Quality Control Analysis: Printed Circuit Board Thickness

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Ross Kelly
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1 Aaron Bennett Joseph Escobar BSAD/STAT /06/03 Quality Control Analysis: Printed Circuit Board Thickness ABSTRACT: This report identifies the problem encountered by a printed-board manufacturer in Ohio with one of their vendors in Silicon Valley, Ca. In anticipation of feedback from Silicon Valley, a Quality Control analyst sampled the lot prior to shipment. As the shipment sent did not satisfy the purchasing company. The small Ohio firm drafted this report to analyze the circuit-board manufacturing process. The outcome of the report identified previously unknown thickness variation, which coincided with an assembly line error and soon thereafter was corrected.

2 1. Definition of the Problem: A circuit board manufacturer in Acron, Ohio produces high quality boards for customers in the Silicon Valley. Recently, complaints about thickness and consistency have been filed. Silicon Valley asserts that manufacturing inconsistencies may have resulted from poor raw materials. An X-bar chart and an S-bar chart were provided in our report to Silicon Valley. The object of the report sent was to establish the reliability of the Ohio firm and find (if possible) another causative of the product defectiveness. 2. Collection of Data: 25 separate samples were taken randomly from the lots marked to be sent to Silicon Valley. The data pertains to manufacturing methods and measurements. The three observations are denoted as x1, x2, x3, and the range of each sample is listed in column five. (see Appendix 1). Circuit boards may have multiple layers, our samples have 4 layers. The typical thickness of circuit boards is between.002 and as our circuit boards do not have any busses they typically are.06 in thickness. (see Appendix 3 for a typical circuit board with bus). Measurements are recorded by machine, then double-checked by hand, this process slows down production but is necessary for quality assurance during the next two weeks (see Appendix 4). 3. Data Analysis Data analysis consisted of a pass-or-fail measurement of printed board thickness. Nonconformity testing was in consideration for surface conformity tests, but was not considered plausible for the thickness test. Since our boards are fabricated in large sheets and then cut to specification, three was considered a large enough sample to achieve control variables. The mean thickness was measured twice daily for two weeks, and the sample mean was

3 taken as an estimate of the midline. An estimator for the midline of the (below) X-bar chart was used because this was the first implementation of quality control at this company. The X-bar chart shows that sample 14 and point 22 both fell outside the three-sigma delimiters. The process did not demonstrate any of the other QC indicators that are used to declare processes out-of-control, but even one 3-sigma crossing point is justification to halt the process. X-bar Chart for x1 - x Sample Mean SL= SL= SL= Mean= SL= SL= SL= Sample Number Figure 1. X-Bar type chart for mean circuit board thickness. In this graph, the sample mean is shown to be and the 3-sigma limits are { , }. There is no established historical mean to establish the midline, so the sample mean was used. After establishing the process state, and halting further production, an S- chart was generated to verify that the deviation between individual sheets supported our conclusions culled from the X-bar chart. Indeed, the variation within samples also indicated that the process was unstable. Points 8-13 are all crowded below the midline. Six points falling below the midline indicates that

4 the samples in question are correlated. This downtrend was immediately followed by point 14 which was the first out-of-control point, and shows that the S-chart accurately predicted the loss of control S Chart for x1 - x3 3.0SL=8.68E-04 Sample StDev SL=6.91E SL=5.15E-04 S=3.38E SL=1.61E SL=0-3.0SL= Sample Number Figure 2: S-Bar type chart of the standard deviations within samples. There is a set of warning points from samples 8-13: which all occur below the midline. This could indicate some problems of correlation between samples. The process continues out-of-control with S-chart points (which oscillate strongly about the midline) followed directly by X-bar point 22, which (unlike 14) falls well below minimum specified thickness. 4. Summary and Conclusion The X-bar chart demonstrates that points 14 & 22 are beyond the three-sigma control limits. There is no immediate resolution to the data, as an assignable cause was not immediately obvious. The X-bar chart is therefore out-of-control, and this prompted inspection of the manufacturing process.

5 The S-bar chart was used as a fail-safe to determine if the out of control points from the X-bar chart could be predicted. Since there were clustered points below the centerline preceding 14 and oscillating points preceding 22, the S-bar chart verified that halting the process in advance of point 14 would be justified. This will be the future strategy of the newly implemented quality control program. Inspection of the 4-layer stamping machines verified that inconsistency in thickness was due to a malfunction in the measurement algorithm, and a representative was called in to repair and reprogram. Purchasing higher quality materials will be unnecessary, and Silicon Valley will be informed that the repair was made quality control methods proved that the process is no longer out of control.

6 Collection of Data: (Appendices) Appendix 1 sample x1 x2 x3 R Data Table 1: The thickness of a printed circuit board is an important quality parameter. Data on board thickness (in inches) are as given.

7 Appendix 2 Appendix 3

Process Behavior Charts

CHAPTER 8 Process Behavior Charts Control Charts for Variables Data In statistical process control (SPC), the mean, range, and standard deviation are the statistics most often used for analyzing measurement