This preview shows pages 1–11. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Six Sigma Lecture 6 ANALYZE PHASE 2 3 Analyze Phase Road Map n Activities n Identify Potential Root Causes n Reduce List of Potential Root Causes n Confirm Root Cause to Output Relationship n Estimate Impact of Root Causes on Key Outputs n Tools n Cause and Effect Analysis n FMEA n Hypothesis Tests/Conf. Intervals n Simple and Multiple Regression n ANOVA n Components of Variation 4 Hypothesis Testing 5 Normal Distribution n Variable X ~ Normal ( μ , σ 2 ) n Probability=area under the density function curve μ 6 Excel Functions μ t μ b a n P(x≤t) = NORMDIST(t, μ,σ ,true) n t=NORMINV(probability, μ,σ29 n P(a<x≤b) =P(x≤b)P(x≤a) =NORMDIST(b, μ,σ ,true) NORMDIST(a, μ,σ ,true) 7 Desirable features of Normal Distribution n If X~Normal( μ,σ 2 ), then Z=(x μ )/ σ ~ Normal(0,1) n This is the Standard Normal Distribution n Claim: Every problem on an arbitrary normal distribution can be transferred to a problem on the Standard Normal Distribution z P(Z≤z) 8 Translation to Z = Normal(0,1) For an arbitrary X~Normal( μ,σ 2 ): μ t μ b a n P(a≤X≤b) = P[(a μ )/ σ ≤ (X μ )/ σ ≤ (b μ )/ σ ] = P[(a μ )/ σ ≤ Z ≤ (b μ )/ σ ] n P(X≤t) = P[(X μ )/ σ ≤ (t μ )/ σ ] = P[Z≤(t μ )/ σ ] Example: Suppose X~Normal(3,25) P(X≤5) = ? P(2≤X≤5) 9 n Usually μ and σ 2 are unknown, we try to estimate them from random samples n Suppose n=sample size n Let xi=outcome of the ith item in the sample n Assumptions: l E(xi)= μ ; var(xi)= σ 2 l The outcomes of the ith item (xi) and the jth item (xj) are independent l Xbar=(x1+x2+…+xn)/n is the sample average l Then, by properties of random variables E(Xbar)= μ and var(Xbar)= σ 2 /n (Central Limit Theorem) Sampling Distribution 10 Z α/2 α/2 α/2 Confidence Interval for Population Mean n Case 1: σ is known l The (1...
View
Full
Document
This note was uploaded on 03/22/2012 for the course ISE 507 taught by Professor Dessouky during the Fall '10 term at USC.
 Fall '10
 Dessouky

Click to edit the document details