Resistors for electronic circuits are manufactured on a high$-$speed automated machine. The machine is set up to produce a large run of resistors of $1,000$ ohms each. Use Exhibit $10\mathrm{.}13.$

To set up the machine and to create a control chart to be used throughout the run, $15$ samples were taken with four resistors in each sample. The complete list of samples and their measured values are as follows: Use three$-$sigma control limits$.$

SAMPLE NUMBER READINGS $($IN OHMS$)$

$11,0961,093978994$

$21,0269761,0191,018$

$31,0191,0201,026970$

$41,0129951,016998$

$51,0189769891,024$

$61,0021,0031,0261,022$

$79999939811,007$

$81,0271,019971994$

$99999881,0241,025$

$109799931,0081,001$

$11979989986978$

$121,023976981971$

$131,0059969861,026$

$141,0091,0261,0291,018$

$151,002971981972$

Calculate the mean and range for the above samples.

Note: Round "Mean" to $2$ decimal places and "Range" to the nearest whole number.

Determine X$=$

and R$$

$.$

Note: Round your answers to $3$ decimal places.

Determine the UCL and LCL for a X$$

chart.

Note: Round your answers to $3$ decimal places.

Determine the UCL and LCL for R$-$chart.

Note: Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers to $3$ decimal places.

What comments can you make about the process?

multiple choice

Process is out of statistical control

Process is in statistical control

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