ONE PROCESS, DIFFERENT RESULTS: METHODOLOGIES FOR ANALYZING A STENCIL PRINTING PROCESS USING PROCESS CAPABILITY INDEX ANALYSES

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1 ONE PROCESS, DIFFERENT RESULTS: METHODOLOGIES FOR ANALYZING A STENCIL PRINTING PROCESS USING PROCESS CAPABILITY INDEX ANALYSES Daryl L. Santos 1, Srinivasa Aravamudhan, Anand Bhosale 3, and Gerald Pham-Van-Diep 1 Systems Science and Industrial Engineering Department T.J. Watson School of Engineering and Applied Science Binghamton University Binghamton, NY , USA santos@binghamton.edu Speedline Technologies, Franklin, MA, USA 3 DCI Automation, Worcester, MA, USA ABSTRACT The purpose of this paper is to compare and contrast different stencil printing process capability results that can be obtained from the same data points, depending upon how the data are analyzed. In estimating a printing process capability to deposit solder paste, it is a common practice (see Mukadam et al. (00) for example) to utilize process capability indices (like C p, C pk, and others). One set of data, depending upon how it is analyzed, can actually provide different values for the index being investigated. For example, if one is interested in the capability of the process for meeting the specifications on one particular component, different results could be obtained if the data were analyzed in the following ways: board-to-board, all deposits, parallel vs. perpendicular pad orientation (w.r.t. squeegee blade direction), and others. This paper will provide an example case study and show that one process, depending upon how it is viewed or analyzed, will in fact produce various results via process capability index analysis. Key words: Process Capability, Stencil Printing PROBLEM Many process engineers are becoming aware, particularly through 6σ types of programs, of the need for a sound statistical approach to understand the capabilities of their processes and are learning many of the tools that will enable them to determine those capabilities and to subsequently improve upon them. One such tool for determining the ability of a process to meet specifications on the product is to calculate what is known as a process capability index. While the practitioner may know the formula to use in order to calculate a process capability index, like C p or C pk, what that same practitioner may not realize is the fact that performing a process capability calculation on a single set of data may actually yield different results. For example, if we consider a stencil printing process and wanted to perform a process capability calculation on the ability to deposit solder for one of the components (say a QFP), then we may get different process capability results if we looked at the data from different viewpoints. In other words, if we calculated C p or C pk on all deposits for that component, that would likely give us a different result than if we calculated C p or C pk while analyzing board-to-board deposits, or analyzing by pad orientation (with respect to squeegee blade direction), etc. Based upon this concept, this paper presents a real-world case study on solder paste deposits for a QFP (one of many examples that could be used) and shows that, depending upon how that one set of data is analyzed, that very different results on process capability estimation can be obtained. Before we do that, a brief review of process capability indices will be provided. PROCESS CAPABILITY FORMULAS As companies have recently begun certifying process engineers and other employees (or sending them for training to be certified) in 6σ programs (e.g., green belt or black belt certification), it should probably not be necessary to present an in-depth review of the various process capability formulas. Instead, we will present a brief review of the common process capability indices (namely, C p and C pk ) and their calculations. A simple process capability index (like C p, C pk,, etc.), as many of us know, is calculated as a ratio of the tolerance of some feature (print tolerance, X-axis accuracy, placement force, etc.) to the variability of the process (as typically measured as a function of standard deviation). The two most common process capability indices that are used are C p and C pk. Given that USL and LSL are the upper and lower specification limits of a feature, respectively, mu (µ) represents the mean of the process, and sigma (σ) represents the standard deviation of the

2 process that is used to produce or make that feature, then the C p and C pk formulas are as follows: C pk USL LSL C p =, and 6σ µ LSL USL µ = min,. 3σ 3σ C p is known as the inherent process capability index and C pk is known as the actual process capability index. The reason for C pk being referred to as the actual process capability index is that it, unlike C p, bases its calculations on two parameters the centering of the process, µ, and the variability in the process, σ. On the other hand, C p does not utilize information about the centering of the process. Therefore, in order to get a true understanding about whether or not the process is actually producing parts outside of specification limits, C pk should be used. As such, we will focus much of the remainder of this discussion on the C pk index. PROCESS CAPABILITY ESTIMATORS Many readers of this article may likely be saying to themselves, I ve calculated C pk dozens of times. This statement is, believe it or not, unlikely to be true in many instances. While numerous process capability studies have been performed and presented by various practitioners over the years, it is most likely the case that in each of those situations, that process capability index estimates have been generated. The process capability indices listed above are based upon a process population parameters. We rarely, if ever, have the population parameters (e.g., µ and σ), instead we typically have the estimates of those population parameters the sample average, or X, and the sample standard deviation, or s (Santos et al., 004). As such, when we calculate the process capability with these sample statistics, we are actually calculating the estimate of the process capability index. For example, considering the estimate of C pk (where the caret or ^ symbol indicates we have an estimate of the parameter), we have the following: ˆ C pk X LSL USL X = min,. 3s 3s CONFIDENCE INTERVALS (CIs) To take the above concept further, it is very important to mention that, since estimations of process capability are being performed, then in order to get a better understanding of the capability of the process, that we should calculate the confidence interval that surrounds that estimate. The reason for this is that, depending upon the sample that is taken from a process, different samples from the same process may produce different estimates of process capability. Consider this example taken from Dogdu (1999): three different samples from one process, all of size 50 (a respectable sample size), may show an average process capability (C pk ) estimate of 1.00, a good (not great) one of 1.47, or a bad one of 0.7, based on the samples being used, but the true C pk may be none of these values! Let us now suppose, continuing the example, that the practitioner only took one sample, and it was the sample that happened to have the estimate of C pk being Most practitioners under that situation (and we cannot exclude ourselves from that list based upon past work) may stop there and say C pk = 1.47 (without further analysis) when in fact that is simply not true, the estimate of C pk may be 1.47, but we may not know, nor will we ever, the true C pk value. However, if we place a confidence interval (CI) about that estimate of the form [LCL, UCL] where LCL is the lower confidence limit and UCL is the upper confidence limit, then we can say with a certain degree of confidence (based upon a stated alpha (α) level) that the true value of C pk lies within that interval. The CI is said to have 100(1-α)% confidence. While alpha is usually between 1% and 10%, a typical value for alpha is 5%, resulting in a confidence interval of 95%. Because C pk is a function of two parameters µ and σ and because there does not exist an unbiased confidence interval that has both µ and σ, then an exact confidence interval for C pk cannot be generated (refer to Santos et al. (004) for more discussion). This is not true for C p. An unbiased confidence interval for σ does exist and therefore the unbiased confidence interval that can be used when estimates of C p are being studied as derived exactly from the unbiased CI for σ is the following: Cˆ p χ 1 α /, n 1 ˆ χ /, n 1 C p C α p n 1 n 1 Where the above is of the following form: LCL C p UCL. The calculation for the above is quite straight-forward and the user need only determine, once they know the estimate of the C p value and the sample size (n), the χ value (obtained from tables in any basic statistics or SPC book). For example calculations using this CI (and on the C pk CI formula to be discussed below), the interested reader is referred to the work by Santos et al. (004) or Msimang (004). Because an exact C pk CI confidence interval cannot be obtained, an approximate C pk CI has been suggested by a variety of researchers - Bissel (1990), Franklin and Wasserman (1991), and Kushler and Hurley (199), among others. Due to its relative ease of computation (as.

3 Cˆ pk compared against the others), we will discuss the approximate CI developed by Bissel. In that formula, the CI uses the standard normal table to obtain the z α/ values in order to calculate the approximate 100(1-α)% CI on C pk as follows: 1 z α 1 1 ˆ 1 1 / 1. ˆ / ˆ 1 + C pk C pk + zα + nc n n pk nc pk As the above formula is not an exact CI, but an approximate one, there are detractors to its use. The obvious criticism is that it is not an exact CI (but an exact CI cannot be generated). Another criticism, common to all of the proposed methods, and not just Bissel s, is that the CIs produced by these methods tend to be of excessive width. A final common criticism is that the methods tend to be computationally complex (although Bissel s is considered to be the easiest to calculate and can be made quite easy to calculate if the formula is automated within, say, a spreadsheet package). A diagram of the apertures on the stencil for this component appears as Figure 1. Different practitioners use different conventions with regards to describing an aperture s position with respect to the squeegee (or squeegee blade travel). The convention/definitions that we will use is based upon comparing the long axis of the aperture and its relationship to the direction of squeegee blade travel: a perpendicular pad is one whose long axis is perpendicular to the direction of squeegee blade travel and a parallel pad is one whose long axis is parallel to the direction of squeegee blade travel. Using this convention, pads 1-5 and are perpendicular pads; pads and are parallel pads. The pad numbers and direction of squeegee blade travel are also noted on Figure Pad While it is true that this is an approximate C pk CI, the widths tend to be large, and the computations are not extremely straight-forward, we caution against not using confidence intervals. Again, if we only use the C pk estimate from a sample, we may be way off-mark as to what the true C pk is from the population. The CI described above may suffer from some criticisms, but in our opinion, being approximately right (about a range of values wherein the true C pk may lie) is better than being precisely wrong (an estimate of C pk is often not equal to the true C pk (see Santos et al. (004) for an experimental study on this) Direction of squeegee travel 104 CASE STUDY DESCRIPTION In order to demonstrate how one set of data can be interpreted in different ways, we will focus on a single component although other components do exist on the test vehicle and stencil that we have used. The component that we will study is a QFP08 with 0mil pitch. The stencil design for the device uses a rectangular aperture with mils (W) x mils (L) stencil opening. The stencil used is 4 mils thick. The area ratio is 1.15, so a transfer efficiency of 100% is assumed. With this transfer efficiency assumption, and given the aforementioned dimensions, we can calculate the target amount of volume of paste for each aperture as: mils x mils x 4 mils = 495 mils 3. Design has allowed for specification limits to be set as ± 40% of target volume, providing the following: LSL = 1497 mils 3 and USL = 3493 mils 3. Figure 1. Layout of QFP08 Apertures. EXPERIMENT & ANALYSIS Thirty (30) different prints (that we will refer to as boards ) were made and this provided the following breakdown of data (lending themselves to various ways of analysis): - Total number of deposits: 6,40; - Total number of perpendicular deposits: 3,10; - Total number of parallel deposits: 3,10; - Each of the 08 pads had 30 deposits; and - Each of the 30 boards had 08 deposits. Given the above breakdown of data, we will now discuss different ways of analyzing the data to assess process capability and the reasoning by which one might select a particular method. Method 1: Calculation of C pk using all deposits. This method has an advantage of being simple and gives only

4 one C pk estimate. This makes it easier to draw a conclusion about process performance. This method can be used for evaluating the entire stencil printing process provided there is good control in each of the sub processes (i.e., stencil printer settings, stencil manufacturing technique, and solder paste meeting the customer requirement, among others). On the other hand, this method is not a good tool for estimating the performance of a stencil printer alone. For example, a low C pk estimate obtained by this method will show how bad the overall process is, but will not give any information which will help to determine the cause of the process defects. Some situations may even arise wherein the C pk estimate is actually very good using this method, but there could be one (or a few) pads that are consistently bad but get masked due to an overall good C pk. If the results using this test are bad, then the entire process can be evaluated in much more depth using one of the other methods later described. In our case study, 6,40 deposits were made and measured. The average deposit was 11.4mil 3 and the standard deviation was mil 3. This resulted in a C pk estimate of Method : Calculation of C pk by pad orientation. This method is suggested primarily in the case of rectangular (or other non symmetric (e.g., home plate ) pads) and need not necessarily be performed for circular or square apertures. This method can be used if results from Method 1 indicate unacceptable C pk values with a suspicion that pad orientation, with respect to direction of squeegee blade travel, is tending to produce poor deposits. Based upon experience, it is typically the case that, using our convention described above, the perpendicular pads perform better than the parallel pads. In our case study, 3,10 deposits were made for each pad orientation. Considering the perpendicular pads, the average deposit was mil 3 and the standard deviation was 60.8 mil 3. This resulted in a C pk estimate of For the parallel pads, the average deposit was mil 3 and the standard deviation was 77.4mil 3. This resulted in a C pk estimate of.36. The perpendicular C pk estimate is better because it has a much better (closer to target) average volume and a slightly better (reduced) standard deviation than does the parallel C pk estimate. It is interesting to note that the C pk estimates for each of the pad orientations was better than the overall C pk in Method 1. This is not a miscalculation the reason is that, when stratified according to pad orientation, the standard deviations within each group (60.8 and 77.4) are smaller than the overall standard deviation after all data are grouped (104.65). Method 3: Calculation of C pk for each pad. Here, a calculation of C pk for each pad can be obtained by using the number of boards run in the experiment as the sample size. The obvious downside is the number of C pk calculations that need to be generated. However, by using this method, one can get a genuine estimate of the printer performance by eliminating the effect of stencil and solder paste. This is the method that we recommend for use by a stencil printer manufacturer (or for a customer in qualifying a stencil printer) as it helps to eliminate or reduce the effects of outside variation. For our case study, Table 1, in the Appendix, provides all of the C pk estimates for each of the pads. We will discuss more of these results in the summary section, below. Method 4: Calculation of C pk based upon a per-board analysis. In this method, one C pk can be obtained. In so doing, the average volume of paste and standard deviation of paste for each board (where the sample size is the number of pads) can be obtained. Subsequently, an amalgamated C pk can be obtained wherein the average of the process can be estimated as the average of the averages and the standard deviation of the process can be estimated utilizing a concept from control charts. When standard deviations from samples are used in control charts, an estimate of the process standard deviation can be obtained using the following formula: s / c4. In the above, s is the average of the standard deviations of each board and c 4 is a factor (based upon size of each of the subgroups (n), this is the number of pads per board, or 08 in our case) utilized in calculating control limits (commonly found in any basic SPC text). For subgroup size > 5, c 4 can be approximated by 4(n-1)/(4n-3). Some customers have even proposed to use the standard deviation of the average volumes (of each of the boards) as an estimate of the process standard deviation this is not statistically correct, and should be avoided. Method 3 may be attractive because it also produces just one C pk estimate from the entire process. In truth, this method is actually an approximation to Method 1. Thus while using this method, like the drawback mentioned with Method 1, the data may become diluted and, if a poor C pk results, it may be difficult to locate any problem areas. We have presented this method as we have come across its use by customers; however, we do not recommend its use (particularly if the standard deviation of the average volumes were used as the estimate of the population standard deviation) and would suggest analysis using the other methods. Nonetheless, we will provide an example of its use with our case study.

5 Table, also in the Appendix, shows the average volumes and sample standard deviation of volume for each of the 30 boards in our case study. The average of the averages is, not surprisingly, 11.4mil 3. The average of the 30 standard deviations is 9.31mil 3. Using the above formulas, the estimate of the process standard deviation is 9.31/ = 9.4mil 3. Now, provided these estimates of process average and standard deviation, this results in a C pk estimate of.5. This is better than that of Method 1 and is so because of the estimate of the population standard deviation is lower here due to the approximation. SUMMARY OF RESULTS To keep in line with an earlier and important point drawn in this paper, what we have presented on our case study according to the various methods are estimates of C pk. To give more information and to summarize the results even further, we will now provide, first in table form, the C pk CIs obtained with each method. Methods 1 and 4 provide one CI. Method provides CIs (one for each pad orientation). For Method 3, instead of presenting a CI for all of the 08 pads, we will show the C pk CIs for the worst estimate (Pad 6, C pk estimate of 1.56), median estimate (we will use the 105 th highest C pk estimate this is, when sorted, Pad 0 with C pk estimate of 3.0), and best estimate (Pad 118, C pk estimate of 6.1). For each of the methods, Table 3 in the Appendix shows the parameters used to calculate the C pk estimates and also shows the upper and lower approximate 95% confidence limits using Bissel s formula. Given those results, we will now present them in graphical form and on the same scale to illustrate just what kind of contrasts we can achieve in the C pk results, with the same data, depending upon how the data are analyzed. Figure displays the C pk estimates (the squares as plot points) and confidence widths (the upper end of the bar indicates the UCL, while the lower end indicates the LCL) for all of the methods discussed herein. Some widths are so small compared to others that they are difficult to detect on this scale (they essentially do not (or barely) make it out of the C pk estimate plot point (square)). The reason why the confidence intervals are of different sizes is directly related to the sample sizes used in their calculations. On the per-pad basis with our example, the sample size is only 30 which is extremely small compared to the other methods (3,10 and 6,40). Thus, the per-pad CIs will be much wider than the other methods. CONCLUSIONS Even a casual glance at Figure or Table 3 demonstrates that, depending upon how one examines the data, the different methods can seemingly tell a different story all from the same process. However, each of the results is, as odd as this may sound, accurate (insofar as the formulas for their calculations are accurate) thus it becomes a matter of which viewpoint one wants to take, or how far the data need to be stratified in order to find any problem areas on the board. Another conclusion of this work is to stress that, even though there are some drawbacks for use of C pk confidence intervals, they should be utilized All Deposits Perpendicular Cpk Estimates and Confidence Intervals Parallel Per board Figure. C pk Estimates and Confidence Intervals for the QFP08 Component. FUTURE WORK AND OTHER CONSIDERATIONS While we have concentrated on the C pk calculations, other process capability indices can be used (e.g., C pm, C pmk, etc.). Furthermore, when dealing with estimates of these other indices, Bissel s formula can be straight-forward applied by substituting any of these estimates, with the C pk estimate. Another so far unstated assumption in this work is that each of the QFP08 apertures is identical in area and volume. If a poorly performing aperture (e.g., Pad 6 in this example) arises, then it could be that that particular pad may not be properly manufactured (e.g., it could have a high taper, the walls may not be smooth, the opening may be too small, etc.). As of the writing of this paper, individual pads on this stencil have not been measured. Another method in which data in a printing process could be analyzed, that we have yet to discuss, concerns the squeegee stroke. It is often the case that variations exist between forward stroke versus backward stroke. As such, if the capability of the printer with regards to stroke direction is of concern, then each of the methods presented herein could be further stratified by stroke direction (cutting each sample size in half). ACKNOWLEDGEMENTS The authors would like to thank Speedline Technologies for the use of the test vehicles, equipment, and QFP data. We would also like to thank the Integrated Electronics Engineering Center at Binghamton University for use of their research library. Worst Pad Median Pad Best Pad

6 REFERENCES [1] A.F. Bissell, How Reliable is Your Capability Index?, Applied Statistics, Vol. 39, No. 3, 1990, [] S. Dogdu, Measurement and Use of Process Capability in Statistical Process Control Activities in the Printed Circuit Board Manufacturing Domain, Ph.D. Dissertation, Binghamton University, [3] L.A. Franklin and G. Wasserman, Bootstrap Confidence intervals of Cpk: An Introduction, Communications in Statistics Simulation and Computation, Vol. 0, 1991, [4] R. Kushler and P. Hurley, Confidence Bounds for Capability Indices, Journal or Quality Technology, Vol. 4, 199, [5] N. Msimang, Neural Network Models for Detecting Concurrent Abnormal Patterns in Control Charts and for Developing Shorter and Non-Biased Intervals for Process Capability Index Estimators, Ph.D. Dissertation, Binghamton University, 004. [6] M. Mukadam, D.L. Santos, and A.J. McLenaghan, A Statistical Based Study for Comparison and Optimization of an Enclosed Print Head Technology, Proceedings of the 7 th Annual Pan Pacific Microelectronics Symposium, February 00, , Maui, HA. [7] D.L. Santos, N. Msimang, and S. Dogdu, Process Capability Studies The Better Way, APEX 004 Conference Proceedings, February 004, pp. S8--1 S8--14, Anaheim, CA.

7 APPENDIX Table 1. C pk estimates for each pad. PadID Cpk est. PadID Cpk est. PadID Cpk est. PadID Cpk est. PadID Cpk est Note: Shaded boxes indicate the worst (Pad 6), median (Pad 0), and best (Pad 118) C pk estimates.

8 Table. Average Volumes and Sample Standard Deviation of Volumes per Board. Board Number Volume Average (Xbar) Volume Std. Dev. (s) Averages Table 3. Summary of Parameters, C pk Estimate, and Confidence Limits by Method. Method n Xbar s LCL Cpk est UCL All Deposits Perpendicular Parallel Per Board Worst Pad Median Pad Best Pad Note: On the Per Board method, the reader may be inclined to think that, since there are only 30 boards, that the sample size, n, should be 30; or since, per board, 08 deposits are analyzed so that may be the sample size. However, in this method, all deposits are used to determine Xbar and s, so n = 6,40. This may lead one to assume that the values for the parameters should be identical for the All Deposits method. The average (Xbar) values are identical, as expected, but the method to calculate sigma in the Per Board method is an approximate calculation, hence the Per Board sigma being different than the All Deposits sigma.