【正文】 others in that particular subgroup (even though their average is not unusual) 80 X,R Charts ? The variation within subgroups ( R ) is used to establish the control limits for the averages of the subgroups ? Because subgroups contain shortterm variation, it is thought that an ―ideal‖ process should be able to perform as well over the long term ? Therefore it is assumed that the moncause variation within subgroups equals the moncause variation between subgroups ? Changes in process variability can be distinguished from changes in process average. 81 Subgroup Selection Subgroups are specially chosen samples of data. How you structure the subgroups has a big influence on whether the chart is valid. The samples are chosen such that: ? As a whole, they will reflect all the sources of moncause (shortterm) variation. ? They contain no sources of specialcause (longterm) variation. In order to minimize the chance of special causes within subgroups: ? Keep subgroup size small (typically 5 or fewer data points) ? Use ―adjacent‖ items in subgroups—made sequentially ?Items made or work processed ―adjacent‖ in time will be more likely to contain only moncause variation 82 Reminder: Long vs. Shortterm Variation Shortterm data are more likely to reflect only moncause variation in a process。 narrower where n is larger Points outside limits 69 Exercise 7: Answers, cont. Question 3: Interpretation a. Average = defects per shipment. b. You can expect about to defects per shipment, depending on how many shipments are inspected. c. Special causes = two points below the LCLs. d. Actions: Investigate why those points are different. Since low numbers are good, find out how to preserve the conditions that led to few defects. e. Future: Continue updating chart to see if actions taken in response to special causes lowers overall number of defects. 70 Examples of Limits That Do Not Look Right Start Type of data ? Equal sample sizes ? Equal opportunity ? p chart p chart np chart chart Individuals chart Individuals chart EWMA chart chart Continuous Yes No Yes Rational Subgroups Discrete Yes No No u chart u chart c chart c chart Do limits look right? Try individuals chart ry individuals chart Need to detect small shifts quickly? Individual measurements or subgroups ? Try transformation to make data normal ry ation to data al Do limits look right? Yes No Either/Or No Yes Individual measurements Occurrences X, R chart , art Items with attribute Counting items with an attribute or counting occurrences? 71 Examples of Limits That Do Not Look Right (p or np chart) Limits do NOT look right Limits do look right 0 5 10 15 20 25 Observation Number Individual Value Individuals Chart Defective Rate X= = = 0 5 10 15 20 25 Sample Number Proportion P Chart Defective Rate P= = = Same data shown in different charts 72 Examples of Limits That Do Not Look Right (p or np chart), cont. ? If about 1/3 or more of the data points are outside the limits, they ―don‘t look right‖ (good indicator that you might be using the incorrect control chart) ? Whenever n 1000, ask yourself if the data really fits a binomial distribution ? The assumption that the expected proportion is constant for each sample does not hold—so the data are not binomial ? In this situation, use an individuals chart instead of a p or np chart Units Defective DefectiveWeek Processed Units Rate1 8259 490 2 7661 368 3 8278 325 4 7788 349 5 7610 360 . . . .. . . .. . . .21 8019 542 22 8868 446 23 7357 590 24 9946 473 25 8937 339 73 Examples of Limits That Do Not Look Right (c or u chart), cont. Limits do NOT look right Limits do look right 0 5 10 15 20 25 0 100 200 Observation Number Individual Value Individuals Chart for Defects X= = = 0 5 10 15 20 25 50 100 150 Sample Number Sample Count C Chart for Defects C= = = Same data shown in different charts 74 Examples of Limits That Do Not Look Right (c or u chart), cont. ? If more than 1/3 of the data points are outside the limits, the chart ―doesn‘t look right‖ ? Whenever the counts 50, ask yourself if the data really fits a Poisson distribution ?If the assumption that the counts are ―rare‖ does not hold—the data are not Poisson ? In that case, use an individuals chart instead of a c or u chart Control Charts For Continuous Data (X, R Charts) 76 Control Charts and Data Types (XBar amp。 Stat Control Chart U 2. Modify features of the chart: Tests Perform all four tests Options ?Symbol Attributes?...Solid Circle Stamp “Date” (Use ―Tick Labels‖ Drop Down Menu Select Use Variables Date) Frame Tick X (?Direction?)..Under ?Positions? Type 1:25/1 If equal opportunities 67 Exercise 7: Construct a u Chart, cont. 3. Interpret the chart: a. What is the average number of defects per shipment? b. What do the control limits represent? c. Are there any special causes? d. What actions do you take? e. How would you use this chart in the future? 68 0 5 1 0 1 5 2 0 2 50123S a m p l e N u m b e rSample CountU C h a r t f o r D e f e c t sU = 1 . 0 6 3U C L = 1 . 9 5 6L C L = 0 . 1 7 0 2Exercise 7: Answers Questions 1 amp。Control Charts for Discrete Data (p, np, c, or u charts) 46 Control Charts and Data Types (p, np, c, or u Charts) Control Chart Type Data Type Individuals chart Continuous or Discrete p chart or np chart Discreteattribute c chart or u chart Discretecount R ,X Con