Part $1$

A control chart plots $1$ sample per day, $7$ days a week. The process is currently in control.

What is the probability of plotting $4$ samples in a row in Zone $B^B?$

On average, an observation will fall into either Zone A or Zone B approximately once every days.

Part $2$

Given a process to fill bottles of water. The water can be sold if the volume is $16\mathrm{.}15$ ounces $+-0\mathrm{.}28$ ounces. The process average is found to be $16\mathrm{.}10$ ounces with a standard deviation of $0\mathrm{.}07$ ounces.

$3.$ What is the Process Capability Ratio?

$4.$ What is the Process Capability Index?

$5.$ Which of the following most accurately describes the actual process quality level?

a$.$ currently better than $3$ Quality

b$.$ currently less than $3$ Quality, and it will still not be capable of $3$ Quality if a shift in location occurs

c$.$ currently less than $3$ Quality, but a shift in location could increase the level to better than $3$ Quality

The design specification for the length of a component is ${14\mathrm{.}56}^{\text{'}\text{'}}+-0\mathrm{.}68."$

Given the following values for the $\stackrel{}{x}-$chart that monitors the process:

$\frac{?}{\text{b}\text{a}\text{r}}(\stackrel{}{x})={14\mathrm{.}56}^{\text{'}\text{'}},LCL={14\mathrm{.}05}^{\text{'}\text{'}},$UCL$={15\mathrm{.}07}^{\text{'}\text{'}}$

Does the process meet the traditional definition of a "Capable" process?

The size of one sigma is approximately inches.

The quality level of the process is sigma. $[$round to $1$ significant digit past the decimal$]$

Does the process meet the definition of true $6$ sigma quality?

A change to the process has resulted in new control chart values: