1. ©2004 Prentice-Hall S. Thomas Foster, Jr. Boise State University PowerPoint prepared by prepared by Dave Magee University of Kentucky Lexington Community College Chapter 13 Statistically-Based Quality Improvement for Attributes

2. Slide 13-2 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Chapter Overview Chapter Overview What is an Attribute? Generic Process for Charts Understanding Attributes Control Charts Interpreting Attributes Charts Choosing the Right Attributes Chart Reliability Models

3. Slide 13-3 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition What Is An Attribute? Slide 1 of 2 What Is An Attribute? Slide 1 of 2 Attribute –Something that either does or does not exist. –In quality, we are asking the question, is it a defect or not? Viewpoint –Customer-based attributes are more associated with customer satisfaction. –Production-related attributes are more internal and engineering oriented.

4. Slide 13-4 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition What Is An Attribute? Slide 2 of 2 What Is An Attribute? Slide 2 of 2 Types of Attributes –Structural attributes have to do with physical characteristics of a particular product or service. –Sensory attributes relate to senses of touch, smell, tast, and sound. –Performance attributes relate to whether or not a particular product or service performs as it is supposed to. –Temporal attributes relate to time.

5. Slide 13-5 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Generic Process for Charts Slide 1 of 3 Generic Process for Charts Slide 1 of 3 Attribute charts are developed and interpreted the same way as variables charts. The only difference is the statistic of interest. Attribute charts deal with state of being. Variable charts deal with measurements.

6. Slide 13-6 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Generic Process for Charts Slide 2 of 3 Generic Process for Charts Slide 2 of 3 A Generic Process for Developing Attributes Charts –Identify critical operations in the process where inspection might be needed. These are operations in which, if the operation is performed improperly, the product will be negatively affected. –Identify critical product characteristics. These are the attributes of the product that will result in either good or poor form, fit, or function of the product. –Determine whether the critical product characteristic is a variable or an attribute.

7. Slide 13-7 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Generic Process for Charts Slide 3 of 3 Generic Process for Charts Slide 3 of 3 A Generic Process for Developing Attributes Charts (continued) –Select the appropriate process chart from among the many types of control charts. –Establish the control limits and use the chart to continually monitor and improve. –Update the limits when changes have been made to the process.

8. Slide 13-8 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 1 of 9 Understanding Attributes Control Charts Slide 1 of 9 Attributes Charts –Deal with binomial and Poisson processes that are not measurements. –Think in terms of defects and defectives rather than diameters and widths. Defect –An irregularity or problem with a larger unit. The larger unit may contain many defects. Defective –A unit that, as a whole, is not acceptable or does not meet performance requirements.

9. Slide 13-9 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 2 of 9 Understanding Attributes Control Charts Slide 2 of 9 p Charts for Proportion Defective –The p chart is a process chart that is used to graph the proportion of items in a sample that are defective (nonconforming to specifications) –p charts are effectively used to determine when there has been a shift in the proportion defective for a particular product or service. –Typical applications of the p chart include things like late deliveries, incomplete orders, and clerical errors on written forms.

10. Slide 13-10 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 3 of 9 Understanding Attributes Control Charts Slide 3 of 9 p Charts for Proportion Defective –The subgroup size is typically between 50 and 100 units. –The subgroups for a p chart may be of different sizes. However, it is best to hold subgroup sizes constant. –Formulas for the p chart Control limits for p = p +/- 3  ((p)(1-p)/n) where: p is the proportion defective p is the average proportion defective n is the sample size

11. Slide 13-11 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 4 of 9 Understanding Attributes Control Charts Slide 4 of 9 np Charts –The np chart is a graph of the number of defectives (or nonconforming units) in a subgroup. –The np chart requires that the sample size of each subgroup be the same each time a sample is drawn. –When subgroup sizes are equal, either the p or np chart can be used. They are essentially the same chart. –Some people find the np chart easier to use because it reflects integer numbers rather than proportions. The uses for the np chart are essentially the same as the uses for the p chart.

12. Slide 13-12 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 5 of 9 Understanding Attributes Control Charts Slide 5 of 9 np Charts (continued) –Formulas for computing control limits

13. Slide 13-13 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 6 of 9 Understanding Attributes Control Charts Slide 6 of 9 c Charts –The c chart is a graph of the number of defects (nonconformities) per unit. –The units must be of the same sample space; this includes size, height, length, volume and so on. This means that the “area of opportunity” for finding defects must be the same for each unit. Several individual units can comprise the sample but they will be grouped as if they are one unit of a larger size. –Like other process charts, the c chart is used to detect nonrandom events in the life of a production process.

14. Slide 13-14 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 7 of 9 Understanding Attributes Control Charts Slide 7 of 9 c Charts (continued) –Typical applications of the c chart include number of flaws in an auto finish, number of flaws in a standard typed letter, and number of incorrect responses on a standardized test. –Formula

15. Slide 13-15 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 8 of 9 Understanding Attributes Control Charts Slide 8 of 9 u Charts –The u chart is a graph of the average number of defects per unit. This is contrasted with the c chart, which shows the actual number of defects per standardized unit. –The u chart allows for the units sampled to be different sizes, areas, heights and so on, and allows for different numbers of units in each sample space. The uses for the u chart are the same as the c chart.

16. Slide 13-16 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Understanding Attributes Control Charts Slide 9 of 9 Understanding Attributes Control Charts Slide 9 of 9 u Charts (continued) –Formula CL u = u ± 3  u/n where: n = average sample size c = process average number of nonconformities per unit

17. Slide 13-17 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Reliability Models Slide 1 of 4 Component Reliability –Is defined as the propensity for a part to fail over a given time. System Reliability –Refers to the probability that a system of components will perform their intended function over a specified period of time. Bathtub-Shaped Hazard Function –Reliability model that shows that products are more likely to fail either very early in their useful life or very late in their useful life.

18. Slide 13-18 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Reliability Models Slide 2 of 4 Bathtub-Shaped Hazard Function Figure 13.9

19. Slide 13-19 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Reliability Models Slide 3 of 4 Series Reliability –Components in a system are in series if the performance of the entire system depends on all of the components functioning properly. –The components need not be physically wired sequentially for the system to be in series. –All parts must function for the system to function. 1122nn

20. Slide 13-20 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Reliability Models Slide 4 of 4 Parallel Reliability –Another word for a backup system is a redundant or a parallel system. –The system can function if a give component in the system fails. Series and Redundant Reliability A A B B C1C1 C1C1 C2C2 C2C2 D D

21. Slide 13-21 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Measuring Reliability Measuring Reliability Failure Rate –Formula Failure rate = λ = number of failures/(units tested) x (number of hours tested) Meantime to failure (MTTF) –Average time before a product will fail –1/ λ Meantime between failures MTBF) –Average time from one failure to the next when a product can be repaired –MTBF = Total operating hours / number of failures

22. Slide 13-22 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition System Availability System Availability Gives the “uptime“ for a product or service. Considers both mean time between failure (MTBF) and mean time to repair (MTTR). Formula System Availability, SA = MTBF/(MTBF + MTTR)

23. Slide 13-23 © 2004 Prentice-Hall Managing Quality: An Integrative Approach; 2nd Edition Summary Summary What is an Attribute? Generic Process for Charts Understanding Attributes Control Charts Interpreting Attributes Charts Choosing the Right Attributes Chart Reliability Models