【正文】 ant safety Predicting Process Yield A) Percent occupancy B) Number of rooms occupied A) Percentage of good product B) Number of good units per 100 units sampled Daily Daily Monthly Monthly Weekly Weekly Situation Data Collected Frequency 1. 2. 3. B) Number of recordable injuries per labor hours worked per month A) Number of recordable injuries, when 16,000 hours worked each month 51 Poisson c = counts of occurrence std c = Binomial Situation n items k with attribute p = = proportion with attribute Control Chart std p = Constructing Control Charts for Discrete Data n k n ) p (1 p c P P C C Proportion Count 52 Assumptions of Charts for Discrete Data p (or np) chart assumptions are based on the binomial distribution: ? Two attributes only (., defective vs. nondefective) ? The expected proportion of items with the attribute, is constant (the same) for each sample ? Occurrence of the attribute is independent from item to item c (or u) chart assumptions are based on the Poisson distribution: ? Can count occurrences, but not nonoccurrences ? Probability of an occurrence is relatively rare (less than 10% of the time) ? Occurrences are independent (one does not influence the occurrence of another) 53 Minitab Follow Along: Construct p and np Charts (Equal Sample Sizes) Background: A manufacturer of operating room equipment has been monitoring surgeons‘ satisfaction by phoning a sample of 50 surgeons who use their instruments each month and asking them to rate their satisfaction on a scale of 1 to 4. Data: c:\BoosterData\ Sample Month Sample Size 3or4scores %3or4scores1 Jan 50 39 2 Feb 50 35 3 Mar 50 38 . . . . .24 Dec 50 28 Poor OK Satisfied Very Satisfied 1 2 3 4 54 Minitab Follow Along: Construct p Charts (Equal Sample Sizes), cont. 1. Make a p chart of the proportion of 3 or 4 scores: Stat Control Charts P NOTE: When n?s are unequal, enter the column name where samples sizes are stored When n?s are equal, enter n here (appropriate choice for this data) 55 Follow Along: Construct p Charts (Equal n), cont. Question 1: Minitab Output 0 5 1 0 1 5 2 0 2 50 . 50 . 60 . 70 . 80 . 9S a m p l e N u m b e rProportionP C h a r t f o r 3 o r 4 S c oP = 0 . 7 0 9 2U C L = 0 . 9 0 1 8L C L = 0 . 5 1 6 556 2. Turn on all the special cause signals: CtrlE Tests 3. Change Rule 2 from 9 to 8 points: Stat Control Charts Define Tests Follow Along: Construct p Charts (Equal n), cont. There are only 4 tests because p charts use the binomial, not the Normal, distribution Choose this 57 Follow Along: Construct p Charts (Equal n), cont. 4. Change other features of the chart: Stat Control Chart p a. Stamp “Month” b. Frame Tick X (?Direction?) Under ?Positions? Type 1:25/1 c. Options ?Symbol Attributes?...Solid Circle Use ―Tick Labels‖ Drop Down Menu Select Use Variables Select Month 4. Change other features of the chart: 58 1S u b g r o u p2 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 . 50 . 60 . 70 . 80 . 9ProportionJanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAugSepOctNovDecM 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