Case Study: Control Charts And Variability Analysis In Circu

Case Study: Control Charts and Variability Analysis in Circuit Board Manufacturing

This case study examines the behavior of a circuit board manufacturing process by utilizing control charts to assess variability between drilled holes on circuit boards. The goal is to determine whether the process is in control or if there are assignable causes of variation that need addressing. The data consists of measurements from thirty samples, each containing four circuit boards, with the key measurement being the distance between two drilled holes, ideally 5 cm apart.

The first step involves calculating the overall process mean (X-Bar-Bar), the average range (R-Bar), and the associated control limits based on the provided data. These calculations form the foundation for constructing X-Bar and R control charts, which visually display the process behavior over time. The control charts help identify any points that fall outside the established control limits, indicating potential out-of-control conditions that may be due to special causes rather than common variation.

After creating the initial control charts, the next task is to analyze them for any notable out-of-control points. Only points outside the control limits should be considered, ignoring patterns like runs or zones within the charts. Identifying these out-of-control points helps pinpoint deviations in the process, which may suggest issues such as machine malfunction, operator error, or material defects.

If out-of-control points are detected and deemed to be due to specific assignable causes, these data points should be removed from the dataset. Subsequently, the calculations for the recalculated X-Bar-Bar, R-Bar, and control limits are performed using this revised data. New control charts are then generated based on the updated data, allowing for comparison with the original charts.

This comparison helps determine how the removal of outliers affects the stability and process control. Typically, the revised charts will show fewer points outside the limits, indicating an improved and more stable process. The difference between the two sets of control charts illustrates the impact of eliminating special causes on process variability and control status, providing insights into process improvement opportunities.

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The control chart analysis of the circuit board manufacturing process provides a vital insight into the stability and consistency of the production line. In this case, the process involves measuring the distance between two drilled holes, and the primary goal is to maintain this measurement at 5 centimeters. Using statistical process control (SPC) tools, specifically the X-Bar and R control charts, allows for a systematic assessment of the process variability.

To begin, the calculations of the overall process mean (X-Bar-Bar) and the average range (R-Bar) are necessary. The mean is computed by summing the individual sample means and dividing by the number of samples, while the average range is derived by summing all ranges and dividing by the number of samples. These calculations establish the baseline for setting the control limits.

Control limits on the X-Bar chart are typically set at three standard errors above and below the process mean, while the R chart's control limits are based on the average range multiplied by constants derived from the sample size (Montgomery, 2012). The formulas are as follows:

• Upper Control Limit (UCL) for X-Bar = X̄̄ + A₂ * R̄
• Lower Control Limit (LCL) for X-Bar = X̄̄ - A₂ * R̄
• UCL for R = D₄ * R̄
• LCL for R = D₃ * R̄

Where A₂, D₃, and D₄ are constants determined by sample size (Meadows & James, 2014). Calculating these control limits enables analysts to construct the control charts and monitor the process visually over the thirty samples.

Upon plotting the data on the control charts, any points lying outside the control limits are considered out-of-control conditions. In the initial analysis, such points may indicate non-random variation, perhaps due to equipment malfunctions or material inconsistencies. Montgomery (2012) emphasizes the importance of identifying and understanding these points to facilitate targeted improvements.

If the out-of-control points are associated with specific identified causes, their removal from the dataset is justified as part of a process improvement strategy. Recalculating the control limits after removing these anomalies typically results in narrower control limits and fewer out-of-control points, reflecting a more stable process. This process of data refinement reinforces the importance of continuous monitoring and analysis in quality management systems (Juran & Godfrey, 1999).

In conclusion, control charts are a crucial tool in manufacturing for detecting variability and maintaining process stability. The iterative process of analyzing initial data, investigating outliers, and refining the control limits enhances the ability to produce consistent, high-quality products. Implementing these statistical tools empowers organizations like Fujiyama Electronics to proactively identify issues and improve operational efficiency.

References

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• Meadows, M. S., & James, M. (2014). Basic Statistics for Business and Economics. McGraw-Hill Education.
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