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© 1997 Prentice-Hall, Inc. S3 - 1 Principles of Operations Management Quality Via Statistical Process Control Chapter S3

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© 1997 Prentice-Hall, Inc. S3 - 2 Learning Objectives n Explain statistical process control n Develop control charts for variables R chart, X chart R chart, X chart n Develop control charts for attributes l P chart, c chart

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© 1997 Prentice-Hall, Inc. S3 - 3 Thinking Challenge In the mid-1980’s, most firms adjusted the process if output varied by ± 3 from average (2,700 defects per million products). In trouble, Motorola decided to use ± 6 . This meant no more than 2 defects per billion products. Should Motorola have followed industry practice, used 6 , or some other standard? © 1995 Corel Corp. AloneGroupClass

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© 1997 Prentice-Hall, Inc. S3 - 4 Statistical Quality Control (SQC) n Uses mathematics (i.e., statistics) n Involves collecting, organizing, & interpreting data n Objective: Regulate product quality n Used to l Control the process as products are produced l Inspect samples of finished products

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© 1997 Prentice-Hall, Inc. S3 - 5 Types of Statistical Quality Control

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© 1997 Prentice-Hall, Inc. S3 - 6 n Characteristics for which you focus on defects n Classify products as either ‘good’ or ‘bad’, or count # defects l e.g., radio works or not n Categorical or discrete random variables Attributes Quality Characteristics n Characteristics that you measure l e.g., weight, length n May be whole number or fractional n Continuous random variables Variables

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© 1997 Prentice-Hall, Inc. S3 - 7 Statistical Process Control (SPC) n Statistical technique used to ensure process is making product to standard n All process are subject to variability l Natural causes: Random variations l Assignable causes: Correctable problems s Machine wear, unskilled workers, poor mat’l n Objective: Identify assignable causes n Uses process control charts

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© 1997 Prentice-Hall, Inc. S3 - 8 Process Control Charts n Graph of sample data plotted over time UCL LCL Assignable Cause Variation Process Average ± 3 Natural Variation

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© 1997 Prentice-Hall, Inc. S3 - 9 Control Chart Purposes n Show changes in data pattern l e.g., trends s Make corrections before process is out of control n Show causes of changes in data l Assignable causes s Data outside control limits or trend in data l Natural causes s Random variations around average

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© 1997 Prentice-Hall, Inc. S3 - 10 Theoretical Basis of Control Charts As sample size gets large enough ( 30)... sampling distribution becomes almost normal regardless of population distribution. Central Limit Theorem

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© 1997 Prentice-Hall, Inc. S3 - 11 Theoretical Basis of Control Charts Properties of normal distribution 99.7% of all X fall within ± 3 X

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© 1997 Prentice-Hall, Inc. S3 - 12 Theoretical Basis of Control Charts 95.5% of all X fall within ± 2 X Properties of normal distribution 99.7% of all X fall within ± 3 X

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© 1997 Prentice-Hall, Inc. S3 - 13 Statistical Process Control Steps

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© 1997 Prentice-Hall, Inc. S3 - 14 Control Chart Types Continuous Numerical Data Categorical or Discrete Numerical Data

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© 1997 Prentice-Hall, Inc. S3 - 15 R Chart n Type of variables control chart l Interval or ratio scaled numerical data n Shows sample ranges over time l Difference between smallest & largest values in inspection sample n Monitors variability in process n Example: Weigh samples of coffee & compute ranges of samples; Plot

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© 1997 Prentice-Hall, Inc. S3 - 16 R Chart Control Limits Sample Range at Time i # Samples From Table S3.1

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© 1997 Prentice-Hall, Inc. S3 - 17 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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© 1997 Prentice-Hall, Inc. S3 - 18 R & X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.32 7.30 + 4.20 + 6.10 + 3.45 + 5.55 5 Sample Mean =

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© 1997 Prentice-Hall, Inc. S3 - 19 R & X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.323.85 7.30 - 3.45 Sample Range = LargestSmallest

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© 1997 Prentice-Hall, Inc. S3 - 20 R & X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.323.85 24.608.707.604.437.626.594.27 35.982.926.204.205.104.883.28 47.205.105.196.804.215.702.99 54.004.505.501.894.464.073.61 610.108.106.505.066.947.345.04 76.775.085.906.909.306.794.22

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© 1997 Prentice-Hall, Inc. S3 - 21 R R R Chart Control Limits Solution From Table S3.1 (n = 5) R k UCLD i i k R 1 4 385427422 7 3894 211438948232.......

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© 1997 Prentice-Hall, Inc. S3 - 22 Partial Table for Control Chart Limits

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© 1997 Prentice-Hall, Inc. S3 - 23 R Chart Control Limits Solution

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© 1997 Prentice-Hall, Inc. S3 - 24 R Chart Control Chart Solution UCL

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© 1997 Prentice-Hall, Inc. S3 - 25 X Chart n Type of variables control chart l Interval or ratio scaled numerical data n Shows sample means over time n Monitors process average n Example: Weigh samples of coffee & compute means of samples; Plot

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© 1997 Prentice-Hall, Inc. S3 - 26 X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i From Table S3.1

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© 1997 Prentice-Hall, Inc. S3 - 27 R & X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange 17.304.206.103.455.555.323.85 24.608.707.604.437.626.594.27 35.982.926.204.205.104.883.28 47.205.105.196.804.215.702.99 54.004.505.501.894.464.073.61 610.108.106.505.066.947.345.04 76.775.085.906.909.306.794.22

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© 1997 Prentice-Hall, Inc. S3 - 28 X Chart Control Limits Solution * From Table S3.1 (n = 5)

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© 1997 Prentice-Hall, Inc. S3 - 29 X Chart Control Chart Solution* UCL LCL

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© 1997 Prentice-Hall, Inc. S3 - 30 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. AloneGroupClass

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© 1997 Prentice-Hall, Inc. S3 - 31 p Chart n Type of attributes control chart l Nominally scaled categorical data s e.g., good-bad n Shows % of nonconforming items n Example: Count # defective chairs & divide by total chairs inspected; Plot l Chair is either defective or not defective

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© 1997 Prentice-Hall, Inc. S3 - 32 c Chart n Type of attributes control chart l Discrete quantitative data n Shows number of nonconformities (defects) in a unit l Unit may be chair, steel sheet, car etc. l Size of unit must be constant n Example: Count # defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot

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© 1997 Prentice-Hall, Inc. S3 - 33 What Is Acceptance Sampling? n Form of quality testing used for incoming materials or finished goods l e.g., purchased material & components n Procedure l Take one or more samples at random from a lot (shipment) of items l Inspect each of the items in the sample l Decide whether to reject the whole lot based on the inspection results

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© 1997 Prentice-Hall, Inc. S3 - 34 What Is an Acceptance Plan? n Set of procedures for inspecting incoming materials or finished goods n Identifies l Type of sample l Sample size (n) l Criteria (c) used to reject or accept a lot n Producer (supplier) & consumer (buyer) must negotiate

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© 1997 Prentice-Hall, Inc. S3 - 35 Producer’s & Consumer’s Risk Producer's risk ( ) Producer's risk ( ) l Probability of rejecting a good lot l Probability of rejecting a lot when fraction defective is AQL n Consumer's risk (ß) l Probability of accepting a bad lot l Probability of accepting a lot when fraction defective is LTPD

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© 1997 Prentice-Hall, Inc. S3 - 36 ConclusionConclusion n Explained statistical process control n Developed control charts for variables R chart, X chart R chart, X chart n Discussed control charts for attributes l P chart, c chart n Explained acceptance sampling l Producer’s & consumer’s risk

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