Please read case study Toledo Custom Manufacturing: Quality Control on page 455 of the text and answer the questions from page 456.

See below for additional help: The analysis for TCM is shown below. The first step is to compute the sample average and the sample range for each sample of five rods. Next, average and range control charts are constructed from the data. The grand average mean and the average range are calculated for each operator-machine combination shown on the bottom of the spreadsheet below. Each sample has its sample average and sample range.

Once all 6 sample are calculated for the average and range then average the 6 for both average and range for both operator 1 and 2. These numbers will be the center lines for both the grand average and grand range for each operator. Now to calculate the UCL and LCL you will need to use the control chart constants chart on page 171* of the latest edition of the text.

The results are used to calculate the UCL, CL and LCL for the average chart and then the range chart.

The formulas from Chapter 9 are used for these calculations along with the constants for a sample of 5. The formula for the average is: UCL =Grand average + (sample size (5) A2* in the chart (grand range) ) LCL = Grand average - (sample size (5) A2* in the chart (grand range)) See page 171 for the example. The formula for the UCL/LCL for the range chart also requires the CL and the UCL and LCL The CL is the grand range for each operator UCL= D4* chart for (5 sample size) times the grand range LCL = D3* chart for (5 sample size) times the grand average

This needs to be done as the grand average for both operators data. Now you have the UCL, CL, LCL for both sets of operator data. Go through and see if any of the data points fall outside these parameters. If they are outside these parameters, then the process is not in control The CP and CPK formulas are on pages 172 and 173 of the text. Understand that the CP uses the actual customer specifications mentioned early in the case study. The CPK uses the data collected from the earlier sample analysis.

I am giving you the following information: Standard deviation of individual parts operator 1 machine 1 is .00298 Standard deviation of individual parts operator 2 machine 2 is .00468 This way you do not have to calculate the SD and can now just finish the calculations.

Finally, read the case study thoroughly and after calculating the numbers required by the study apply the actual sample data to see if the processes are both in control and capable.