Basic Analysis and Graphing - SAS

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74 Performing Univariate Analysis Chapter 2 Statistical Details for the Distribution Platform σ = 1 r n r ij i i= 1 j= 1 n j −1 j ( X − X ) where X i 1 = n n j j j= 1 X ij This formula is commonly referred to as the Root Mean Square Error, or RMSE. Table 2.19 Descriptions of Capability Indices and Computational Formulas Index Index Name Formula CP process capability ratio, C p (USL - LSL)/6s where: • USL is the upper spec limit • LSL is the lower spec limit CIs for CP Lower CI on CP Upper CI on CP CP χ 2 α ⁄ 2, n – 1 ------------------------- n – 1 CP χ 2 1 – α ⁄ 2, n – 1 --------------------------------- n – 1 CPK (PPK for AIAG) process capability index, C pk min(CPL, CPU) CIs for CPK See Bissell (1990) Lower CI Ĉ pk 1 – Φ – 1 ( 1 – α ⁄ 2 ) 1 --------------- 2 + 1 2 ------------------- ( n – 1) 9nĈpk Upper CI Ĉ pk 1 + Φ – 1 ( 1 – α ⁄ 2 ) 1 1 --------------- 9nĈpk 2 + ------------------- 2( n – 1) CPM process capability index, C pm min --------------------------------------------------------------------------- ( target – LSL, USL – target) 3 s 2 + ( mean – target) 2 CIs for CPM Lower CI on CPM Upper CI on CPM CPM χ 2 n1 x – Target ----------------------- α ⁄ 2, γ s 2 ------------------ , where γ = ---------------------------------------------------- γ 1 + 2----------------------- x Target 2 s CPM χ 2 1 – α ⁄ 2, γ -------------------------- γ where γ = same as above.
Chapter 2 Performing Univariate Analysis 75 Statistical Details for the Distribution Platform Table 2.19 Descriptions of Capability Indices and Computational Formulas (Continued) Index Index Name Formula CPL CPU process capability ratio of one-sided lower spec process capability ratio of one-sided upper spec (mean - LSL)/3s (USL - mean)/3s • A capability index of 1.33 is considered to be the minimum acceptable. For a normal distribution, this gives an expected number of nonconforming units of about 6 per 100,000. • Exact 100(1 - α)% lower and upper confidence limits for CPL are computed using a generalization of the method of Chou et al. (1990), who point out that the 100(1 - α) lower confidence limit for CPL (denoted by CPLLCL) satisfies the following equation: Pr{ T n – 1 ( δ = 3 n)CPLLCL ≤ 3CPL n} = 1 – α where T n-1 (δ) has a non-central t-distribution with n - 1 degrees of freedom and noncentrality parameter δ. • Exact 100(1 - α)% lower and upper confidence limits for CPU are also computed using a generalization of the method of Chou et al. (1990), who point out that the 100(1 - α) lower confidence limit for CPU (denoted CPULCL) satisfies the following equation: Pr{ T n – 1 ( δ = 3 n)CPULCL ≥ 3CPU n} = 1 – α where T n-1 (δ) has a non-central t-distribution with n - 1 degrees of freedom and noncentrality parameter δ. Note: Because of a lack of supporting research at the time of this writing, computing confidence intervals for capability indices is not recommended, except for cases when the capability indices are based on the standard deviation. • Sigma Quality is defined as the following % outside Sigma Quality = Normal Quantile1 – ---------------------- 100 + 1.5 % above Sigma Quality Above = Normal Quantile1 – ------------------- + 1.5 100 % below Sigma Quality Below = Normal Quantile1 – ------------------- + 1.5 100 For example, if there are 3 defects in n=1,000,000 observations, the formula yields 6.03, or a 6.03 sigma process. The results of the computations of the Sigma Quality Above USL and Sigma Quality Below LSL column values do not sum to the Sigma Quality Total Outside column value because calculating Sigma Quality involves finding normal distribution quantiles, and is therefore not additive.
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USE, DATA OR PROFITS, WHETHER IN AN
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6 Options for Categorical Variables
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8 Nonparametric Bivariate Density R
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10 Example of the Power Option . .
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12 Statistical Details for the Logi
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14 Use Categorical Variables . . .
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16 Control Animation for Dynamic Bu
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18 Launch the Scatterplot Matrix Pl
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Contents Book Conventions. . . . .
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22 Learn about JMP Chapter 1 Book C
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124 Performing Bivariate Analysis C
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126 Performing Bivariate Analysis C
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Contents Overview of Oneway Analysi
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130 Performing Oneway Analysis Chap
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Contents Example of Contingency Ana
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186 Performing Contingency Analysis
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Contents Overview of Logistic Regre
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218 Performing Simple Logistic Regr
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Contents Overview of the Matched Pa
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238 Comparing Paired Data Chapter 8
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Contents Example of Bootstrapping .
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250 Bootstrapping Chapter 9 Example
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252 Bootstrapping Chapter 9 Unstack
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254 Bootstrapping Chapter 9 Analysi
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Contents Overview of Graph Builder
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258 Interactive Data Visualization
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Contents Example of the Chart Platf
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314 Creating Summary Charts Chapter
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340 Creating Overlay Plots Chapter
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354 Creating Three-Dimensional Scat
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Contents Example of a Contour Plot
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374 Creating Contour Plots Chapter
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Contents Example of a Dynamic Bubbl
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384 Creating Bubble Plots Chapter 1
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Contents Overview of Mapping . . .
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406 Creating Maps Chapter 16 Exampl
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418 Creating Maps Chapter 16 Backgr
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450 Creating Parallel Plots Chapter
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Contents Example of a Cell Plot. .
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460 Creating Cell Plots Chapter 18
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Contents Example of Tree Maps . . .
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468 Creating Tree Maps Chapter 19 E
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470 Creating Tree Maps Chapter 19 E
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472 Creating Tree Maps Chapter 19 T
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474 Creating Tree Maps Chapter 19 A
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486 Creating Scatterplot Matrices C
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Contents Example of a Ternary Plot
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496 Creating Ternary Plots Chapter
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504 References Becker, R.A. and Cle
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506 References Dunnett, C.W. (1955)
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508 References Hosmer, D.W. and Lem
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510 References McLachlan, G.J. and
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512 References Robertson, T., Wrigh
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514 References Wadsworth, H. M., St
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516 Index examples 459, 463-464 lau
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518 Index Horizontal option 268, 32
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520 Index Proportion of Densities o
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522 Index examples 467-468, 473-482
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Basic Analysis and Graphing - SAS

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