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Chapter Topics Total Quality Management (TQM) Theory of Process Management (Deming’s Fourteen points) The Theory of Control Charts Common Cause Variation Vs Special Cause Variation Control Charts for the Proportion of Nonconforming Items Process Variability Control charts for the Mean and the Range

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Control Charts Monitors Variation in Data –Exhibits Trend - Make Correction Before Process is Out of control Show When Changes in Data Are Due to –Special or Assignable Causes Fluctuations Not Inherent to a Process Represents Problems to be Corrected Data Outside Control Limits or Trend –Chance or Common Causes Inherent Random Variations

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Graph of sample data plotted over time Assignable Cause Variation Random Variation Process Average Mean Process Control Chart UCL LCL

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Control Limits UCL = Process Average + 3 Standard Deviations LCL = Process Average - 3 Standard Deviations Process Average UCL LCL X + 3 - 3 TIME

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Types of Error First Type: Belief that Observed Value Represents Special Cause When in Fact it is Due to Common Cause Second Type: Treating Special Cause Variation as if it is Common Cause Variation

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Comparing Control Chart Patterns XXX Common Cause Variation: No Points Outside Control Limit Special Cause Variation: 2 Points Outside Control Limit Downward Pattern: No Points Outside Control Limit

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When to Take Corrective Action 1. Eight Consecutive Points Above the Center Line (or Eight Below) 2. Eight Consecutive Points that are Increasing (Decreasing) Corrective Action should be Taken When Observing Points Outside the Control Limits or When a Trend Has Been Detected:

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p Chart Control Chart for Proportions Shows Proportion of Nonconforming Items – e.g., Count # defective chairs & divide by total chairs inspected Chair is either defective or not defective Used With Equal or Unequal Sample Sizes Over Time – Unequal sizes should not differ by more than ± 25% from average sample size

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p Chart Control Limits Average Group Size Average Proportion of Nonconforming Items # Defective Items in Sample i Size of Sample i # of Samples LCL p =UCL p = p _

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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?

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p Chart Hotel Data # Not Day# RoomsReadyProportion 1200160.080 2200 70.035 3200210.105 4200170.085 5200250.125 6200190.095 7200160.080

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n n k p X n p i i k i i k i i k 11 1 1400 7 200 121 1400 0864 3 3 1 200 08640596.1460...... or,.0268 p Chart Control Limits Solution 16 + 7 +...+ 16 ( ) ( ) _

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p Chart Control Chart Solution UCL LCL 0.00 0.05 0.10 0.15 1234567 P Day Mean p _

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Variable Control Charts: R Chart Monitors Variability in Process Characteristic of interest is measured on interval or ratio scale. Shows Sample Range Over Time Difference between smallest & largest values in inspection sample e.g., Amount of time required for luggage to be delivered to hotel room

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UCLDR LCLD R R R k R R i i k 4 3 1 R Chart Control Limits Sample Range at Time i # Samples From Table

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R Chart Example 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?

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R Chart & Mean Chart Hotel Data SampleSample DayAverageRange 15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

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R R k UCLD R LCLD R i i k R R 1 4 3 385427422 7 3894 211438948232 038940........ R Chart Control Limits Solution From Table E.9 (n = 5) _

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R Chart Control Chart Solution UCL 0 2 4 6 8 1234567 Minutes Day LCL R _

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Mean Chart (The X Chart) Shows Sample Means Over Time – Compute mean of inspection sample over time – e.g., Average luggage delivery time in hotel Monitors Process Average

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UCL X A R LCLXA R X X k R R k X X i i k i i k 2 2 11 and Mean Chart Sample Range at Time i # Samples Sample Mean at Time i Computed From Table _ _ _ _ _ _ _ _ _ __ _

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Mean Chart Example 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?

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R Chart & Mean Chart Hotel Data SampleSample DayAverageRange 15.323.85 26.594.27 34.883.28 45.702.99 54.073.61 67.345.04 76.794.22

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X X R X R R X k R k UCL A LCLA i i k i i k X X 1 1 2 2 532659679 7 5813 385427422 7 3894 5813057738948060 5813057738943566................ Mean Chart Control Limits Solution From Table E.9 (n = 5) _ _ _ _ __ _ __ _ _ _

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Mean Chart Control Chart Solution UCL LCL 0 2 4 6 8 1234567 Minutes Day X _ _

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Six sigma SIGMAPPM (best case) PPM (worst case) MisspellingsExamples 1 sigma317,400697,700170 words per pageNon-competitive 2 sigma45,600308,73325 words per pageIRS Tax Advice (phone-in) 3 sigma2,70066,8031.5 words per pageDoctors prescription writing (9,000 ppm) 4 sigma646,2001 word per 30 pages (1 per chapter) Industry average 5 sigma0.62331 word in a set of encyclopedias Airline baggage handling (3,000 ppm) 6 sigma0.0023.41 in all of the books in a small library World class

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