1. Chapter 7: Control Charts For Attributes
By Drew Kelly
IET 603
Introduction to Statistical Quality Control.
Douglass C. Montgomery

2. 7-1 Introduction
In this Chapter we deal with what is called Attributes Data.
Attributes Data deals with classifications of a product that is either defective or non-defective.
Taken from Google

3. 7-1 Introduction
The terms nonconformity and nonconforming are used more in today’s time.
However many feel that saying defect and defective gives a more clear distinction between the two.
Attribute Charts are not as statistically informing as Variable charts. Simple due to the amount of numerical information Variable charts have to offer
Attribute charts are not as informative as variable charts due to the lack of numerical information.

4. 7-2 The Control Chart for Fraction Nonconforming
The fraction nonconforming is the ratio of the number of nonconforming units in a population to the total number of units in the population.
Again nonconforming item simply means that the entire product is defective. And should not be put out for use.

5. 7-2-1 Development and Operation of the Control Chart
The control chart is also called the P- Chart.
Again this is for the fraction of nonconforming
Equations for the control chart are:
Taken from Google
The control limits given here are called trial control limits.

6. 7-2-1 Continued
There are three parameters that must be need to be specified: the sample size, the frequency of sampling, and the widths of the control limits.
When interpreting points on the control charts, one must use caution.
Often it is found that points below the lower control limit do not represent a real improvement in process quality.
Bullet 3: Frequently caused by errors in the inspection process

7. NP Control Chart
The np chart is used when you want to display the number of nonconforming instead of the fraction nonconforming.
The equations for the np chart are :
Look at example 7.2 on page 310
Taken from Google
So instead of there being a fration of non conforming items in a population to the population as a whole.

8. NP Control Chart
Taken From Google.

9. Questions?

10. 7-2-2 Variable Sample Size
In some occasions the sample is a inspection of process output over a period of time. This will cause the control chart to have a variable sample size.
There are three methods to construct control charts with variable sample sizes.

11. Variable-Width Control Limits
Determine the control limits for each individual sample that are based on the specific sample size.
The equations the same as if you were using it for the p chart
If you will look at page 311 in your book to see an example

12. Control limits based on an average sample size
Based on average sample size
Which will give an approximation of the control charts.
This approach assumes that future sample sizes will not differ from the ones previously used.
To find the average sample size you take the total of the sample size, denoted by ni, and divide by the total number of observations.
Then solve like you would for the p chart
Look at page 312 if you feel the need to.

13. The Standardized control Chart
Where the points are plotted in standard deviation units.
Center line must be at 0
And control limits are at +3 and -3

14. 7-2-4 Operating-Characteristic Function
The OC function is of the fraction of nonconforming control chart; is a graphic display of the probability of incorrectly accepting the hypothesis of SC against the process fraction nonconforming.
This mean it is a type II error (failure to reject the incorrect hypothesis)

15. Questions?

16. 7-3 Control charts for Nonconformities
Review: A nonconforming item is an unit of product that does not meet one or more of the specifications for that particular product. ( Defective unit )
A nonconformity is the specific point where the specification is not met. ( Defect within a unit )
Not all products with nonconformities will be nonconforming.
Depending on the degree of severity it may still pass operations

17. Constant Sample size
Control charts can be created for either the total number of nonconformities in a unit or the average.
The control chart is called a c-chart. And is for the number of nonconformities, or defects.
Taken from Google

18. Further Analysis of Nonconformities
Other useful techniques of further analyzing nonconformities are cause and effect diagrams.
Defect or nonconformity data is more useful that defective data because there are always going to be more nonconformity data.
Out-of-control-action plans can be and should be done when your process is out of control.
Nonconformities give better detail to help create a OCAP because there will be several different types of nonconformities.

19. Choice of sample size
The sample size should be chosen according to statistical considerations, such as picking a size large enough to make positive lower control limits.
Economic factors should be considered when determining the sample size.

20. U chart
The best approach for setting up an u chart is to use the following equations:
Taken From Google
The u chart is used when the sample size is considered a variable sample size
And is the control chart for average number of nonconformities per unit.

21. 7-3-3 Demerit Systems
Demerit systems are ways to classify the seriousness of defect within the unit.
This method is best used when you have a very complex product such as a car, computer, electrical appliances.

22. Demerit System Classification
Class A-Very serious. Unit is completely unfit for service.
Class B- Serious. The unit will most likely suffer a class A operating failure.
Class C- Moderately Serious. The unit will possibly fail service or cause a good deal of trouble
Class D- Minor. The unit will not fail but has minor defects.

23. Demerit Class Weights Class A-100 Class B-50 Class C-10 Class D-1
From this you can get the equation:
D=100ciA+50ciB+10ciC+1ciD

24. Dealing with low Defect levels
When the defect level drops, c and u charts become ineffective.
Time between occurrence control charts are a good way to deal with this
They chart the time between the successive occurrences of the defect.
Taken from
pqsystems.com

25. Questions?

26. 7-4 Choice Between Attributes and Variable Control Charts
Attribute Control Charts
Easy to understand
Easy to make
Avoids the hassle of having to make several Xbar or Rbar charts, like you would have to with Variable Control Charts.

27. 7-4 Choice Between Attributes and Variable Control Charts
Provide much more useful information about process performance.
Produce identification of impending trouble and allow management to take action to prevent defects from even happening.

28. 7-5 Guidelines for Implementing Control Charts
Every process can benefit from SPC
There are general guide lines that are used in order to implement the correct control chart.
In total there are 5

29. Guidelines for selecting the appropriate control chart
Determining which process characteristic to control
Determining where the charts should be implemented
Choosing the proper type of control chart
Taking action to improve processes as the result of control chart analysis
Selecting data collection systems and computer software.

30. Review Any final Questions?
Attribute charts are mostly used where there is not much information to be given
Nonconforming and nonconformities are not the same thing.
Nonconforming means defective.
Nonconformity mean defect.
Variable charts are more complex to make but provide useful information
Any final Questions?

31. References
management/quality-control/p-charts.aspx
chart-formula/
chart-formula/
ols/t_chart.php
Douglass C. Montgomery, Intro to Statistical Quality Control.