Problem $2$

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$H$

As part of the process for improving the quality of their cars, Honda engineers have identified a potential improvement to the process that makes a washer that is used in the accelerator assembly. The tolerances in the thickness of the washer are fairly large since the fit can be loose, but if it does happen to get too large, it can cause the accelerator to bind and create a potential problem for the driver.

Let's assume that, as a first step to improving the process, a sample of $40$ washers coming from the machine that produces the washers was taken and the thickness meaured in millimeters. The following table has the measurements from the sample.

Questions

The upper specification limit on the thickness is $2\mathrm{.}5$ and the lower specification limit is $1\mathrm{.}4.$ What is the Cpk for the process?

Set up an $x-$bar and $R-$chart set of control charts for the current process. Assume the operators will take samples of $10$ washers at a time $($calculate the UCL and LCL for each chart, you DO NOT have a create a 'graph' or 'chart'$).$

Does the current process appear to be in control? Use the Excel sheet and show the formulas