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DATA FOR THE ASSIGNMENT:

Pulley Engineering manufactures needle bearings for use in high-tech machinery. The target diameter for one particular bearing is 200 mm. To monitor the precision of the bearing diameter, the Head Engineer of Pulley Engineering plans to use appropriate control charts to keep track of the accuracy of the bearing diameters. To implement his plan, the Head Engineer instructed the quality control staff to collect daily samples, each of five observations, for a consecutive period of 20 days (“Initial Data”). The quality control team would then use the Initial Data (i.e. the 20-day data) to determine the locations of the ‘centerlines’, ‘upper control limits (UCL)’, and the lower control limits (LCL)’ for the bar-x control chart (x̅-chart) and the R-chart. The Head Engineering and the quality control team would then use control charts to track the average diameters and their fluctuation ranges of the subsequently produced bearings. Table – 1 and Table – 2 below are the data for respectively, the 20 daily samples (“Initial Data”) and the subsequent production batches:

Requirements:

1. Use the samples above (Table – 1) to determine the locations of (i) the ‘center’ lines, (ii) UCL, and (iii) LCL of the x̄-chart and R-chart.
2. Construct the x̄-chart and R-chart using the findings from #1 above.
3. Map the quality data (Table – 2) of the samples collected subsequently to the control charts you constructed. Each subsequent sample should appear independently (as a ‘dot’) without being linked in the plot to others (i.e., keep the format of the plot for live data a scatter format) on the control charts.
4. Assume that the upper and lower tolerant limits of Pulley Engineering have been set at +/- 10 mm, assess the process capability (assuming a 99.7% coverage) for Pulley based on the actual running mean and standard deviation of the production process.

Hint: Use all the data i.e., the 20 samples for the chart making plus all subsequent sample data, to hypothesize the population mean and standard deviation.

Required 2:

1. Use the provided report template and answer the questions thereon, provide a summary of your evaluation of the product quality based on the above observations. In your report, you must base on your statistical quality control data obtained in your analysis and the evaluation guidelines we discussed in class to address the following questions:
2. The control charts
   1. In one or two sentences, explain the core function of the two control charts.
   2. Explain concisely: the upper control limit (UCL), centerline, and lower control limit (LCL) in the two control charts.
3. Do the quality data from the subsequent productions show a pattern deviating from the trend set by the Initial Data (i.e. the 20 samples)?
4. Do the UCL and LCL exceed or stay within the upper tolerance and lower tolerance limits required by Pulley’s clients?
5. Based on the Initial Data and the subsequent production data, is Pulley Engineering capable of keeping the required process capability?

Your report needs to have a cover page with a proper report title, in short-form and business professional standard. Using the provided report template is mandatory.

Your deliverable to be uploaded using the link provided on Canvas should include:

• The EXCEL file (template provided) that contains the data, A2, D3 & D4 Table, and the working to support requirements #1-3 above
• A report document (either Word or PDF file) for requirement #4