chapter 3 variation statistical process control (spc) 2 1 1 (1) 2

7/29/2019 Chapter 3 Variation Statistical Process Control (SPC) 2 1 1 (1) 2

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Variation & StatisticalProcess Control (SPC)

School of TechnologyEnterprise Quality Planning


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Concept of Variation

Understand the concept and types of variation

Learn the differences between quantitative and

qualitative data

Learn to construct frequency distributions

Understand the measures of central tendency and

dispersionLearn about the attributes of a normal distributions

Making predictions with normal distributions


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To control and reduce variation you must first understand,quantify, AND interpret variation in a data set.

The smaller the variation the more consistent and

predictable your process will be.Although variation can never be eliminated it does impact

quality, costs, and customer satisfaction.

No two objects, product or actions are alike, therefore,

variation exists everywhere!

o Service quality

o Product performance

o Process outputs


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Concept of Variation What is it?


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Concept of Variation What is it?Common-Cause Variation Special-Cause Variation


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Discrete Data (also known as Qualitative orAttribute)Data that is counted or classified and not measured on a scale

Only a finite number of values is possible

Values cannot be subdivided meaningfullyThe counts can be made up of either:

Data either meets or fails to meet some criteria

yes/no

pass/fail agree/disagree

The sum of a particular event

number of patient falls

number of C-sections

number of incorrect prescriptions


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Continuous Data (also known as Quantitativeor Variable)

Information that can take be measured on a continuous scale

Can take on almost any numeric value and be

broken down into finer increments:

o waiting time in minutes

o body weight in kilograms

o length of stay in days

o temperatureo cost

Meaningful information exists between variables


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Data Summary

**Continuous data yields the most information


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Frequency Tables


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Frequency Tables


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E.g. Length of Stay (LOS) in an Orthopedic unit


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Frequency Distribution Table


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Frequency Distribution Table


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Relative frequency Histogram


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Cumulative Relative frequency Histogram


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Distributions


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Levels of MeasurementData can be classified into 1 of 4 levels of measurement.

These levels of measurement is important, because certain

calculations can be done with only certain kinds of data.

Nominal

Ordinal

Interval

Ratio


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Nominal dataWeakest level of data is called nominal level data.

Nominal level data is made up of values that are distinguished by

name only.

There is no standard ordering scheme to this data.

E.g. The colors of popsicles is an example of nominal level data.

This data is distinguished by name only.

There is no agreed upon ordering of this data, although we eachmay have an opinion about which should be listed first.


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Ordinal dataOrdinal level data is similar to nominal level data in that the data is

distinguished by name

But it is different than nominal level data because there is an

ordering scheme.

E.g. People are classified as low-income, middle-income, or high-

income.

This is an example of ordinal level data.

We do know that people in the low-income bracket earn less thanthe people in the middle-income bracket, who in turn earn less than

the people in the high-income bracket.

So there is an ordering scheme to this data.

The thing that ordinal level data lacks is that you can't measure the

difference between two pieces of data

E i


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Interval dataInterval level data is similar to ordinal level data in that it has a

definite ordering scheme

But it is different in the fact the differences between data is

meaningful and can be measured.

E.g. The boiling temperatures of different liquids are listed. This is an

example of interval level data.

We can tell whether a temperature is higher or lower than another,so we can put them in an order.

If water boils at 100 degrees and another liquid boils at 75 degrees,

the second temperature is 25 degrees lowerr than the first.

So the differences between data are measurable and meaningful.

E t i


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Interval data continuedE.g. A cookie recipe calls for the brownies to be cooked at 400

degrees for 30 minutes.

Would the results be the same if you cooked them at 200 degrees

for 60 minutes?How about at 800 degrees for 15 minutes?

We would get 3 different types of brownies : just right, awful gooey,

and awful crunchy.

The problem is that 200 degrees is not half as hot as 400 degrees,

and 800 degrees is not twice as hot as 400 degrees.

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Ratio dataRatio level data is just like interval level data, except that ratios make

sense

E.g. Four people are randomly selected and asked how much money

they have with them. Here are the results : $21, $50, $65, and $300.Is there an order to this data?

Yes, $21 < $50 < $65 < $300.

Are the differences between the data values meaningful?

Sure, the person who has $50 has $29 more than the person with

$21.

Can we calculate ratios based on this data?

Yes because $0 is the absolute minimum amount of money a person

could have with them. The person with $300 has 6 times as much as

the person with $50.

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Stem & leaf plotsAnother way to organize data is to use a Stem and Leaf Display.

This is a "shorthand" notation for representing numbers.

We break each number into 2 parts.

The last digit is called the leaf, and the rest of the number is calledthe stem.

The number 75 has a stem of 7 and a leaf of 5. The number 129 has

a stem of 12 and a leaf of 9.We then collect all numbers with the same stem and place them in

a row.

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Stem & leaf plotsHere is a set of data points:

22 19 30 21 41 24 19 23 27 32 30 20

22 36 24 26 39 20 21 19 19 19 22 30

31 17 18 21 26 21 25 21 22 22 20 4023 19 21 17 20 33 22 31 19 24 37 22

Stem Leaf1

2 2

3

4

The first number is 22, which has a stem of 2 and a leaf of 2, so we put a 2 in the

row with a stem of 2,

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Stem & leaf plotsAfter the first row, your display should look like this :

Stem Leaf

1 9 9

2 2 1 4 2 7 0

3 0 2 0

4 1

Starting at the top, the display tells us that we have values of 19, 19, 22, 21,

24, 22, 27, 20, 30, 32, 30 and 41.

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Stem & leaf plotsFinally, here is what we should have after all values have been used :

Stem Leaf

1 9 9 9 9 9 7 8 9 7 9

2 2 1 4 2 7 0 2 4 6 0 1 2 1 6 1 5 1 2 2 0 3 1 0 2 4 2

3 0 2 0 6 9 0 1 3 1 7

4 1 0

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Stem & leaf plotsThe last step is to put the leaves in increasing order, like so:

Stem Leaf

1 7 7 8 9 9 9 9 9 9 9

2 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 4 4 4 5 6 6 7

3 0 0 0 1 1 2 3 6 7 9

4 0 1

If you create a stem and leaf display first, it will make it easier to create a

frequency

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Frequency Distribution TableThe last step is to put the leaves in increasing order, like so:

Stem Leaf

1 7 7 8 9 9 9 9 9 9 9

2 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 4 4 4 5 6 6 7

3 0 0 0 1 1 2 3 6 7 9

4 0 1

chapter 3 variation statistical process control (spc) 2 1 1 (1) 2

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