Module 11C

# Module 11C - IE 361 Module 11 Shewhart Control Charts for...

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IE 361 Module 11 Shewhart Control Charts for Measurements ("Variables" Data) Reading: Section 3.2, Statistical Quality Assurance Methods for Engineers Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 11 1 / 20

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Shewhart Control Charts for Measurements In this module we consider Shewhart control charts for measurements (or so called "variables data" in old time SQC jargon). As our featured example, we will use the data from an IE 361 Deming drama. These are of the current "brown bag," i.e. had process parameters μ = 5 and σ = 1 . 715 and was approximately normal.) Vardeman and Morris (Iowa State University) IE 361 Module 11 2 / 20
Deming Drama Data Figure: Data from an IE 361 Deming Drama Vardeman and Morris (Iowa State University) IE 361 Module 11 3 / 20

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Charts for Means We introduced the topic of Shewhart control charts in Module 10 using the most famous of all such charts, the ¯ x charts. To review, we saw that the (approximately) normal distribution of ¯ x (with mean μ ¯ x = μ and σ ¯ x = σ / p n ) leads to standards given control limits for ¯ x UCL x = μ + 3 σ p n and LCL x = μ 3 σ p n Further, we saw that in a retrospective situation like that illustrated on panel 3 where sample means ¯ x and sample ranges R are computed, estimates ˆ μ = x and ˆ σ = ¯ R / d 2 can be substituted to produce retrospective control limits for ¯ x UCL x = x + 3 ¯ R d 2 p n and LCL x = x 3 ¯ R d 2 p n Vardeman and Morris (Iowa State University) IE 361 Module 11 4 / 20
Charts for Means (Example 11-1) In fact, it is traditional to set A 2 = 3 d 2 p n and rewrite these retrospective control limits as UCL x = x + A 2 ¯ R and LCL x = x A 2 ¯ R Example 11-1 We saw in Module 10 that (since for the brown bag μ = 5 and σ = 1 . 715) standards given control limits for ¯ x are UCL x = 5 + 3 1 . 715 p 5 = 7 . 3 and LCL x = 5 3 1 . 715 p 5 = 2 . 7 These limits are marked on the ¯ x control chart on panel 3 and we can see that if they had been applied to ¯ x have been detected at sample 16. Vardeman and Morris (Iowa State University) IE 361 Module 11 5 / 20

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Example 11-1 continued The 18 sample means and ranges from panel 3 average to x = 5 . 744 and ¯ R = 4 . 278 So retrospective limits for ¯ x are (since the sample size is n = 5) UCL x = 5 . 744 + . 577 ( 4 . 278 ) = 8 . 21 and LCL x = 5 . 744 . 577 ( 4 . 278 ) = 3 . 28 When these limits are applied retrospectively to the 18 sample means, we see that the last 3 values are outside of these, and there is thus evidence of process instability in the data on panel 3. Vardeman and Morris (Iowa State University)
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Module 11C - IE 361 Module 11 Shewhart Control Charts for...

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