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Unformatted text preview: ENGR 4045U Quality Control Lecture 5 1 Lessons Learned • Example of frequency distribution and histogram construction • Normal distribution • Definition of statistical inference • Chi squared distribution • Confidence interval • Tdistribution 2 Schedule • Week 3 – Part III: Basic Methods of Statistical Process Control and Capability Analysis. – Chapter 5: Methods and Philosophy of Statistical Process Control. – Chapter 6: Control Charts for Variables. • Week 4 – Chapter 7: Control Charts for Attributes. – Chapter 8: Process and Measurement System Capability Analysis. • Week 5 – Midterm1 3 Review • What is Quality • Methods for Quality Control • Process, Product, Plant Modeling (IDEF0) • Population / Sample • PDSA/PDCA DMAIC • Model Process Quality • Statistical Methods, Mean, Variance, Standard Deviation, Median, Mode • Histogram, Frequency Diagram • Normal Distribution 4 Cumulative Normal Distribution • The cumulative normal distribution is defined as the probability that the normal random variable x is less than or equal to some value (a) • Where (.) is the cumulative distribution function of the standard normal distribution (mean = 0, standard deviation – 1). 5 ) ( 2 1 ) ( 2 ) ( 2 1 a a z P a x P dx e a F a x P a x Example • Tensile strength of paper used to make grocery bags is an important quality characteristic. It is known that the strength say, x is normal distribution with mean = 40 lb/in2 and standard deviation = 2 lb/in2, denoted x ~ N(40,2^2). The purchaser of the bags requires them to have a strength of at least 35 lb/in2. Calculate the probability that bags produced from this paper will meet or exceed the specifications. 6 Solution • The probability that a bag produced from this paper will meet or exceed the specification is: • P{x>=35}=1P{x<=35}=P{z<=(3540)/2} • P{Z<=2.5}= (2.5)=0.0062 • P{x>=35}=1P{x<=35}=10.0062=0.9938 7 Sampling from Normal Distribution • X is a normal distribution with mean and variance 2....
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 Fall '10
 ahmadbarari
 Normal Distribution, Standard Deviation, Frequency

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