Assessing Machinery For Shaft Manufacturing: A Comparative A

Assessing Machinery for Shaft Manufacturing: A Comparative Analysis

As a line manager at Superior Car Parts' Ellisville manufacturing plant, responsible for overseeing the production of steel shafts for gearboxes, it is crucial to select machinery that meets quality standards while maximizing efficiency and minimizing costs. The decision involves evaluating two vendor-supplied machines based on their machining accuracy data. The acceptable shaft diameter is 2.5 ± 0.05 inches, with the ideal being exactly 2.5 inches. Given that the equipment is nearing the end of its operational life, a careful analysis of the machines’ precision and consistency is necessary to determine the best investment for the company’s future manufacturing capabilities.

Introduction

The manufacturing of automotive shafts requires high precision to ensure product quality, durability, and proper fitment in the assembly process. Variations in shaft diameters can lead to increased rejection rates, rework costs, and potential warranty issues. Therefore, selecting machinery that consistently produces shafts within specified tolerances is paramount. In this context, two vendors—Abano Machines Inc. and Li Equipment Corp.—have supplied data derived from machining 100 shafts each. The assessment focuses on comparing their machining accuracy profiles, considering their mean diameters and variability, and understanding the implications for production quality and process capability.

Data Summary and Analysis

According to the supplied information, the diameter of shafts produced by the two machines follows a normal distribution, characterized by their respective means and standard deviations:

  • Abano Machines Inc.: Mean = 2.49 inches, Standard deviation = 0.030 inches
  • Li Equipment Corp.: Mean = 2.53 inches, Standard deviation = 0.015 inches

The acceptable tolerance range of 2.5 ± 0.05 inches spans from 2.45 to 2.55 inches. Our goal is to produce shafts centered as close as possible to 2.5 inches with minimal variability, thus ensuring most shafts fall within the specified tolerance limits.

Process Capability Analysis

Process capability indices, such as Cp and Cpk, are valuable metrics to quantify the machine’s ability to produce within specifications. The Cp index assesses potential capability assuming the process is centered, while the Cpk considers the current centering of the process.

The calculation of Cp is as follows:

Cp = (USL - LSL) / (6 × σ)

where USL = 2.55 inches, LSL = 2.45 inches, and σ is the process standard deviation.

Applying this to our data:

  • Abano Machines Inc.: Cp = (2.55 - 2.45) / (6 × 0.030) ≈ 0.1667
  • Li Equipment Corp.: Cp = (2.55 - 2.45) / (6 × 0.015) ≈ 0.6667

Similarly, Cpk factors in the process mean (μ) in relation to the center of the tolerance range:

Cpk = min[(USL - μ) / (3 × σ), (μ - LSL) / (3 × σ)]

Calculations yield:

  • Abano Machines Inc.: Cpk = min[(2.55 - 2.49) / (3 × 0.030), (2.49 - 2.45) / (3 × 0.030)] ≈ min[0.6667, 0.4444] = 0.4444
  • Li Equipment Corp.: Cpk = min[(2.55 - 2.53) / (3 × 0.015), (2.53 - 2.45) / (3 × 0.015)] ≈ min[0.4444, 1.7778] = 0.4444

While both machines demonstrate similar Cpk values (~0.44), the mean of Li Equipment’s process is closer to the target diameter of 2.5 inches, though its variability is significantly lower than that of Abano Machines Inc.

Implications of Variability and Mean

The narrow standard deviation of Li Equipment’s machine (0.015 inches) indicates a highly consistent process, reducing the risk of producing shafts outside the tolerance limits. The mean of 2.53 inches, slightly above the target, is still within the upper specification limit but closer to the upper tolerance boundary. Conversely, the Abano Machines Inc. machine produces shafts with a mean of 2.49 inches and higher variability, which might lead to a higher rejection rate due to shafts falling outside the acceptable range.

Assuming a normal distribution, the probability of producing out-of-spec shafts can be calculated using the z-score formula. For Li Equipment, the probability of producing a shaft exceeding 2.55 inches (USL) is negligible due to its low mean but minimal variability. For Abano Machines, the greater variability increases the likelihood of out-of-spec shafts especially since its mean is below the target.

Decision-Making Considerations

Beyond the capability indices, other factors influence the selection decision. These include equipment durability, maintenance costs, vendor support, and the ability of machine adjustments to future process improvements. However, from a purely statistical perspective, Li Equipment’s machine offers superior process control, evidenced by its lower standard deviation and process consistency, which are critical in a high-volume, quality-sensitive manufacturing environment.

The slightly higher mean (2.53 inches) of Li Equipment’s machine should be managed via calibration adjustments to bring the average closer to the target of 2.5 inches if necessary. Nonetheless, its consistent output ensures that most shafts are within the desired range, reducing scrap and rework costs.

Additional considerations include the total cost of ownership, vendor reliability, and potential for technological upgrades. A machine with better precision and stability aligns with lean manufacturing principles, leading to reduced waste and improved product quality.

Conclusion and Recommendation

Based on the statistical analysis of machining accuracy, process capability, and variability, Li Equipment Corp.’s machine emerges as the preferable choice. Its lower standard deviation indicates higher machine precision and process consistency, essential for producing shafts within strict tolerances. Although its mean is slightly above the target, this can be corrected through calibration adjustments. The higher process capability index also suggests the potential for maintaining quality with less variability.

Investing in Li Equipment’s machine is likely to result in fewer rejected parts, lower rework costs, and improved overall product quality, translating into operational efficiencies and customer satisfaction. It aligns with the company’s strategic goal of maintaining high manufacturing standards while reducing defect rates. Therefore, it is recommended that Superior Car Parts adopt Li Equipment Corp.’s solution for shaft machining at the Ellisville facility.

References

  • Montgomery, D. C. (2019). Introduction to Statistical Quality Control. John Wiley & Sons.
  • Evans, J. R., & Lindsay, W. M. (2014). Managing for Quality and Performance Excellence. Cengage Learning.
  • Helmerson, C. (2020). "Process capability analysis and process improvement." Journal of Manufacturing Processes, 45, 123-135.
  • Jurado, J., et al. (2018). "Precision machining and quality control." International Journal of Machine Tools and Manufacture, 135, 115-127.
  • Kumar, S., et al. (2021). "Impact of machine accuracy on manufacturing quality." Manufacturing Letters, 29, 10-14.
  • Roberts, P. (2017). Industrial Process Control. CRC Press.
  • Sharma, N., & Tan, K. (2019). "Statistical analysis of manufacturing processes." Quality Engineering, 31(2), 226-236.
  • Yadav, R., & Saini, R. (2022). "Evaluating equipment performance in manufacturing." Production and Manufacturing Research, 10(1), 45-60.
  • Zhang, Q., et al. (2015). "Reducing variability in precision machining." International Journal of Production Research, 53(20), 6249-6263.
  • ISO 9001:2015. (2015). Quality Management Systems – Requirements. International Organization for Standardization.

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