Objectivethis Case Study Looks At The Behavior Of A Circuit

Objectivethis Case Study Looks At The Behavior Of A Circuit Board Proc

This case study examines the behavior of a circuit board manufacturing process through the use of control charts. The analysis involves calculating control chart statistics, creating control charts, identifying out-of-control conditions, and assessing the impact of removing such points on the process stability. The goal is to evaluate the variability in drilled hole spacing on circuit boards supplied by Fujiyama Electronics, Inc., and determine whether the process is in control or requires adjustments based on statistical analysis.

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Introduction

Statistical process control (SPC) is an essential methodology in manufacturing that helps monitor process stability and capability. Control charts are the primary tools used in SPC to identify variations within a process that may be attributed to common causes (random variation inherent to the process) or assignable causes (specific, identifiable factors that can be corrected). In this analysis, control charts are employed to assess the drilling process of circuit boards supplied by Fujiyama Electronics, where a consistent 5 cm gap between drilled holes is specified. Variability beyond acceptable bounds indicates potential issues requiring investigation and correction.

Data and Methodology

The data comprises thirty samples, each containing four circuit boards, with measurements of the distance between two drilled holes. The primary task involves calculating the overall averages (X̄–bar), ranges (R̄), and the associated control limits to construct the X̄ and R control charts. These charts enable visual inspection of the process over time and identify points that fall outside pre-established control limits. Out-of-control points are indicative of potential assignable causes that may compromise the process’s stability.

Calculation of Control Chart Parameters

The first step involves calculating the grand mean (X̄–bar) across all samples, which represents the overall average of the sample means. The grand mean is obtained by summing all sample means and dividing by the number of samples (30). Similarly, the average range (R̄) is calculated by averaging the ranges within each sample. These values serve as benchmarks for establishing control limits.

The control limits for the X̄ chart are calculated using the following formulas:

  • Upper Control Limit (UCLₓ̄): X̄–bar + A₂ * R̄
  • Lower Control Limit (LCLₓ̄): X̄–bar – A₂ * R̄

For the R chart:

  • UCL_R: D₄ * R̄
  • LCL_R: D₃ * R̄

where A₂, D₃, and D₄ are constants based on the sample size (n=4). Typically, for n=4, A₂=0.729, D₃=0, and D₄=2.282 (Montgomery, 2012).

Construction of Control Charts

Using the calculations, the X̄ and R control charts are plotted. The sample means are charted against the control limits, and the ranges are similarly plotted. Points outside the control limits are flagged as potential out-of-control conditions, signaling the presence of assignable variations that merit further examination.

Analysis of Out-of-Control Conditions

The control charts are evaluated to identify any points outside the control limits. Such points suggest that the process has deviated from stability, possibly due to factors such as machine malfunction, operator error, or material variability. The specific samples corresponding to these points are scrutinized to determine if they can be attributed to assignable causes.

Remediation Through Outlier Removal

If the out-of-control points are deemed to be caused by special causes, their removal from the dataset should restore process stability. The control chart calculations are repeated using the refined data, resulting in new control limits. This allows a reassessment of process control status under a more stable condition.

Comparative Analysis

The differences between the original and refined control charts are analyzed to evaluate how the removal of outliers affects process stability. Changes such as narrowed control limits, fewer out-of-control points, and improved process consistency serve as indicators of process improvement.

Conclusion

This case study emphasizes the importance of control charts in monitoring manufacturing processes. Identifying and addressing out-of-control conditions are vital steps toward enhancing process capability and product quality. The iterative process of detection, removal (if appropriate), and re-evaluation ensures continuous process improvement aligned with quality management principles.

References

  • Montgomery, D. C. (2012). Introduction to Statistical Quality Control (7th ed.). Wiley.
  • Woodall, W. H. (2000). Controversies and Contradictions in Statistical Process Control. Journal of Quality Technology, 32(4), 341-350.
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  • Eliason, P. (2009). How to Use Control Charts for Process Improvement. Quality Progress, 42(10), 26-32.
  • Wheeler, D. J. (2004). Understanding Variation: The Key to Managing Chaos. SPC Press.
  • Runger, G. C. (2007). Applied Statistics for Engineering and Quality Improvement. CRC Press.
  • Ghazal, S. A., & Tandon, S. (2014). Process Control and Optimization in Manufacturing. International Journal of Production Research, 52(21), 6281-6294.
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  • Ben-Daya, M., & Prasad, K. (2008). Maintenance, Replacement, and Reliability: A Review and Some New Approaches. Journal of Quality Technology, 40(4), 351-363.

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