Ch 7 Attribute CC

# Ch 7 Attribute CC - Chapter 7: Quality Control Instructor:...

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1 Chapter 7: Quality Control Instructor : Linda Boyle, University of Washington Industrial and Systems Engineering Civil and Environmental Engineering Chapter 7, Attribute Control Charts

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2 Control Charts Variables Control Charts (Chapter 6) Apply to data that follows a continuous distribution (measurement data). Attributes Control Charts (Chapter 7) These charts are applied to data that follow a discrete distribution (count data, defects). Data that can be categorized or classified (e.g., conforming or non conforming) are known as attribute data.
3 Attribute Control Charts Fraction nonconforming (p and np charts) Nonconformities (c charts) Nonconformities per unit (u charts)

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4 Fraction Nonconforming Control charts for fraction nonconforming are based on what distribution? items of # Total ing nonconform # of
5 The binomial distribution with parameters n 0 and 0 < p < 1, is given by The mean and variance of the binomial distribution are x n x p p x n x p - - = ) 1 ( ) ( ) 1 ( 2 p np np - = = σ μ Fraction Nonconforming

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6 Assume n = number of units of product selected at random D = number of nonconforming units from the sample p = probability of selecting a nonconforming unit from the sample. x = the number of nonconforming parts you are looking for Then: x n x p p x n x D P - - = = ) 1 ( ) ( Fraction Nonconforming
7 The sample fraction nonconforming is given as where is a random variable with mean and variance n D p = ˆ p ˆ n p p p ) 1 ( 2 - = = σ μ Fraction Nonconforming n = the number of samples within “one dot” on the control chart How do we use this in a control chart for fraction nonconforming?

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8 Standard Given If a standard value of p is given, then the control limits for the fraction nonconforming are: n p p p LCL p CL n p p p UCL ) 1 ( 3 ) 1 ( 3 - - = = - + = Control Charts for Fraction Nonconforming
9 No Standard Given If no standard value of p is given, then the control limits for the fraction nonconforming are: n p p p LCL p CL n p p p UCL ) 1 ( 3 ) 1 ( 3 - - = = - + = m p mn D p m i i m i i = = = = 1 1 ˆ where Control Charts for Fraction Nonconforming m is the “number of dots” on your control chart

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10 Control Charts for Fraction Nonconforming Standard Given No Standard Given n p p p LCL p CL n p p p UCL ) 1 ( 3 ) 1 ( 3 - - = = - + = n p p p LCL p CL n p p p UCL ) 1 ( 3 ) 1 ( 3 - - = = - + = n = the number of samples within “one dot” on the control chart
11 Example A process that produces bearing housings is investigated. Ten samples of size 100 are selected. Is this process operating in statistical control? Sample # 1 2 3 4 5 6 7 8 9 10 # Nonconf. 5 2 3 8 4 1 2 6 3 4 Control Charts for Fraction Nonconforming D i

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12 Example n (sample) = 100, m (subgroup) = 10 Sample # 1 2 3 4 5 6 7 8 9 10 # Nonconf. 5 2 3 8 4 1 2 6 3 4 Fraction Nonconf.
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## Ch 7 Attribute CC - Chapter 7: Quality Control Instructor:...

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