Module 15C

Module 15C - IE 361 Module 15 The Average Run Length...

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IE 361 Module 15 The Average Run Length Concept Reading: Section 3.5 of 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 15 1 / 15
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Quantifying What a Monitoring Scheme Can Be Expected to Do: the ARL Concept The general question addressed here is "How does one quantify the likely performance of a process monitoring scheme?" Once one begins to contemplate alternative schemes for issuing out-of-control signals based on process-monitoring data, the need quickly arises to quantify what a given scheme might be expected to do. For example, what are the pros and cons of adding the Western Electric set of alarm rules to a control charting scheme? The most e/ective means known for making this kind of prediction is the "Average Run Length" (ARL) notion. Vardeman and Morris (Iowa State University) IE 361 Module 15 2 ± 15
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The ARL It is useful to adopt the notation T = T is called the (random) run length for the scheme. The probability distribution of T is called the run length distribution , and the mean or average value of this distribution is called the Average Run Length (ARL) for the process-monitoring scheme. That is, ARL = μ T When one is setting up a process monitoring scheme, it is desirable that it produce a large ARL when the process is stable at standard values for process parameters and small ARLs under other conditions. Vardeman and Morris (Iowa State University) IE 361 Module 15 3 / 15
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The ARL (the Simplest Case) Evaluating ARLs is not usually elementary. But there is one circumstance where an explicit formula for ARLs is possible and we can illustrate the meaning and usefulness of the ARL concept in elementary terms. That is the situation where
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The ARL Example 15-1 (Some ARLs for Shewhart x-bar Charts) x chart based on samples of size n = 5. If standard values for the process mean and standard deviation are respectively μ and σ , the relevant control limits are
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Module 15C - IE 361 Module 15 The Average Run Length...

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