【正文】 efects 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。 Occurrences are independent Poisson distribution Used for c Charts Probability of occurrence is constant。 you read across the rows to get the four samples in a subgroup 88 Minitab Follow Along: X, R Chart, cont. 0S u b g r o u p 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 01 01 52 0Sample Mean6 / 3 6 / 5 6 / 1 0 6 / 1 2 6 / 1 7 6 / 1 9 6 / 2 4 6 / 2 6D a t e22274444M e a n = 1 5 . 2 2U C L = 1 9 . 7 2L C L = 1 0 . 7 3051 01 5Sample RangeR = 6 . 1 7 0U C L = 1 4 . 0 8L C L = 0X b a r / R C h a r t f o r S a m p l e 1 S a m p l e 489 Follow Along: X, R Chart, cont. 2. Look at Session window output Test Results for Xbar ChartTEST 2. 9 points in a row on same side of center line.Test Failed at points: 49 50 51 TEST 4. 14 points in a row alternating up and down.Test Failed at points: 77 78 79 80 TEST 7. 15 points within 1 sigma of center line (above and below CL).Test Failed at points: 76 Test Results for R Chart90 Follow Along: X, R Chart, cont. 3. Interpret the chart. a. What is the average time of pletion to inspect, clean, and refuel a returned rental car? b. What do the control limits represent? ? X chart ? R chart c. Are there any specialcause signals? d. What actions will you take? 91 Follow Along Answers: X, R Chart, cont. 3. Interpret the chart. a. What is the average time of pletion to inspect, clean, and refuel a returned rental car? min b. What do the control limits represent? ? X chart upper and lower limits of subgroup averages ? R chart upper and lower limits of subgroup ranges c. Are there any specialcause signals? ? Test 2 indicates a shift in the average。 R Chart) Start Type of data ? Equal sample sizes ? Equal opportunity ? p chart p rt np chart rt Individuals chart I i i al rt EWMA chart rt Continuous Yes No Yes Rational Subgroups Discrete Yes No No u chart u rt c chart c rt Do limits look right? Try individuals chart r i i i als chart Need to detect small shifts quickly? Individual measurements or subgroups ? Try transformation to make data normal r tr sformati to make ta rmal Do limits look right? Yes No Either/Or No Yes Individual measurements Occurrences X, R chart , rt Items with attribute Counting items with an attribute or counting occurrences? 78 When to Use X, R Charts ? Though used in both administrative and manufacturing applications, it is the tool of first choice in many manufacturing applications ? Advantages over other charts: ?Subgroups allow for a precise estimate of ―local‖ variability ? Changes in process variability can be distinguished from changes in process average ? Small shifts in process average can be detected 79 X, R Charts X, R Chart Average Transaction Time Each data point on the top chart represents the average of a subgroup. Each corresponding point on the lower chart represents the range within that subgroup. UCL = LCL = X = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 (4 samples each) (minutes) Range within subgroup (minutes) 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 UCL = R = Note:A special cause is signaled on the range chart indicating that one or two of the samples is very different from the 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。 3 p 177。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 Continuous p = proportion c = count 47 Control Charts and Data Types (p, np, c, or u Charts) Start Type of data ? Equal sample sizes ? Equal opportunity ? p chart p rt np chart