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This case study looks at the behavior of a circuit board process through the use of control charts. At least two control charts will need to be constructed, and from them you will be asked to provide an assessment of what you see.  You are not required to use this template, however, it will greatly facilitate the solution.

Problem Statement
    Fujiyama Electronics, Inc. has had difficulties with circuit boards purchased from an outside supplier. Unacceptable variability occurs between two drilled holes that are supposed to be 5 cm apart on the circuit boards. Thirty samples of four boards each were taken from shipments from the supplier as shown in the data from the worksheet below. 

Fujiyama ElectronicsObservationsSample123414.924.264.944.2924.655.5455.4235.775.264.764.7946.254.885.664.4455.275.416.024.9165.225.385.084.6575.474.684.564.785.714.544.174.8795.245.584.725.41104.425.184.794.73115.144.264.715.48124.925.785.55.05135.793.834.34.78144.924.84.755.59155.685.744.655.2165.434.815.274.96174.796.044.475.18184.435.083.696.43196.355.956.295.89205.034.665.254.46216.326.095.575.91224.35.474.274.34236.074.975.515.02245.114.95.914.66254.55.244.864.35264.914.795.745.03274.654.714.815.32284.


    The student will complete and/or answer the following questions:

Calculate X-Bar-Bar, R-Bar, and associated control limits using the data in the table above.         Create X-Bar•R (Average & Range) Control Charts from the data in the table above.         Discuss notable out-of-control conditions displayed in the completed X-Bar•R (Average & Range) Control Charts. Only consider points outside the control limits. Do not consider runs, set of points within certain zones, and so forth.         If the conditions you note could be defined as assignable conditions, and they are removed from the process, then what will happen to the X-Bar•R Control Chart?         Remove the data related to the out-of-control points you observed from the original data, and recalculate new X-Bar-Bar, R-Bar, and associated control limits.             Create new X-Bar•R (Average & Range) Control Charts from your updated data. Discuss how the two sets of Control Charts are different. What has changed?

    The format of the case study should conform to the Publication Manual for the American Psychological Association (APA), 6th edition, for the title page and text. Citations and references are not required. A basic APA tutorial can be found in the Webliography, and a paper template can be found in Doc Sharing. The completed case study will be submitted to your Dropbox as an MS Word document. All graphics and charts will be a part of the Word document and submitted as a file. Documents authored in other applications such as WordPerfect or MS Works will not be accepted.

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