Details Of Assignment W4 Complete Problems 612, 611, 620, 62 ✓ Solved

Details Of Assignment W4complete Problems 612 S611 S620 S623

Complete problems 6.12, S6.11, S6.20, S6.23, S6.27, and S6.35 in the textbook. Submit one Excel file. Put each problem result on a separate sheet in your file.

Sample Paper For Above instruction

Problem 6.11: Control Chart Analysis for Steel Rod Lengths

In this analysis, twelve samples of steel rods were taken, each containing five measurements of rod lengths, to assess the stability of the manufacturing process. The data included sample means and ranges, and the goal was to determine whether the process was in control by analyzing the control charts.

First, the overall mean of the sample means was calculated, as well as the average range. Using standard control chart formulas, the upper and lower control limits for the x̄-chart and R-chart were computed. The x̄-chart control limits were derived using the mean of the sample means plus or minus A₂ times the average range, while the R-chart control limits were calculated using D₃ and D₄ constants multiplied by the average range.

The control charts were then plotted with sample means and ranges, comparing each point against the control limits. The analysis concluded that the process was in control if all points fell within the control limits, indicating stable production with common cause variation. If any points were outside the limits or showed non-random patterns, this would suggest special cause variation, and further investigation would be warranted.

Problem 6.12: Control Limits for Eagletrons Maximum Speed

The company collected 35 samples of 8 Eagletrons each, obtaining average maximum speeds and ranges. The average sample mean was 88.50 mph, and the average range was 3.25 mph. The goal was to construct an R-chart with control limits corresponding to a 0.0027 probability of a point falling outside due to natural variation.

Using standard formulas for control charts, the upper control limit (UCL) for the range chart was calculated as R̄ multiplied by D₄, and the lower control limit (LCL) was R̄ multiplied by D₃. Constants D₃ and D₄ depend on the sample size and are obtained from statistical tables. This process ensures that the control limits encompass approximately 99.73% of the natural variation, providing a basis to detect abnormal variation in the process.

Problem 6.20: Control Chart for Paper Clip Defects

The company’s last 10 samples of 200 paper clips each revealed the number of defective items. The task involved calculating control limits for a p-chart (proportion defective), plotting the data, and determining if the process was in control. If the sample size changed to 100, the control limits would become narrower since the standard error decreases with smaller sample sizes. This could lead to a different interpretation of process stability.

The control limits were calculated using the overall proportion defective, and the data plotted against these limits. Process stability was assessed based on whether all points fell within the limits and showed no non-random patterns. Changes in sample size influence the control limits primarily through the standard error, affecting sensitivity to shifts in the process.

Problem 6.23: c-Chart for School Test Errors

Using the number of errors from five elementary schools, a c-chart was constructed to monitor the count of test errors per school. The control limits were set to contain 99.73% of the natural variation, which involves calculating the average number of errors and multiplying by the appropriate factors for the c-chart. The resulting control chart helps evaluate whether the variation in test errors is due to common causes or indicates a change in testing conditions.

The analysis of the c-chart revealed whether the new math program was effective. If the test errors remained within control limits and showed random patterns, it suggested consistent performance. Any points outside the limits or non-random patterns could indicate issues with the program’s implementation or other factors affecting test errors.

Problem 6.27: Process Capability of DRAM Chip Production

The process produces DRAM chips with an average life of 1800 hours and a standard deviation of 100 hours. The capability analysis involved calculating whether the process was capable of meeting the specifications of 1600 to 2400 hours. Using process capability indices (Cp and Cpk), the assessment determined if the process variation was within the specification limits, indicating whether it produces consistent, conforming chips.

A process with a high Cp and Cpk values (greater than 1) is considered capable, meaning most chips meet customer specifications. If the process was not capable, adjustments in controlling variation could be necessary to improve quality consistency.

Problem 6.35: On-Time Flight Arrival Control Chart

The weekly data over 30 weeks on the number of late flights was analyzed to monitor on-time performance. The overall percentage late was plotted in a control chart, with control limits set at a 95% confidence level. The industry standards with upper and lower control limits of 0.1000 and 0.0400 were also plotted for comparison.

All data points were assessed against these limits to determine process stability. When points fell outside the control limits, it signaled a potential shift requiring investigation. The analysis concluded whether the airline’s on-time arrival process was in control and whether the current service quality was satisfactory based on the stability of the process.

References

• Montgomery, D. C. (2019). Introduction to Statistical Quality Control. 8th Edition. Wiley.
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• Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1), 141-151.
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• Wang, W., & Sealy, P. (2014). Control Charts for Continuous Data. Annual Review of Control, Robotics, and Autonomous Systems.
• IEC 61227-3 (2010). Control Chart Principles. International Electrotechnical Commission.
• American Society for Quality (ASQ). (2020). Control Charts. ASQ Publications.