【正文】 SepOctNovDecM o n t hP C h a r t f o r 3 o r 4 S c o2P = 0 . 7 0 9 2U C L = 0 . 9 0 1 8L C L = 0 . 5 1 6 5Follow Along: Construct p Charts (Equal n), cont. 5. Interpret the chart: a. Are there any special causes? b. What action will you take? Scale is proportion, not count 59 Follow Along: Construct p Charts (Equal n), cont. Question 5: Answers a. There are 8 points below the centerline, a signal of a special cause b. Appropriate action would be to investigate why the proportion of satisfied customers shifted down beginning last spring or summer When investigating special causes, keep in mind the cause may not have occurred at exactly the same points where the signal starts or stops. For instance, a point outside the limits could have been caused by something that happened earlier in time. In this example, the pany must look for a change that occurred sometime after April. 60 Follow Along: Construct p Charts (Equal n), cont. 6. Suppose the pany changed the packaging of the product during the Summer, and this was declared to be the special cause. To obtain limits that reflect only mon cause variation, recalculate the control limits omitting the last 4 data points: CtrlE Select ?Estimate? Type in these row numbers (SeptDec) 61 Follow Along: Construct p Charts (Equal n), cont. 7. Why is the range of moncause variation so large (almost 40%)? 8. (Optional) Suppose n = 150. How does that change the range of moncause variation in the proportions? 1S u b g r o u p 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 40 . 5 00 . 5 50 . 6 00 . 6 50 . 7 00 . 7 50 . 8 00 . 8 50 . 9 00 . 9 5ProportionJanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDecM o n t hP C h a r t f o r 3 o r 4 S c o22P = 0 . 7 3 4U C L = 0 . 9 2 1 5L C L = 0 . 5 4 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。 Stat Control Chart P : Enter subgroup size= 150) ? The range of moncause variation is about 20%—decreased by half because the sample size increased from 50 to 150 checking accounts surveyed each month (.. Increase the ability to detect a change). 63 Caution! Not All Percentages Should Be Plotted on a p Chart Since ―p‖ stands for ―proportion‖ or ―percentage,‖ some people mistakenly assume that any proportion or percentage should be plotted on a p chart. ? However, a p chart is used for only attribute data where both the numerator and denominator are counts (.. plaints/day) ? For proportions derived from continuous data in both the numerator and denominator, use an individuals chart 64 Caution! Not All Percentages Should Be Plotted on a p Chart, cont. Ex a mp l e s o f Pe r c e n t a g e Da t a Ap p r o p r i a t e Ch a r t? % t im e co m p u t e r is d o wn? % p r o d u ct t h a t is sc r a p ( wh e r e b o t hp r o d u ct a n d sc r a p a r e we ig h e d o rm e a su r e d : e . g . , t o n s o f st e e l, f e e t o fp a p e r )? a cc o u n t in g r a t io s su ch a s% e f f icie n cy , %p r o f it, %p r o d u ct ivit y,e t c. ( wh e r e r a t io s a r e b a se d o nvo lu m e , d o lla r s, t im e , e t c. )? I n d ivid u a ls ch a r t? I n d ivid u a ls ch a r t? I n d ivid u a ls ch a r t65 Exercise 7: Construct a u Chart Objective: Use Minitab to construct and interpret a u chart. Time: 10 mins. Data: c:\BoosterData\ Background: A manufacturer of consumer goods samples ining orders each day and counts the number of defects. Unequal opportunities Date Defects Orders Inspected 1/10 3 10 1/11 9 10 1/12 5 5 . . . 2/3 8 12 66 Exercise 7: Construct a u Chart, cont. Instructions: 1. Construct a u chart。 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。 2: Minitab output Limits are wider where n is smaller。 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 Th