91Ó°ÊÓ

Mean:

The Mean or the arithmetic mean $\left(\stackrel{¯}{x}\right)$is given as the summation of measured values divided by the number of measurements $\left(n\right)$Mean is also called as average.

$\stackrel{¯}{x}=\frac{{\displaystyle \underset{i}{∑}}xi}{n}$

Standard deviation:

The standard deviation $\left(s\right)$is given by the formula:

$s=\sqrt{\frac{{{\displaystyle \underset{i}{∑\left(x_i-\stackrel{¯}{x}\right)}}}^2}{n-1}}$

Given table:

Using mean formula,

$\stackrel{¯}{\mathrm{x}}=\frac{{\displaystyle \underset{\mathrm{i}}{∑}\mathrm{xi}}}{\mathrm{n}}=08411$

Mean of the samples calculated was 0.8411.

Using standard deviation formula,

$\mathrm{s}=\sqrt{\frac{{\displaystyle {\underset{\mathrm{i}}{∑\left({\mathrm{x}}_{\mathrm{i}}-\stackrel{¯}{\mathrm{x}}\right)}}^2}}{\mathrm{n}-1}}=0.1888$

Standard The standard deviation of the samples calculated was 0.1888.

The stability criteria for the control chart are.

- There shouldn't be observations outside the action lines-on day 101 one observation lies above the line.

- There are no two out of 3 consecutive measurements between warning and action lines-OK.

- There are no seven7 consecutive measurements all above or below the centre line-OK.

- There are no six consecutive measurements all steadily increasing or all steadily decreasing, wherever they are located.

- There are no fourteen consecutive points alternating up and down, nevertheless of where they are located-OK.

- There is no obvious non-random pattern-OK.