Statistical Process Control Operations Management
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Statistical Process Control Operations Management

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Statistical Process Control Operations Management Statistical Process Control Operations Management Presentation Transcript

  • Statistical Process Control Operations Management Dr. Ron Tibben-Lembke
  • Designed Size 10 11 12 13 14 15 16 17 18 19 20
  • Natural Variation 14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5
  • Theoretical Basis of Control Charts 95.5% of all  X fall within ± 2  Properties of normal distribution
  • Theoretical Basis of Control Charts Properties of normal distribution 99.7% of all  X fall within ± 3 
  • Design Tolerances
    • Design tolerance:
      • Determined by users’ needs
      • UTL -- Upper Tolerance Limit
      • LTL -- Lower Tolerance Limit
      • Eg: specified size +/- 0.005 inches
    • No connection between tolerance and 
      • completely unrelated to natural variation.
  • Process Capability and 6 
    • A “capable” process has UTL and LTL 3 or more standard deviations away from the mean, or 3 σ .
    • 99.7% (or more) of product is acceptable to customers
    LTL UTL 3  6  LTL UTL
  • Process Capability LTL UTL Capable Not Capable LTL UTL LTL UTL LTL UTL
  • Process Capability
    • Specs: 1.5 +/- 0.01
    • Mean: 1.505 Std. Dev. = 0.002
    • Are we in trouble?
  • Process Capability
    • Specs: 1.5 +/- 0.01
      • LTL = 1.5 – 0.01 = 1.49
      • UTL = 1.5 + 0.01 = 1.51
    • Mean: 1.505 Std. Dev. = 0.002
      • LCL = 1.505 - 3*0.002 = 1.499
      • UCL = 1.505 + 0.006 = 1.511
    1.499 1.51 1.49 1.511 Process Specs
  • Capability Index
    • Capability Index (C pk ) will tell the position of the control limits relative to the design specifications.
    • C pk >= 1.0, process is capable
    • C pk < 1.0, process is not capable
  • Process Capability, C pk
    • Tells how well parts produced fit into specs
    Process Specs 3  3  LTL UTL
  • Process Capability
    • Tells how well parts produced fit into specs
    • For our example:
    • C pk = min[ 0.015/.006, 0.005/0.006]
    • C pk = min[2.5,0.833] = 0.833 < 1 Process not capable
  • Process Capability: Re-centered
    • If process were properly centered
    • Specs: 1.5 +/- 0.01
      • LTL = 1.5 – 0.01 = 1.49
      • UTL = 1.5 + 0.01 = 1.51
    • Mean: 1.5 Std. Dev. = 0.002
      • LCL = 1.5 - 3*0.002 = 1.494
      • UCL = 1.5 + 0.006 = 1.506
    1.494 1.51 1.49 1.506 Process Specs
  • If re-centered, it would be Capable 1.494 1.51 1.49 1.506 Process Specs
  • Packaged Goods
    • What are the Tolerance Levels?
    • What we have to do to measure capability?
    • What are the sources of variability?
  • Production Process Make Candy Package Put in big bags Make Candy Make Candy Make Candy Make Candy Make Candy Mix Mix % Candy irregularity Wrong wt. Wrong wt.
  • Processes Involved
    • Candy Manufacturing:
      • Are M&Ms uniform size & weight?
      • Should be easier with plain than peanut
      • Percentage of broken items (probably from printing)
    • Mixing:
      • Is proper color mix in each bag?
    • Individual packages:
      • Are same # put in each package?
      • Is same weight put in each package?
    • Large bags:
      • Are same number of packages put in each bag?
      • Is same weight put in each bag?
  • Your Job
    • Write down package #
      • Weigh package and candies, all together, in grams and ounces
      • Write down weights on form
    • Optional:
      • Open package, count total # candies
      • Count # of each color
      • Write down
      • Eat candies
    • Turn in form and empty complete wrappers for weighing
  •  
  • Peanut Color Mix
    • website
    • Brown 17.7% 20%
    • Yellow 8.2% 20%
    • Red 9.5% 20%
    • Blue 15.4% 20%
    • Orange 26.4% 10%
    • Green 22.7% 10%
    • Class website
    • Brown 12.1% 30%
    • Yellow 14.7% 20%
    • Red 11.4% 20%
    • Blue 19.5% 10%
    • Orange 21.2% 10%
    • Green 21.2% 10%
    Plain Color Mix
  • So who cares?
    • Dept. of Commerce
    • National Institutes of Standards & Technology
    • NIST Handbook 133
    • Fair Packaging and Labeling Act
  • Acceptable?
  •  
  • Package Weight
    • “Not Labeled for Individual Retail Sale”
    • If individual is 18g
    • MAV is 10% = 1.8g
    • Nothing can be below 18g – 1.8g = 16.2g
  • Goal of Control Charts
    • collect and present data visually
    • allow us to see when trend appears
    • see when “out of control” point occurs
  • Process Control Charts
    • Graph of sample data plotted over time
    UCL LCL Process Average ± 3  Time X
  • Process Control Charts
    • Graph of sample data plotted over time
    Assignable Cause Variation Natural Variation UCL LCL Time X
  • Attributes vs. Variables
    • Attributes:
    • Good / bad, works / doesn’t
    • count % bad (P chart)
    • count # defects / item (C chart)
    • Variables:
    • measure length, weight, temperature (x-bar chart)
    • measure variability in length (R chart)
  • p Chart Example
    • You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control (use z = 3)?
    © 1995 Corel Corp.
  • p Chart Hotel Data
    • No. No. Not Day Rooms Ready Proportion
    • 1 200 16 16/200 = .080 2 200 7 .035 3 200 21 .105 4 200 17 .085 5 200 25 .125 6 200 19 .095 7 200 16 .080
  • p Chart Control Limits n n k i i k      1 1400 7 200
  • p Chart Control Limits 16 + 7 +...+ 16 p X n i i k i i k        1 1 121 1400 0864 . n n k i i k      1 1400 7 200
  • p Chart Control Limits # Defective Items in Sample i Sample i Size UCL p z p n p X n p i i k i i k          (1 - p) 1 1
  • p Chart Control Limits # Defective Items in Sample i Sample i Size UCL p z p p) n p X n p i i k i i k           (1 1 1 z = 2 for 95.5% limits; z = 3 for 99.7% limits # Samples n n k i i k    1
  • p Chart Control Limits # Defective Items in Sample i # Samples Sample i Size z = 2 for 95.5% limits; z = 3 for 99.7% limits LCL p z n n k p X n p i i k i i k i i k            1 1 1 and p p) n   (1 UCL p z p p) n p      (1
  • p Chart p      3 0864 3 . p X n i i k i i k        1 1 121 1400 0864 . n n k i i k      1 1400 7 200 16 + 7 +...+ 16 n p p)   (1 200 .0864 * (1-.0864)
  • p Chart   0864 0596 1460 . . . or & .0268 p      3 0864 3 . p X n i i k i i k        1 1 121 1400 0864 . n n k i i k      1 1400 7 200 16 + 7 +...+ 16 n p p)   (1 200 .0864 * (1-.0864)
  • p Chart UCL LCL
  • R Chart
    • Type of variables control chart
      • Interval or ratio scaled numerical data
    • Shows sample ranges over time
      • Difference between smallest & largest values in inspection sample
    • Monitors variability in process
    • Example: Weigh samples of coffee & compute ranges of samples; Plot
    • You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control ?
    Hotel Example
  • Hotel Data
    • Day Delivery Time
    • 1 7.30 4.20 6.10 3.45 5.55 2 4.60 8.70 7.60 4.43 7.62 3 5.98 2.92 6.20 4.20 5.10 4 7.20 5.10 5.19 6.80 4.21 5 4.00 4.50 5.50 1.89 4.46 6 10.10 8.10 6.50 5.06 6.94 7 6.77 5.08 5.90 6.90 9.30
  • R &  X Chart Hotel Data
    • Sample
    • Day Delivery Time Mean Range
    • 1 7.30 4.20 6.10 3.45 5.55 5.32
    7.30 + 4.20 + 6.10 + 3.45 + 5.55 5 Sample Mean =
  • R &  X Chart Hotel Data
    • Sample
    • Day Delivery Time Mean Range
    • 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85
    Largest Smallest 7.30 - 3.45 Sample Range =
  • R &  X Chart Hotel Data
    • Sample
    • Day Delivery Time Mean Range
    • 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22
  • R Chart Control Limits Sample Range at Time i # Samples From Exhibit 6.13
  • Control Chart Limits
  • R Chart Control Limits R R k i i k         1 3 85 4 27 4 22 7 3 894 . . . . 
  • R Chart Solution From 6.13 ( n = 5) R R k UCL D R LCL D R i i k R R                 1 4 3 3 85 4 27 4 22 7 3 894 (2.11) (3.894) 8 232 (0) (3.894) 0 . . . . . 
  • R Chart Solution UCL
  •  X Chart Control Limits UCL X A R X X k X i i k       2 1 Sample Range at Time i # Samples R R k i i k    1
  •  X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i From 6.13
  • Exhibit 6.13 Limits
  • R &  X Chart Hotel Data
    • Sample
    • Day Delivery Time Mean Range
    • 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22
  •  X Chart Control Limits X X k R R k i i k i i k                 1 1 5 32 6 59 6 79 7 5 813 3 85 4 27 4 22 7 3 894 . . . . . . . .  
  •  X Chart Control Limits From 6.13 ( n = 5) X X k R R k UCL X A R i i k i i k X                       1 1 2 5 32 6 59 6 79 7 5 813 3 85 4 27 4 22 7 3 894 5 813 0 58 * 3 894 8 060 . . . . . . . . . . . .  
  •  X Chart Solution From 6.13 ( n = 5) X X k R R k UCL X A R LCL X A R i i k i i k X X                           1 1 2 2 5 32 6 59 6 79 7 5 813 3 85 4 27 4 22 7 3 894 5 813 (0 58) 5 813 (0 58) (3.894) = 3.566 . . . . . . . . . . . .   (3.894) = 8.060
  •  X Chart Solution* 0 2 4 6 8 1 2 3 4 5 6 7  X, Minutes Day UCL LCL
  • Thinking Challenge
    • You’re manager of a 500-room hotel. The hotel owner tells you that it takes too long to deliver luggage to the room (even if the process may be in control). What do you do?
    © 1995 Corel Corp. N
    • Redesign the luggage delivery process
    • Use TQM tools
      • Cause & effect diagrams
      • Process flow charts
      • Pareto charts
    Solution Method People Material Equipment Too Long
  • Dilbert’s View 11/27/06
  • Fortune Story
    • 58 large companies have announced Six Sigma efforts
    • 91% trailed S&P 500 since then, according to Qualpro, (which has its own competing system)
    • July 11, 2006
    • Qualpro’s “Six Problems with Six Sigma”
      • Six sigma novices get “low hanging fruit” “Without years of experience under the guidance of an expert, they will not develop the needed competence”
      • Green belts get advice from people who don’t have experience implementing it
      • Loosely organized methodology doesn’t guarantee results (and they do?)
      • Six Sigma uses simple math – not “Multivariable Testing” (MVT)
      • Six Sigma training for all is expensive, time-consuming
      • Pressure to “do something” – low value projects
  • Six Sigma
    • Narrow focus on improving existing processes
    • Best and Brightest not focused on developing new products
    • Fortune July 11, 2006
    • Can be overly bureaucratic
  • Final Thought
    • Early 1980’s, IBM Canada, (Markham Ont.)
    • Ordered from new supplier in Japan.
    • Acceptable quality level 1.5% defects, a fairly high standard at the time .
    • The Japanese firm sent the order with a few parts packed separately, & the following letter ...
    © 1995 Corel Corp.
  • Final Thought
    • Dear IBM:
    • We don’t know why you want 1.5% defective parts, but for your convenience we have packed them separately.
    • Sincerely,
    © 1995 Corel Corp.