Resistors are electronic circuits that are manufactured on a high-speed automated machine. One of the key measurements is its resistance. To set up the machine and develop control charts, we measured 4 randomly selected resistors at 5 time periods (samples) over a day. (Details shown in the table below)

Time period X1 X2 X3 X4 1 1010 991 985 986 2 995 996 1009 994 3 990 1003 1015 1008 4 1015 1020 1009 998 5 1013 1019 1005 993

1. Mean Resistance of No. 5 = 1007.5 Ohms.

2. Standard Deviation of resistance metric of sample number 4 = 8.2 Ohms

3. Grand mean across all samples = 1002.7 ohms

4. Probability that Z is less than -0.3329 is approximately 0.3707 or 37.07%

Now, assume that the design specifications are the following:

LSL: 980 Ohms

USL: 1,020 Ohms

Target value: 1,000 Ohm

5. If the standard deviation of the process is 6.28 Ohms, what is the Capability Index of the process?

Cpk = min (USL - Xbar/3 standard deviation, Xbar - LSL/3 standard deviation

6. Is this process capable? Explain.