Engineering Statistics Handbook Episode 4 Part 15 docx

Graph responses, then explanatory versus response, then conditional plots The order that generally proves most effective for data analysis is to first graph all of the responses against

3 Production Process Characterization

3.4 Data Analysis for PPC

3.4.2 Exploring Relationships

The first

analysis of

our data is

exploration

Once we have a data file created in the desired format, checked the data integrity, and have estimated the summary statistics on the response variables, the next step is to start exploring the data and to try

to understand the underlying structure The most useful tools will be various forms of the basic scatter plot and box plot.

These techniques will allow pairwise explorations for examining relationships between any pair of response variables, any pair of explanatory and response variables, or a response variable as a function of any two explanatory variables Beyond three dimensions

we are pretty much limited by our human frailties at visualization.

Graph

everything

that makes

sense

In this exploratory phase, the key is to graph everything that makes sense to graph These pictures will not only reveal any additional quality problems with the data but will also reveal influential data points and will guide the subsequent modeling activities.

Graph

responses,

then

explanatory

versus

response,

then

conditional

plots

The order that generally proves most effective for data analysis is to first graph all of the responses against each other in a pairwise fashion Then we graph responses against the explanatory variables This will give an indication of the main factors that have an effect on response variables Finally, we graph response variables, conditioned on the levels of explanatory factors This is what reveals interactions between explanatory variables We will use nested boxplots and block plots to visualize interactions.

3.4.2 Exploring Relationships

http://www.itl.nist.gov/div898/handbook/ppc/section4/ppc42.htm [5/1/2006 10:17:39 AM]

3.4.2.1 Response Correlations

The second graph is a box plot of the number of large particles added for each cassette type. 3.4.2.2 Exploring Main Effects

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We conclude from these two box plots that cassette does not appear to be an important factor for small or large particles.

There is a

difference

between

slots for

small

particles,

one slot is

different for

large

particles

We next generate box plots of small and large particles for the slot variable First, the box plot for small particles.

3.4.2.2 Exploring Main Effects

Next, the box plot for large particles.

3.4.2.2 Exploring Main Effects

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We conclude that there is a difference between slots for small particles We also conclude that one slot appears to be different for large particles.

Load lock

may have a

slight effect

for small

and large

particles

We next generate box plots of small and large particles for the load lock variable First, the box plot for small particles.

3.4.2.2 Exploring Main Effects

Next, the box plot for large particles.

3.4.2.2 Exploring Main Effects

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We conclude that there may be a slight effect for load lock for small and large particles.

For small

particles,

temperature

has a

strong

effect on

both

location

and spread.

For large

particles,

there may

be a slight

temperature

effect but

this may

just be due

to the

outliers

We next generate box plots of small and large particles for the temperature variable First, the box plot for small particles.

3.4.2.2 Exploring Main Effects

Next, the box plot for large particles.

3.4.2.2 Exploring Main Effects

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We conclude that temperature has a strong effect on both location and spread for small particles We conclude that there might be a small temperature effect for large particles, but this may just be due to outliers.

3.4.2.2 Exploring Main Effects

We conclude from this plot that for small particles, the load lock effect is not as strong for high temperature as it is for low temperature.

The same

may be true

for large

particles

but not as

strongly

The following is the box plot of large particles for load lock nested within temperature.

3.4.2.3 Exploring First Order Interactions

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We conclude from this plot that for large particles, the load lock effect may not be as strong for high temperature as it is for low temperature However, this effect is not as strong as it is for small

particles.

3.4.2.3 Exploring First Order Interactions