1. An example of Alternative # 4 for P Charts With Variable Subgroup Sizes

2. The C Chart Number of defects/unit data when there is a constant area of opportunity. Used for more complex products where there can be more than one defect present/unit (e.g., number of defects/car, number of defects/circuit board) Control Limits:

3. For C charts the zones should be large enough to use zone rules (otherwise meaningless) As a rule of thumb, the zone boundries should not be used for C charts with average counts of less than 20 When average count is low the control chart may lead to overadustments (tampering) and underadjustments (too little sensitivity) –May use a set of fixed control limits (Probability Control Limits developed using the Poisson probability model) –See Figure 6.21, page 201 –Often leads to similar results as formula provides

4. Example The average number of surface imperfections in painted sheet metal pieces of equal size is 9. What are the Upper and lower control limits? Formula: Probability limits:

5. The U Chart Number of defects/unit data when area of opportunity changes from subgroup to subgroup (e.g., number of defects in various types of circuit boards) Control Limits: Two alternatives for dealing with variable areas of opportunity: 1.Calculate approximate control limits based on average area of opportunity (most applicable when variation in subgroup size is less than ±25%) 2.Calculate two sets of control limits, inner and outer limits(most applicable when variation in subgroup size is more than ±25%)

6. Example (problem 6.10, page 226)

7. Disadvantages of Attribute Charts Difficult to make further improvements after a certain point. Difficult to distinguish different sources of variation Do not provide as clear a direction for process improvement as variables data.

8. Variable Control Charts Range (R) Chart: Detects shifts in process variability Control Limits:

9. Xbar (Mean) Chart: Detects shifts in process mean Control limits:

10. Constructing Xbar and Range Control Charts I.Select about 25-50 samples of sizes 4 to 6 Use rational sampling: minimize variability within samples so variability across subgroups can be detected. II. Calculate the mean and Range of each sample III. Calculate the grand average (average of the averages) and the average of the ranges. IV.Calculate the control limits for the Xbar Chart, plot the sample ranges, eliminate any sample that indicates a special cause of variation, recalculate the control limits and repeat until no special causes of variation are present. V.Calculate the control limits for the Xbar chart, plot sample averages, eliminate any sample that indicates a special cause of variation, recalculate the control limits and repeat until no special causes of variation are present.

11. Consider a process by which coils are manufactured. Twenty five samples of Size 5 are randomly selected from the process over time and the resistance values (ohms) are measured. Construct an Xbar and Range Chart for this data. 12022212322 21918222020 32518201722 42021222121 51924232220 62220181819 71820191820 82018232021 92120242322 102119202020 112020232220 122221202223 131922191819 142021222122 152024242323 162120242021 172018182020 182024222323 192019232019 202221212422 212322222022 222118181719 232124242323 242022212120 251920212122