LECTURE 12

# LECTURE 12 - ENGR 4045U Quality Control Lecture 12 1...

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ENGR 4045U Quality Control Lecture 12 1

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Schedule Week 6 Part IV: Other Statistical Process-Monitoring and Control Techniques. Chapter 9: Cumulative Sum and Exponentially Weighted Moving Average Control Charts. Chapter 10: Other Univariate Statistical Process Monitoring and Control Techniques. Week 7 Chapter 11: Multivariate Process Monitoring and Control. Chapter 12: Engineering Process Control and SPC. 2
Schedule Week 8 Part V: Process Design and Improvement with Designed Experiments. Chapter 13: Factorial and Fractional Experiments for Process Design and Improvements. Week 9 Chapter 14: Process Optimization and Designed Experiments. Week 10 Midterm-2 3

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Multivariate Process Monitoring Bearing has inner (x1) and outer (x2) diameter that both determines the usefulness of the part The process is in control if x1 and x2 fall within their respective control limit, plot the pair of x1, and x2 Probability that either of x1 or x2 exceeds three- sigma = 0.0027 Probability that both exceeds three- sigma=(0.0027)(0.0027)=0.00000729 Probability that both x1 and x2 fall within three sigma = (0.9973)(0.9973)=0.99460729 4
Multivariate Process Monitoring 5

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Multivariate For independent variables: P{all p means plot in control} = There are p variables [x1, x2, …, xp] With mean ’ = [ 1, 2, …, p] Variances and covariances of the random variables in x be in p x p covariance matrix The main diagonal elements of are the variances of the x’s and off-diagonal elements are the covariances. The squared standardized distance from x to is 6 p ) 1 ( 1 ' p ) 1 ( ) ( ) ( 1
Multivariate Normal Probability Density Function Multivariate normal probability density function: Sample mean vector: Sample covariance matrix S: Sample variance on the main diagonal of the matrix S Sample covariances: 7 p j x e f j p ,..., 2 , 1 , ) 2 ( 1 ) ( ) ( ) ( 2 1 2 / 1 2 / n i i n 1 1 ) )( ( 1 1 1 i n i i n S ) )( ( 1 1 ) ( 1 1 1 2 1 2 n i k ik j ij jk n i j ij j x x x x n S x x n S

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Multivariate Normal Distribution 8
Hotelling Control Chart Is multivariate control chart to monitor mean vector of the process, has two types: Subgrouped data Individual data 9 2 T

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Subgroup Data For x1 and x2 as bivariate normal distribution 1, 2 are the mean, 1, 2 are the standard deviations, and covariance between x1 and x2 is 12.
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## This note was uploaded on 10/18/2010 for the course ENGR 3360 taught by Professor Ahmadbarari during the Fall '10 term at UOIT.

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LECTURE 12 - ENGR 4045U Quality Control Lecture 12 1...

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