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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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Presentation on theme: "© 1997 Prentice-Hall, Inc. S3 - 1 Principles of Operations Management Quality Via Statistical Process Control Chapter S3."— Presentation transcript:

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

2 © 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

3 © 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

4 © 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

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

6 © 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

7 © 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

8 © 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

9 © 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

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

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

12 © 1997 Prentice-Hall, Inc. S 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

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

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

15 © 1997 Prentice-Hall, Inc. S 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

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

17 © 1997 Prentice-Hall, Inc. S 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?

18 © 1997 Prentice-Hall, Inc. S R &  X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange Sample Mean =

19 © 1997 Prentice-Hall, Inc. S R &  X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange Sample Range = LargestSmallest

20 © 1997 Prentice-Hall, Inc. S R &  X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange

21 © 1997 Prentice-Hall, Inc. S R R R Chart Control Limits Solution From Table S3.1 (n = 5) R k UCLD i i k R       

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

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

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

25 © 1997 Prentice-Hall, Inc. S  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

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

27 © 1997 Prentice-Hall, Inc. S R &  X Chart Hotel Data Sample Sample DayDelivery TimeMeanRange

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

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

30 © 1997 Prentice-Hall, Inc. S 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

31 © 1997 Prentice-Hall, Inc. S 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

32 © 1997 Prentice-Hall, Inc. S 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

33 © 1997 Prentice-Hall, Inc. S 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

34 © 1997 Prentice-Hall, Inc. S 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

35 © 1997 Prentice-Hall, Inc. S 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

36 © 1997 Prentice-Hall, Inc. S 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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