Chapter 7: Control Charts F or Attributes

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

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.

7. NP Control Chart • The np chart is used when you want to display the number of nonconforminginstead of the fraction nonconforming. • The equations for the np chart are : • Look at example 7.2 on page 310 Taken from Google

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.

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 • 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 • 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 • http://www.transtutors.com/homework-help/operations-management/quality-control/p-charts.aspx • http://www.qimacros.com/control-chart-formulas/u-chart-formula/ • http://www.qimacros.com/control-chart-formulas/np-chart-formula/ • http://www.six-sigma-material.com/SPC-Charts.html • http://www.pqsystems.com/qualityadvisor/DataAnalysisTools/t_chart.php • Douglass C. Montgomery, Intro to Statistical Quality Control.