Based on the dataset I gave you, your textbook, and tutorials such as this:

• Statistical Process Control (SPC), and
• Xbar-R Charts

And given the following:

• Sample size, n = 7

Respond to the following questions:

1. Calculate or obtain Sum, x̄, x̿, R, R̄, A2, D3, D4 for the dataset I gave you (use this web site to get the right symbols).
2. Calculate the standard deviation or SD, for the whole dataset (include all the x values in the table).
3. Calculate x̄ UCL, x̄ LCL, R UCL, and R LCL, assuming the z-value of 2.58 (desired control limit=99.0%, read pages 237-240).
4. Calculate x̄ central line and R central line.
5. Draw x̄ and R charts (charts like what are seen on p. 239 are needed) assuming the z-value is known (i.e. 2.58).
6. Interpret the x̄ and R charts as to explain if the process is in control or out of control and why (full explanation is needed as for why this or that interpretations might be valid).
7. Given the Upper Specification Limit of 8.8, Lower Specification Limit of 8.2, and the SD you calculated in the previous question, now calculate Cp and Cpk (see pp. 246-7 of your textbook). Now, explain if and why the process is capable or incapable. (Tip: First you need to calculate and explain what Cp and Cpk are in this case, i.e. the actual numbers. Then you need to explain what those numbers mean. See page 247).

Note: Please provide the calculations to show how you came up with the numbers that you produced. Simply showing a number in your paper with no calculation or explanation as for where and how they came about will not be enough. Marks will only be awarded to answers with clear explanations for how a given number is calculated.

Resources

Pre-flight checklist

The marking scheme

• Share a digital copy of your final paper with me via Google Docs (use my gmail address)
• Day 5 is the last day for this assignment (there will be a penalty for late submissions)