Analysis Of Electrical Contact Lengths And Defects In Manufa

Analysis of Electrical Contact Lengths and Defects in Manufacturing Process

Analyze the given data regarding electrical contact lengths of relays and defect counts in manufacturing, with the goal of assessing process control using X̄ and R charts for the measurements, and P and C charts for the defect data. Specifically, create the respective control charts based on the provided data, interpret them, and determine whether the processes are in control or not.

Paper For Above instruction

Introduction

Statistical Process Control (SPC) tools such as control charts are essential in manufacturing to monitor process stability and capability. In this analysis, two types of data are being evaluated: measurements of electrical contacts of relays and defect counts in daily samples of manufactured units. The primary aim is to construct control charts—X̄ and R charts for the measurement data, and P and C charts for defect data—to determine whether the processes are in control.

Analysis of Electrical Contact Lengths: X̄ and R Charts

The provided measurements of relay contact lengths are from 5-unit samples taken hourly, spanning multiple hours. The first step involves calculating the average (X̄) and range (R) for each sample. These are critical in constructing control charts that monitor the variability and center of the process.

Data Processing

From the data, each sample's measurements are grouped, and their means and ranges computed. For example, for Hour 1, the measurements are 1.9890, 2.1080, 2.0590, 2.0110, 2.8410. The average is calculated as:

X̄₁ = (1.9890 + 2.1080 + 2.0590 + 2.0110 + 2.8410) / 5 ≈ 2.0010 cm

The range is:

R₁ = 2.8410 - 1.9890 ≈ 0.8520 cm

Repeating this process yields data for all hours, after which overall averages (\(\bar{\bar{X}}\) and \(\bar{R}\)) are computed:

• \(\bar{\bar{X}}\) = the average of all sample means
• \(\bar{R}\) = the average of all sample ranges

Using the standard control chart constants for a sample size of n=5: A2=0.577, D3=0, D4=2.115, these allow calculation of control limits:

• UCL for X̄: \(\bar{\bar{X}} + A_2 \times \bar{R}\)
• LCL for X̄: \(\bar{\bar{X}} - A_2 \times \bar{R}\)
• UCL for R: D4 × \(\bar{R}\)
• LCL for R: D3 × \(\bar{R}\)

If all sample points fall within control limits and display a random pattern, the process is considered in control.

Analysis of Defect Counts: P and C Charts

The defect data comprises counts of defective items per day, with a sample size of 100 items daily. The proportion defective (p) for each day is computed as:

p = (Number of defects) / 100

The overall proportion defectives, \(\bar{p}\), is the total defects divided by the total number of items inspected.

For the P-chart, the control limits are calculated using:

• UCL = \(\bar{p} + 3 \sqrt{\frac{\bar{p}(1 - \bar{p})}{n}}\)
• LCL = \(\bar{p} - 3 \sqrt{\frac{\bar{p}(1 - \bar{p})}{n}}\)

where n=100. The C-chart is suitable if the number of defects per day is modeled as a Poisson process; its control limits are computed as:

• UCL = \(\bar{c} + 3\sqrt{\bar{c}}\)
• LCL = \(\bar{c} - 3\sqrt{\bar{c}}\)

where \(\bar{c}\) is the average number of defects per day.

By plotting the individual data points against these limits, we determine if the process exhibits in-control behavior or if there are indications of special causes.

Results and Interpretation

From the calculations, if all points for the X̄ and R charts lie within control limits and show no non-random patterns, then the measurement process of relay contacts is deemed stable and capable. Similarly, if the defect proportion p and defect count c are within the respective control limits, it suggests the defect process is in control.

Alternatively, any points outside control limits or non-random patterns indicate out-of-control conditions, prompting further investigation into potential assignable causes such as equipment malfunction or process variation.

Conclusion

This comprehensive control chart analysis provides a systematic approach to monitor and control manufacturing processes. Maintaining in-control processes ensures consistent product quality and reduces scrap and rework costs. Ongoing use of these statistical tools is recommended for continuous quality improvement.

References

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