【正文】 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 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? C P NP U Constant variable Discrete count Discrete attribute Exponentially Weighted Moving Average Chart 48 Exercise 4: Selecting Appropriate Control Chart for Discrete Data Objective: Practice selecting an appropriate control chart to use for discrete data situations. Time: 10 mins. Instructions: Fill in the last column with an appropriate control chart for each situation (p, np, c, or u), using the flowchart. 49 Exercise 4: Selecting Appropriate Control Chart for Discrete Data Type of Chart Predicting hotel occupancy Monitoring plant 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 50 p np c u p np Exercise 4: Answers Type of Chart Predicting hotel occupancy Monitoring plant 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 . 9ProportionJanFebMarAprMayJunJulAugSepOctNovDecJanFebMarAprMayJunJulAug