Problem $10-25($Algo$)$

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$)$

$11,0921,0991,016979$

$21,0119781,023976$

$39741,003996998$

$49819881,0011,007$

$59929769781,001$

$69881,0301,0301,014$

$71,0221,0101,021990$

$81,010998981975$

$99971,0189831,024$

$101,028974989989$

$119721,0101,007992$

$121,0139811,0021,009$

$131,0051,0219961,014$

$14995973971975$

$151,0111,0019871,015$

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