7.12: Panther insertions policy comparison with the same tester capacity Tester
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Conclusion
The conclusion from this analysis is that the split insertion policy decreases the makespan of testing 50,000 Matterhorn integrated circuits decreases significantly when tested on the split insertion policy. The drawback is that on a low tester capacity for example two testers available for testing, the number of changeovers between different test programs increases significantly.
The reason for this significant decrease in makespan 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 (table 7.1) and thus giving the split insertion policy a great advantage in test parallelism which
results in the decrease of process time.
results in the decrease of process time.