Fujiyama Electronics Inc. Has Had Difficulties With Circuit

Fujiyama Electronics Inc Has Had Difficulties With Circuit Boa

Fujiyama Electronics, Inc. has experienced variability issues with the circuit boards supplied by an outside vendor. Specifically, the problem involves two drilled holes that are supposed to be 5 cm apart, but inconsistent measurements have been observed. Thirty samples, each comprising four boards, were taken from shipments to analyze the variability. The task requires calculating the overall process mean (X-Bar-Bar), average range (R-Bar), and their control limits. Additionally, you need to construct X-Bar and R control charts based on the sample data. Noticing any out-of-control points—those outside the control limits—is crucial, and only these points should be considered when identifying special causes or assignable reasons for variation.

The next step involves examining the impact of removing out-of-control points from the dataset. After eliminating these points, recalculate the process mean, range, and control limits, then produce updated control charts. Finally, evaluate how the control charts differ before and after removal of outliers, discussing what changes occurred and what those changes imply about the process stability.

This analysis must be presented following the APA 6th edition formatting guidelines, including a title page and proper in-text citations where applicable. The completed report should be submitted as a Microsoft Word document, including all graphics and control charts embedded within the document.

Paper For Above instruction

Fujiyama Electronics Inc. has encountered significant process variability issues concerning the spacing between drilled holes on their circuit boards, which are supposed to be precisely 5 centimeters apart. To analyze this problem, a statistical process control (SPC) approach is necessary, focusing on the data derived from sampling shipments from the supplier. The ultimate objective is to identify whether the process is in statistical control and what adjustments are necessary based on the data analysis.

Data Analysis and Control Chart Construction

The sample data consist of measurements from 30 different shipments, with four boards sampled per shipment. To begin, it is essential to compute the overall process mean, represented as X-Bar-Bar, and the average of the sample ranges, R-Bar. Calculation of these values involves summing all individual sample means and ranges, then dividing by the number of samples, which in this case is 30. After obtaining X-Bar-Bar and R-Bar, the next step involves calculating the control limits for the X-Bar and R charts.

The control limits are determined using standard formulas. For the X-Bar chart, the upper and lower control limits (UCL and LCL) are calculated as:

• UCL = X-Bar-Bar + A2 * R-Bar
• LCL = X-Bar-Bar - A2 * R-Bar

Similarly, the R chart control limits are:

• UCL = D4 * R-Bar
• LCL = D3 * R-Bar

Here, A2, D3, and D4 are constants based on the sample size (n=4). For n=4, these are:

• A2 = 0.729
• D3 = 0
• D4 = 2.282

Using the appropriate formulas, all control limits are computed, and then control charts are constructed by plotting individual sample means and ranges against the calculated control limits.

Identifying Out-of-Control Points

Once the control charts are plotted, points outside the control limits indicate special causes of variation. Based on the data, certain points might fall outside the UCL or LCL on either the X-Bar or R chart, signaling potential issues in the process that require investigation. These out-of-control points should be examined carefully to understand their causes, which could range from measurement errors to equipment malfunctions or operator inconsistencies.

Re-Analysis After Removing Out-of-Control Points

If the identified out-of-control points are considered attributable to assignable causes that can be eliminated, removing these data points from the dataset is advisable. This process involves recalculate the overall process mean and average range, then derive new control limits based on the remaining data. Once the new control limits are established, corresponding revised control charts are produced.

This reanalysis allows an assessment of the process's behavior when outliers are excluded. Typically, the control limits become narrower, indicating improved process stability. The comparison of the original and revised control charts reveals how removing assignable causes affects process variability and control status.

Discussion of Control Chart Differences

Compared to the initial control charts, the updated charts after removing the outliers often display data points within the control limits, suggesting a more stable process. The shifts in control limits—usually narrower—reflect decreased variability. Such changes infer that the process has been stabilized by eliminating the sources of assignable variation. This analysis supports decision-making about whether the process is under statistical control and guides efforts toward process improvement.

Conclusion

In conclusion, statistical process control is an invaluable tool for diagnosing and improving manufacturing processes like those at Fujiyama Electronics Inc. By calculating process control statistics, constructing control charts, identifying out-of-control points, and re-evaluating the process after their removal, organizations can better understand their process stability. This strategic approach enables targeted corrective actions, fostering higher quality and consistency in production outputs.

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