Quality and Reliability Methods - SAS

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106 Cumulative Sum Control Charts Chapter 6 Formulas for CUSUM Charts Two-Sided Cusum Schemes If the cusum scheme is two-sided, the cumulative sum S t plotted for the t th subgroup is S t = S t - 1 +z t for t = 1, 2,..., n. Here S 0 =0, and the term z t is calculated as z t = ( X t – μ 0 ) ⁄ ( σ ⁄ n t ) where X is the t th subgroup average, and n t is the t th t subgroup sample size. If the subgroup samples consist of individual measurements x t , the term z t simplifies to z t = (x t – μ 0 )/σ Since the first equation can be rewritten as S t t t = z i = ( X i – μ 0 ) ⁄ σ Xi i = 1 i = 1 the sequence S t cumulates standardized deviations of the subgroup averages from the target mean μ 0 . In many applications, the subgroup sample sizes n i are constant (n i = n), and the equation for S t can be simplified. S t t = ( 1 ⁄ σ ) X ( X i – μ 0 ) = i = 1 ( n ⁄ σ) ( X i – μ 0 ) i = 1 In some applications, it might be preferable to compute S t as t S t = ( X i – μ 0 ) i = 1 t which is scaled in the same units as the data. In this case, the procedure rescales the V-mask parameters h and k to h' = hσ ⁄ n and k' = kσ ⁄ n , respectively. Some authors use the symbols F for k' and H for h'. If the process is in control and the mean μ is at or near the target μ 0 , the points will not exhibit a trend since positive and negative displacements from μ 0 tend to cancel each other. If μ shifts in the positive direction, the points exhibit an upward trend, and if μ shifts in the negative direction, the points exhibit a downward trend.
Chapter 7 Multivariate Control Charts Quality Control for Multivariate Data Multivariate control charts address process monitoring problems where several related variables are of interest. Figure 7.1 Example of a Multivariate Control Chart
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6 Nelson Rules . . . . . . . . . .
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Chapter 2 Statistical Control Chart
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Chapter 11 Pareto Plots 191 Two-Way
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Chapter 11 Pareto Plots 193 Defect
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Chapter 19 Reliability and Survival
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References Abernethy, Robert B. (19
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References 407 Carroll, R.J., Ruppe
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References 409 Haaland, P.D. (1989)
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References 411 Lawless, J.F. (1982)
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References 413 Nelson, W.B. (2003),
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References 415 Snee, R.D. and Marqu
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Index JMP Quality and Reliability M
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Index 419 Fit SEV 242 Fit Weibull 2
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Index 421 Q Quantiles table 356 R R
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Index 423 Weibull Plot 360 Westgard
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Quality and Reliability Methods - SAS

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