L26_SPC - Slide 1 Lecture 26 Statistical Process Control...

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Unformatted text preview: Slide 1 Lecture 26 Statistical Process Control Slide 2 Learning Objectives Construct control charts Interpret mean and range charts Evaluate process capability Slide 3 Control Charts for Variables Slide 4 Samples The process (population) Observations n = 4 Samples = = deviation Standard Mean The sample deviation Standard of mean Mean n x x x = = = = = 1 12.11 12.10 12.11 12.08 12.10 x 2 12.15 12.12 12.10 12.11 12.12 3 12.09 12.09 12.11 12.15 12.11 4 12.12 12.10 12.08 12.10 12.10 5 12.09 12.14 12.13 12.12 12.12 Average To construct the control chart, we need to know the sample mean and sample standard deviation. If we know and (from past experience, we use them to compute the sample mean and standard deviation If we do not know and/or , we need to estimate sample mean and standard deviation from the sample data. 1 2 3 4 Slide 5 Control Charts for Variables Mean control charts Used to monitor the central tendency of a process. ( x- x- bar) charts Two approaches to construct 1. Using the standard deviation 2. Using the sample range R Range control charts Used to monitor the process dispersion R R charts x Slide 6 Mean Control Chart Using with Known Is the process under control with respect to a 3-sigma control limits, If we know the that process has =12.1 and = 0.02 ? Observations n = 4 Samples 1 12.11 12.10 12.11 12.08 12.10 x 2 12.15 12.12 12.10 12.11 12.12 3 12.09 12.09 12.11 12.15 12.11 4 12.12 12.10 12.08 12.10 12.10 5 12.09 12.14 12.13 12.12 12.12 Average 1 2 3 4 3-sigma control limits z = 3 Also, 0.01 4 02 . , 1 . 12 , 4 = = = = = = n x n x LCL UCL-3 x +3 x 07 . 12 01 . 3 1 . 12- = - = = x z x LCL 13 . 12 01 . 3 1 . 12 = + = + = x z x UCL All are within the limits. The process is in-control! x Slide 7 Mean Control Chart Using with Unknown Is the process under control with respect to a 3-sigma control limits, If don t know the process mean, and = 0.02 ? Observations n = 4 Samples 1 12.11 12.10 12.11 12.08 12.10 x 2 12.15 12.12 12.10 12.11 12.12 3 12.09 12.09 12.11 12.15 12.11 4 12.12 12.10 12.08 12.10 12.10 5 12.09 12.14 12.13 12.12 12.12 Average 1 2 3 4 08 . 12 01 . 3 11 . 12- = - = = x z x LCL 14 . 12 01 . 3 11 . 12 = + = + = x z x UCL LCL UCL-3 x +3 x 11 . 12 5 / ) 12 . 12 10 . 12 11 . 12 12 . 12 10 . 12 ( = + + + + = x 3-sigma control limits z = 3 Also, Compute 0.01 4 02 ....
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L26_SPC - Slide 1 Lecture 26 Statistical Process Control...

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