Fujiyama Electronics, Inc.: Control Chart Analysis Of Circui

Fujiyama Electronics, Inc.: Control Chart Analysis of Circuit Board Variability

Fujiyama Electronics, Inc. has experienced variability issues with circuit boards received from an outside supplier, specifically concerning the distance between two drilled holes intended to be 5 centimeters apart. To evaluate the process stability and identify potential assignable causes of variation, a statistical analysis utilizing control charts was conducted. This involved calculating average and range metrics from sample data, establishing control limits, and examining the control charts for signs of out-of-control conditions. Subsequently, the analysis considered the impact of removing outliers—points indicating out-of-control conditions—on the process stability, reflected through recalculated control limits and charts. The purpose of this report is to interpret the control chart data and provide insights into process improvement opportunities for Fujiyama Electronics.

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Introduction

Quality control in manufacturing processes is essential for ensuring product consistency and minimizing defects. Control charts, particularly X-Bar and R charts, serve as vital tools for monitoring process stability by tracking sample means and ranges over time. In the case of Fujiyama Electronics, a key quality attribute—the distance between drilled holes on circuit boards—has exhibited variability. To address this issue, a systematic statistical analysis was performed to determine whether the process is in control, identify any out-of-control signals, and evaluate the effects of eliminating such points. This approach aids in diagnosing process stability and guiding corrective actions.

Data and Methodology

The data consisted of 30 samples, each containing measurements from 4 circuit boards, with the observed distances between two drilled holes recorded in inches. The data was organized in a worksheet, and calculations of the overall process mean (X-Bar-Bar) and average range (R-Bar) were performed. Control limits were then established using standard formulas for X-Bar and R charts based on sample data. Out-of-control points were identified by examining if they fell outside the upper or lower control limits. Subsequent calculations involved removing these points and recalculating the process parameters and control limits to analyze the impact on process stability.

Calculation of X-Bar-Bar, R-Bar, and Control Limits

Using the sample data, the average measurement for each sample was computed, followed by obtaining the overall average (X-Bar-Bar). The ranges of each sample were calculated and subsequently averaged to find R-Bar. Control limits for the X-Bar chart were determined using the average range and specific constants (A2), while the control limits for the R chart employed constants (D3 and D4). The formulas applied are standard in statistical process control methodology:

• X-Bar Control Limits: UCLx = X-Bar-Bar + A2 × R-Bar; LCLx = X-Bar-Bar - A2 × R-Bar
• R Control Limits: UCLr = D4 × R-Bar; LCLr = D3 × R-Bar

Constants depend on the sample size; for n=4, A2≈0.729, D3=0, D4=2.282.

Construction of Control Charts and Analysis

Control charts were plotted for the sample means (X-Bar chart) and ranges (R chart). The plots visually revealed points outside the control limits, indicating potential assignable causes of variation. Specific out-of-control points from the initial data were noted, prompting a re-evaluation after their exclusion. This process involved removing the identified outliers and recalculating the mean, range, and control limits, resulting in updated charts reflecting a potentially more stable process.

Out-of-Control Conditions and Their Implications

Analysis of the initial control charts identified certain points outside the control limits, suggesting the process experienced some special causes affecting consistency. For example, some samples displayed unusually high or low measurements inconsistent with inherent process variation. These outliers merit further investigation to identify possible causes such as equipment malfunction, operator error, or material inconsistencies. Their removal generally led to a narrower control band and a more stable process, as evidenced by the updated control charts.

Effect of Removing Out-of-Control Data

Removing out-of-control points resulted in updated calculations: the new X-Bar-Bar and R-Bar were typically closer, and control limits became tighter. This indicates that the process, once free of special causes, is capable of maintaining a consistent performance level. The comparison between the initial and revised control charts highlights the importance of identifying and eliminating special causes of variation to achieve process stability. Such practices ultimately contribute to improved quality and reduced defect rates in manufacturing.

Discussion

The differences observed between the initial and updated control charts demonstrate the impact of out-of-control points on process assessment. Initially, the charts suggested instability, requiring corrective actions. After removing the outliers, the process appeared more controlled, with points well within new control limits. This emphasizes that process variability can be significantly influenced by exceptional events, and that vigilant monitoring coupled with targeted interventions can optimize manufacturing quality. These findings validate the importance of control charts in ongoing process improvement efforts for Fujiyama Electronics and similar manufacturing settings.

Conclusion

The application of X-Bar and R control charts effectively identified variability and out-of-control points in the circuit board drilling process. Removing special cause variations yielded more stable process measures, underscoring the need for continuous monitoring and corrective measures. Implementing these statistical tools will assist Fujiyama Electronics in maintaining high-quality standards, reducing defect rates, and fostering a culture of continuous quality improvement.

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