# Chapter 6.1 & 6.2

## Properties of Nominal Curve

1. The curve is bell- shaped, with the highest point over the mean u.

2. The curve is symmetrical about a vertical line through u.

3. The curve approches the horizontal axis but never touches or crosses it.

4. The inflection (transition) points between cupping upward and downward occur above u + o and u - o.

5. The area under the entire curve is 1.

## M & O

O= standard deviations

M= mean

## Control Chart

A control chart for a random variables x is a plot of observed x variables in time sequence order.

1. Find the mean u and standard deviation o of the x distibutuion by

(a) using past data from a period during which the process was "in control" or

(b) using specified "target" values for u and o.

2. Create a graph in which the vertical axis resprents x vaules and the horizontal axis represents time.

3.Draw a horizontal line at height u and horizontal, dashed control-limit lines at u +_ 2o and u= +_ 3o.

4. Plot the variables x on the graph in time sequence order. Use line segments to connect the points in time sequence order.

## Out of Control Siganls

1. Out of Control Signal I: One point falls beyond the 3o level.

2. Out of Control Signal II: A run of nine consecutive points on one side of the center line (the line at target value u)

3.Out control Signal III: At leaast two of three consecutive points lie beyond the 2o level on the same side of the center line

## Standard Scores

A standard score or z score of measurement tells us the number of standard deviations the measurment is from the mean

## Z- Scores- Calculating

The z value and z score (also known as standard score) gives the number of standard deviations between the original measurements x and the mean u of the x distributions.

z= x-u/o

## Empirial Rule

For a distribution that is symmetrical and bell-shpaed (in particular, for normal distribution):

Approximately 68% of the data values will lie within 1 standard deviation on each side of the mean.

Approximatley 95% of the data values will lie within 2 standard deviations on each side of the mean.

Approximately 99.7% (or almost all) of the data values will lie within 3 standard deviations on each side of the mean.

## Using Z- scores & Appendex w/ Probabilities

1. Treat any area to the left of a z value smaller than -3.49 as 0.000.

2. Treat any area to the left of a z value greater than 3.49 as 1.000.