Chap09 (3)

# Chap09 (3) - Chapter 9 Cumulative Sum and Exponentially...

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Chapter 9 Cumulative Sum and Exponentially Weighted Moving Average Control Charts

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Introduction Chapters 5 through 7 focused on Shewhart control charts. Major disadvantage of Shewhart control charts is that it only uses the information about the process contained in the last plotted point. Two effective alternatives to the Shewhart control charts are the cumulative sum (cusum) control chart and the exponentially weighted moving average (EWMA) control chart. Especially useful when small shifts are desired to be detected.
Introduction to Statistical Quality Control, 4th Edition 9-1. The Cumulative-Sum Control Chart 9-1.1 Basic Principles: The Cusum Control Chart for Monitoring the Process Mean The cusum chart incorporates all information in the sequence of sample values by plotting the cumulative sums of the deviations of the sample values from a target value. If μ 0 is the target for the process mean, is the average of the jth sample, then the cumulative sum control chart is formed by plotting the quantity μ - = = i 1 j 0 j i ) x ( C j x

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Chapter 9 4 9.1 The Cumulative Sum Control Chart
Chapter 9 5 The Cumulative Sum Control Chart

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9-1.2 The Tabular or Algorithmic Cusum for Monitoring the Process Mean Let x i be the ith observation on the process If the process is in control then Assume σ is known or can be estimated. Accumulate derivations from the target μ 0 above the target with one statistic, C + Accumulate derivations from the target μ 0 below the target with another statistic, C C + and C -- are one-sided upper and lower cusums, respectively. ) , ( N ~ x 0 i σ μ
9-1.2 The Tabular or Algorithmic Cusum for Monitoring the Process Mean The statistics are computed as follows: The Tabular Cusum starting values are K is the reference value (or allowance or slack value ) If either statistic exceed a decision interval H , the process is considered to be out of control. Often taken as a H = 5 σ .

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