Basic Analysis and Graphing - SAS

76 Performing Univariate Analysis Chapter 2
Statistical Details for the Distribution Platform
• Here are the Benchmark Z formulas:
Z USL = (USL-Xbar)/sigma = 3 * CPU
Z LSL = (Xbar-LSL)/sigma = 3 * CPL
Z Bench = Inverse Cumulative Prob(1 - P(LSL) - P(USL))
where:
P(LSL) = Prob(X < LSL) = 1 - Cum Prob(Z LSL)
P(USL) = Prob(X > USL) = 1 - Cum Prob(Z USL).
Statistical Details for Continuous Fit Distributions
Normal
LogNormal
This section contains statistical details for the options in the Continuous Fit menu.
The Normal fitting option estimates the parameters of the normal distribution. The normal distribution is
often used to model measures that are symmetric with most of the values falling in the middle of the curve.
Select the Normal fitting for any set of data and test how well a normal distribution fits your data.
The parameters for the normal distribution are as follows:
• μ (the mean) defines the location of the distribution on the x-axis
• σ (standard deviation) defines the dispersion or spread of the distribution
The standard normal distribution occurs when μ = 0 and σ = 1 . The Parameter Estimates table shows
estimates of μ and σ, with upper and lower 95% confidence limits.
1 ( x – μ) pdf: ----------------- exp –-------------------
2
for ; ; 0 < σ
2πσ 2 2σ 2 – ∞ < x < ∞ – ∞ < μ < ∞
E(x) = μ
Var(x) = σ 2
The LogNormal fitting option estimates the parameters μ (scale) and σ (shape) for the two-parameter
lognormal distribution. A variable Y is lognormal if and only if X = ln( Y)
is normal. The data must be
greater than zero.
–( log( x)
– μ)
2
exp ----------------------------------
1
pdf: --------------
2σ
------------------------------------------------- 2
for 0 ≤ x ; – ∞ < μ < ∞; 0 < σ
σ 2π x
E(x) = exp( μ+
σ 2 ⁄ 2)
Var(x) = exp( 2( μ + σ 2 ))
– exp( 2μ+
σ 2 )