【正文】 6 562 Follow Along: Construct p Charts (Equal n), cont. Question 7 ? Why is the range of moncause variation so large (almost 40%)? ? Because n = 50 is a relatively small sample for discrete data Question 8 ? (Optional) Suppose n = 150. How does that change the range of moncause variation in the proportions? ? You must remake the p chart with a subgroup size of 150 to find the answer。 2: Minitab output Limits are wider where n is smaller。 longterm data will likely be influenced by special causes as well. Ideally, you want your subgroup to include only shortterm (moncause) variation because limits are calculated from it. S h o rtte rm d a taLong te rm d a t aTi m eYDis trib utio nsLong t e r m d a t aS h o r t t e r m d a t a83 HighVolume Administrative Processes ? Subgroup sampling is used less often in administrative processes, even those that are high volume ? In manufacturing, it is easier to e up with a rational basis for subgroups, since it is usually related to time (items processed closely in time will have been subjected to very similar process conditions) ? In administrative situations, time is not a good basis for selecting subgroups because even in a short time frame, items originate from very different circumstances (legibility of handwriting, plexity of request, attitude of caller, etc.) Are there situations in your business where subgroup sampling makes sense? 84 HighVolume Administrative Processes, cont. ? It is often better to use systematic sampling, such as sampling every 10th unit (phone call, payment, application) and use the data to construct an individuals chart ? The individuals chart is easier to interpret and explain to others ? Changes in process variability (based on subgroups) are usually more meaningful when samples in a subgroup are timerelated ? If you choose to use subgroup sampling and construct an X, R chart, make sure you have a reason for needing the subgroups (usually related to time) 85 Cautions for Subgroups Batches and Subgroups ? Many people equate sampling from ―batched‖ processes with subgroup sampling, but data from batched processes should not be used in an X, R chart. ? Manufacturing processes where items are treated in batches: furnace runs, press loads, chemical baths, lots, etc. ? Items within a batch are treated ―identically‖ and can therefore be expected to show little variation. ? In contrast, the difference between batches may be great—even if the differences are due only to mon causes. ? An X, R chart will calculate limits from the withinbatch differences—this tends to make the limits too narrow and produces many false signals of special causes. ? It‘s better to use an individuals chart for batchtype data. Systematic Causes Hide in Subgroups ? Take care constructing subgroups so that no systematic special cause is found within a subgroup. ? Suppose you sample four machines and one is usually out of alignment. The special cause is systematic. This tends to make the limits too wide. ? Some special causes will not be signaled. 86 Minitab Follow Along: X, R Chart Background: Of interest is the processing time to inspect, clean, and refuel a returned rental car in order to ready it for its next rental at one rental location. Four cars are sampled and their preparation is timed (in minutes) every 3 hours during the month of June to establish a baseline and to monitor the cycle time. Data: c:\BoosterData\ Date Time Sample1 Sample2 Sample3 Sample46/1 89am 13 12 14 196/1 1112am 14 13 17 146/1 23pm 18 13 15 196/1 56pm 8 20 14 156/2 89am 10 10 16 136/2 1112am 17 13 17 136/2 23pm 17 16 16 146/2 56pm 17 12 15 20. . . . . .6/30 89am 15 14 16 166/30 1112am 17 15 19 166/30 23pm 13 19 18 136/30 56pm 22 12 16 1387 Minitab Follow Along: X, R Chart, cont. 1. Make an X, R chart of the average cycle times by subgroups. Stat Control Charts XbarR Select ?Tests‘ Perform All Eight Tests。 low), or different cavities ? Test 7 shows a reduction in variation, which is good. d. What actions will you take? Determine what the special cause is specifically and address that issue. 92 Summary: X, R Charts ? For continuous data ? For highvolume processes where rational subgroups, usually related to time, can be defined and sampled ? Underlying assumption: moncause variation within subgroups is equal to the moncause variation between subgroups ? If this assumption does not hold, the X limits will either be too wide or too narrow ? Think carefully about how the subgroups are chosen and the implications it will have on the assumption ? You can check the assumption by making both the X, R chart and the IMRR chart and paring them Summary: Control Charts 94 Procedure for Using Control Charts 1. Decide what type of control chart to use. ? What type of data are you plotting? ? How is it collected—individually or in subgroups? 2. Construct the control chart (use Minitab). 3. Assess the control limits. ? Do they look ―right?‖ If not, – Try an individuals chart. – Try a transformation. ? Omit special causes from calculation of limits. 4. Interpret the control chart. ? Look for signals of special causes. ? Determine appropriate actions. 5. Maintain the control chart. ? Update the plotted points as they occur. ? Determine appropriate actions immediately. ? Recalculate limits when appropriate (mark ?temporary‘ on control limits until you have enough data points). 95 Summary of Assumptions for Control Charts Distribution Related Control Charts Assumptions Normal distribution Used for Individuals Charts, X, R Charts Data distributed symmetrically around a mean。 A R u