# 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 σ μ = = deviation Standard Mean The sample deviation Standard of mean Mean n x x x σ σ μ = = = = = 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 μ and σ (from past experience, we use them to compute the sample mean and standard deviation If we do not know μ and/or σ , 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 σ 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 σ with Known μ Is the process under control with respect to a 3-sigma control limits, If we know the that process has μ =12.1 and σ = 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 σ σ μ μ LCL UCL-3 σ x +3 σ x 07 . 12 01 . 3 1 . 12- = ×- = = x z x LCL σ 13 . 12 01 . 3 1 . 12 = × + = + = x z x UCL σ All are within the limits. The process is in-control! x Slide 7 Mean Control Chart – Using σ with Unknown μ Is the process under control with respect to a 3-sigma control limits, If don ’ t know the process mean, and σ = 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 σ 14 . 12 01 . 3 11 . 12 = × + = + = x z x UCL σ LCL UCL-3 σ x +3 σ 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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