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IENG 486 - Lecture 11

IENG 486 - Lecture 11. Hypothesis Tests to Control Charts. Assignment: . Exam: It was supposed to be a long, difficult exam … I’m assuming that you prepared well … Exam Results … 1 st page of hypothesis tests looks grim. Reading: CH5: 5.3 (already read 5.1-5.2 & 5.4)

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IENG 486 - Lecture 11

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  1. IENG 486 - Lecture 11 Hypothesis Tests to Control Charts IENG 486 Statistical Quality & Process Control

  2. Assignment: • Exam: • It was supposed to be a long, difficult exam … I’m assuming that you prepared well … • Exam Results … 1st page of hypothesis tests looks grim. • Reading: • CH5: 5.3 (already read 5.1-5.2 & 5.4) • Start on CH6: all except 6.3.2 & 6.4 • Homework 4: • Textbook Problems CH5: 9, 11, 13, 23, and 24 IENG 486 Statistical Quality & Process Control

  3. Statistical Quality Control and Improvement Improving Process Capability and Performance Continually Improve the System Characterize Stable Process Capability Head Off Shifts in Location, Spread Time Identify Special Causes - Bad (Remove) Identify Special Causes - Good (Incorporate) Reduce Variability Center the Process LSL 0 USL Process for Statistical Control Of Quality • Removing special causes of variation • Hypothesis Tests • Ishikawa’s Tools • Managing the process with control charts • Process Improvement • Process Stabilization • Confidence in “When to Act” IENG 486 Statistical Quality & Process Control

  4. UCL 0 CL LCL 0 Sample Number 2-Sided Hypothesis Test Sideways Hypothesis Test Shewhart Control Chart  2  2  2  2 Moving from Hypothesis Testing to Control Charts • A control chart is like a sideways hypothesis test • Detects a shift in the process • Heads-off costly errors by detecting trends IENG 486 Statistical Quality & Process Control

  5. Test of Hypothesis • A statistical hypothesis is a statement about the value of a parameter from a probability distribution. • Ex. Test of Hypothesis on the Mean • Say that a process is in-control if its’ mean is m0. • In a test of hypothesis, use a sample of data from the process to see if it has a mean of m0 . • Formally stated: • H0: m = m0 (Process is in-control) • HA: m ≠ m0 (Process is out-of-control) IENG 486 Statistical Quality & Process Control

  6. Test of Hypothesis on Mean (Variance Known) • State the Hypothesis • H0: m = m0 • H1: m ≠ m0 • Take random sample from process and compute appropriate test statistic • Pick a Type I Error level (a) and find the critical value za/2 • Reject H0 if |z0| > za/2 IENG 486 Statistical Quality & Process Control

  7. UCL and LCL are Equivalent to the Test of Hypothesis • Reject H0 if: • Case 1: • Case 2: • For 3-sigma limits za/2 = 3 IENG 486 Statistical Quality & Process Control

  8. Two Types of Errors May Occur When Testing a Hypothesis • Type I Error - a • Reject H0 when we shouldn't • Analogous to false alarm on control chart, i.e., • point lays outside control limits but process is truly in-control • Type II Error -b • Fail to reject H0 when we should • Analogous toinsensitivityof control chart to problems, i.e., • point does not lay outside control limits but process is never-the-less out-of-control IENG 486 Statistical Quality & Process Control

  9. x UCL CL LCL Sample x UCL CL LCL Sample Choice of Control Limits:Trade-off Between Wide or Narrow Control Limits • Moving limits further from the center line • Decreases risk of false alarm, BUT increases risk of insensitivity • Moving limits closer to the center line • Decreases risk of insensitivity, BUT increases risk of false alarm x UCL CL LCL Sample IENG 486 Statistical Quality & Process Control

  10. Consequences of Incorrect Control Limits • NOT GOOD: • A control chart that never finds anything wrong with process, but the process produces bad product • NOT GOOD: • Too many false alarms destroys the operating personnel’s confidence in the control chart, and they stop using it IENG 486 Statistical Quality & Process Control

  11. Differences in Viewpoint Between Test of Hypothesis & Control Charts IENG 486 Statistical Quality & Process Control

  12. Example: Part Dimension • When process in-control, a dimension is normally distributed with mean 30 and std dev 1. Sample size is 5. Find control limits for an x-bar chart with a false alarm rate of 0.0027. • r.v. x - dimension of part • r.v. x - sample mean dimension of part IENG 486 Statistical Quality & Process Control

  13. Distribution of x vs. Distribution of x IENG 486 Statistical Quality & Process Control

  14. Ex. Part DimensionCont'd • Find UCL: • The control limits are: IENG 486 Statistical Quality & Process Control

  15. Ex. Modified Part Limits • Consider an in-control process. A process measurement has mean 30 and std dev 1 and n = 5. • Design a control chart with prob. of false alarm = 0.005 • If the control limits are not 3-Sigma, they are called "probability limits". IENG 486 Statistical Quality & Process Control

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