1. Chapter 9- Control Charts for Attributes
Quality Improvement
Chapter 9- Control Charts for Attributes
PowerPoint presentation to accompany
Besterfield, Quality Improvement, 9e 1

2. Outline Attribute Control Charts for Nonconforming Units
Control Charts for Count of Nonconformities
A Quality Rating System 2

3. Learning Objectives When you have completed this chapter you should:
Know limitations of variable control charts and the different types of attibute charts.
Know the objectives of the p chart group and the applicable distribution.
Be able to construct a:
Fraction defective chart- fixed subgroup size
Fraction defective chart-variable subgroup size
Percent defective chart
Number defective chart 3

4. Learning Objectives cont’d.
When you have completed this chapter you should:
Know how to minimize the effect of variable subgroup size.
Know the applications of the c chart group, the applicable distribution and two conditions.
Be able to construct a c chart and a u chart and know the difference between them.
Know the three classes of defect severity 4

5. Attribute
The term Attribute refers to those quality characteristics that conform to specifications or do not conform to specifications.
Attribute are used:
Where measurements are not possible.
Where measurements can be made but are not made because of time, cost, or need.

6. Attribute
A nonconformity is a departure of a quality characteristic from its intended level or state that occurs with a severity sufficient to cause an associated product or service not to meet a specification requirement.
Defect is concerned with satisfying intended normal, or reasonably foreseeable, usage requirement.

7. Attribute
Defect is appropriate for use when evaluation is in terms of usage.
Nonconformity is appropriate for conformance to specifications.
The term Nonconforming Unit is used to describe a unit of product or service containing at least one nonconformity.

8. Attribute
Defective is analogous to defect and is appropriate for use when unit of product or service is evaluated in terms of usage rather than conformance to specifications.
Limitations of variable control charts: These charts cannot be used for quality characteristics which are attributes.
Variable can be translated to attribute but not visa versa

9. Attribute Types of Attribute Charts:
Nonconforming Units (based on the Binomial distribution): p chart, np chart.
Nonconformities (based on the Poisson distribution): c chart, u chart.
Used when there are to many variables in a control chart
Gives and “overall quality chart”
These will look like the other control charts

10. The P Chart
The P Chart is used for data that consist of the proportion of the number of occurrences of an event to the total number of occurrences.
It is used in quality to report the fraction or percent nonconforming in a product, quality characteristic, or group of quality characteristics.

11. The P Chart
Formula:
The fraction nonconforming, p, is usually small, say, 0.10 or less.
Because the fraction nonconforming is very small, the subgroup sizes must be quite large to produce a meaningful chart.
Np = # non-conforming units in the sample
Example 9-1

12. The P Chart
It can be used to control one quality characteristic, as is done with X bar and R chart,
Or to control a group of quality characteristics of the same type or of the same part,
Or to control the entire product.
It can be established to measure the quality produced by a work center, by a department, by a shift, or by an entire plant.

13. The P Chart
It is frequently used to report the performance of an operator, group of operators, or management as a means of evaluating their quality performance.
The subgroup size of the P chart can be either variable or constant.

14. The P Chart Objectives of the P Chart:
Determine the average quality level: This information provides the process capability in terms of attributes.
Bring to the attention of management any changes in the average.
Improve the product quality: Ideas for quality improvement.

15. The P Chart Objectives of the P Chart cont’d:
Evaluate the quality performance of operating and management personnel.
Suggest places to use Xbar and R chart: They are more sensitive to variation.
Determine acceptance criteria of a product before shipment to the customer.

16. The P Chart P-Chart Construction for Constant Subgroup Size
Select the quality characteristic(s):
Single quality characteristic.
Group of quality characteristics.
A part.
An entire product.
A number of products.
It can be established for performance control of an
operator, work center, department, shift, plant, or corporation

17. The P Chart P Chart Construction for Constant Subgroup Size cont’d.
Determine the subgroup size and method:
The size of the subgroup is a function of the proportion nonconforming.
A minimum size of 50 is suggested as a starting point.
So you do not have lots of 0s on your chart
There is a formula on p 125 to determine sample size.

18. The P Chart P Chart Construction for Constant Subgroup Size cont’d.
Collect the data:
At least 25 subgroups.
Different sources (Check sheet).
For each subgroup the proportion nonconforming is calculated by the formula P = np/n

19. The P Chart P Chart Construction for Constant Subgroup Size
Calculate the trial central line and the control limits:
This sigma is sample proportion from before
If LCL <0 then set = 0

20. FIGURE 9-2 A p Chart to Illustrate the Trial Central Line and Control Limits Using the Data from Table 9-1

21. The P Chart P Chart Construction for Constant Subgroup Size cont’d.
Establish the revised central line and control limits.

22. FIGURE 9-3 Continuing Use of the p Chart for Representative Values of the Proportion Nonconforming, p

23. The P Chart
The P Chart is most effective if it is posted where operating and quality personnel can view it.
The control limits are usually three standard deviations from the central value. Therefore, approximately 99% of the plotted points, P, will fall between the upper and lower control limits.

24. The P Chart
A P Chart will also indicate long-range trends in quality, which will help to evaluate changes in personnel, methods, equipment, tooling, materials, and inspection techniques.
P-chart is based on the binomial distribution.

25. FIGURE 9-4 Various Techniques for Presenting p -Chart Information

26. The P Chart P Chart Construction for Variable Subgroup Size
Collect the data.
Determine the trial central line and control limits: Since the subgroup size changes each day, limits must be calculated for each day.
Control limits are not known until the end of the day.

27. FIGURE 9-5 Preliminary Data, Central Line, and Trial Control Limits
What are the changes in UCL/LCL due to? Subgroup size.
FIGURE 9-5 Preliminary Data, Central Line, and Trial Control Limits

28. The P Chart P Chart Construction for Variable Subgroup Size cont’d.
As the subgroup size gets larger, the control limits are closer together.
Establish revised central line and control limits:

29. The P Chart P Chart Construction for Variable Subgroup Size cont’d.
If Po is known, the process of data collection and trial control limits is not necessary.
P is the proportion (fraction) nonconforming in a single subgroup.
Pbar is the average proportion (fraction) nonconforming of many subgroups.

30. The P Chart P Chart Construction for Variable Subgroup Size cont’d.
Po is the standard or reference value of the proportion (fraction) nonconforming based on the best estimate of PBar.
Φ is the population proportion (fraction) nonconforming.

31. The P Chart Minimizing the Effect of Variable Subgroup Size
Control limits for an average subgroup size: By using an average subgroup size, one limit can be calculated and placed on the control chart.

32. May 11, large subgroup size means smaller UCL so need to check individually.
May 24, small “ “ “ ‘ larger “ “ “ “ “
FIGURE 9-7 Chart for May Data Illustrating Use of an Average Subgroup Size

33. The P Chart Minimizing the Effect of Variable Subgroup Size cont’d.
Case I: This case occurs when a point (subgroup fraction nonconforming) falls inside the limits and its subgroup size is smaller than the average subgroup size.
Case II: This case occurs when a point (subgroup fraction nonconforming) falls inside the average limits and its subgroup size is larger than the average subgroup size.

34. The P Chart Minimizing the Effect of Variable Subgroup Size cont’d.
Case III: This case occurs when a point (subgroup fraction nonconforming) falls outside the limits and its subgroup size is larger than the average subgroup size.
Case IV: This case occurs when a point (subgroup fraction nonconforming) falls outside limits and its subgroup size is less than the average subgroup size.

35. FIGURE 9-8 p Chart Illustrating Central Line and Control Limits for Different Subgroup Sizes

36. The np Chart Number Nonconforming Chart (np):
The np chart is easier for operating personnel to understand than the p chart.
The limitation that this chart has is that the subgroup size needs to be constant.

37. The np Chart

38. The np Chart Number Nonconforming Chart (np):
If the fraction nonconforming po is unknown, then it must be determined by collecting data, calculating trial control limits, and obtaining the best estimate of po.

39. FIGURE 9-9 Number Nonconforming Chart ( np Chart)

40. Process Capability For an attribute this process is much simpler.
The process capability is the central line of the control chart.
Management is responsible for the capability.
When the plotted point is outside the control limit, operating personnel are usually responsible.

41. FIGURE 9-10 Process Capability Explanation and Responsibility

42. Control Charts for Count of Non-conformities
The nonconformities chart controls the count of nonconformities within the product or service.
An item is classified as a nonconforming unit whether it has one or many nonconformities.
Count of nonconformities (c) chart.
Count of nonconformities per unit (u) chart.

43. Control Charts for Count of Non-conformities
Since these charts are based on the Poisson distribution, two conditions must be met:
The average count of nonconformities must be much less than the total possible count of nonconformities.
The occurrences are independent.

44. Control Charts for Count of Non-conformities
Objectives:
Determine the average quality level: This information gives the initial process capability.
Bring to the attention of management any changes in the average.
Improve the product quality: Ideas for quality improvement.

45. Control Charts for Count of Non-conformities
Objectives cont’d.:
Evaluate the quality performance of operating and management personnel.
Suggest places to use Xbar and R chart.
Determine acceptance criteria of a product before shipment to the customer.

46. Control Charts for Count of Non-conformities
C Chart construction:
Select the quality characteristic(s):
Single quality characteristic.
Group of quality characteristics.
A part.
An entire product.
A number of products.
It can be established for performance control of an: operator, work center, department, shift, plant, or corporation

47. Control Charts for Count of Non-conformities
C Chart construction cont’d:
Determine the subgroup size and method:
Collect the data:
At least 25 subgroups.
Different sources.

48. Control Charts for Count of Non-conformities
c-Chart Construction cont’d:
Calculate the trial central line and the control limits:

49. FIGURE 9-11 Control Chart for Count of Nonconformities ( c Chart), Using Preliminary Data

50. Control Charts for Count of Non-conformities
Establish the revised central line and control limits

52. Control Charts for Count of Non-conformities
C chart construction cont’d:
Achieve the objectives: The reason for the control chart is to achieve one or more of the previously stated objectives.

53. Control Charts for Count of Non-conformities/Unit
Chart for Count of Nonconformities/Unit (u Chart)

54. FIGURE 9-13 u Chart for Errors on Waybills

55. Control Charts for Count of Non-conformities
Chart for Count of Nonconformities/Unit
(u Chart)
Scale selected is continuous for the u chart. For the c chart is discrete.
Subgroup size for the u chart can vary. For the c chart is 1.
The u chart is limited in that we do not know the location of the nonconformities.

56. A Quality Rating System
Nonconformity Classification:
Critical nonconformities: Unsafe conditions for individuals using, maintaining, or depending upon the product.
Major nonconformities: Result in failure or reduce materially the usability of the product for its intended purpose.
Minor nonconformities: Reduce materially the usability of the product for its intended purpose.

57. Control Charts for Demerits/Unit

58. FIGURE 9-16 Demerit-Per-Unit Chart ( D Chart)

59. Control Chart Selection
Quality Characteristic
Variable
Attribute
Defective
Defect no
n>1?
x and MR
yes
constant
sample
size?
yes
Sampling
Unit one
p or np no
n>=10?
x and R
yes no no
yes
p-chart with
variable sample
size
c u
x and s

60. Computer Program
EXCEL/Minitab program files on the website will solve for:
p chart
np chart
c chart
U chart

61. Homework
5, 7, 16b, 23