A metal fabricator produces connecting rods with an outer diameter that has a $1\backslash$pm $0\mathrm{.}04$ inch specification.

A machine operator takes several sample measurements over time and determines the sample mean

outer diameter to be $1\mathrm{.}002$ inches with a standard deviation of $0\mathrm{.}009$ inch.

a$.$ Calculate the process capability index for this example. $($Round your answer to $3$ decimal places.$)$

b$.$ Is the process capable of producing the desired quality? Explain

Problem $2$

Ten samples of $15$ parts each were taken from an ongoing process to establish a p$-$chart for control. The

samples and the number of defectives in each are shown in the following table:

SAMPLE n

Number of

Defective Items

in the Sample

$1153$

$2153$

$3151$

$4152$

$5150$

$6153$

$7153$

$8152$

$9150$

$10153$

a$.$ Determine the p$,$ Sp$,$ UCL and LCL for a p$-$chart of $95$ percent confidence $(1\mathrm{.}96$ standard

deviations$).($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Round your answers

to $3$ decimal places. Round any negative LCL up to zero.$)$

b$.$ What comments can you make about the process? Why?

b$\mathrm{.}1$ Process is out of statistical control

b$\mathrm{.}2$ Process is in statistical control.