# Control chart exercise.pptx

27 May 2023
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### Control chart exercise.pptx

• 1. Exercise for X bar - R Chart 10.4 13.0 10.4 7.4 6.3 6.1 11.9 9.6 8.2 8.8 10.6 8.6 11.9 11.0 10.0 6.6 8.2 9.5 12.4 9.4 9.6 10.3 8.9 9.1 10.6 11.7 9.4 11.4 10.9 9.3 10.9 9.4 9.1 8.7 11.2 9.7 10.2 9.2 9.8 8.4 9.3 10.5 10.6 8.5 9.5 10.4 10.4 9.8 9.9 5.8 Prepare X bar - R chart using following Xs. Analyze the data and present the same
• 2. X bar - R Chart • Collect the data • Calculate avarage (X bar) and range (R) of each sub-group • X bar = (X1+X2+……+Xn)/n • R = Xhighest - Xlowest Calculate X double bar and R bar X double bar = (X1 bar + X2 bar + ………..+Xn bar) / n R bar = (R1 + R2 +……….+ Rn) / n
• 3. Constants for Control Limits : X bar - R Chart Sub Group Size A2 D4 D3 2 1.880 3.267 0 3 1.023 2.527 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076
• 4. Formula for Control Limits : X bar - R Chart • For Average control chart Upper Control Limit, UCLx = X(Double bar) + A2 x R bar Lower Control Limit, LCLx = X(Double bar) - A2 x R bar • For range control chart Upper Control Limit, UCLr = D4 x R bar Lower Control Limit, LCLr = D3 x R bar
• 5. X Bar - R Charts Draw lines for the following on the control chart X double bar R bar control limits
• 6. 6 PROCESS CAPABILTY RATIOS SPC Cp & Cpk are two key measures of process capability Cp = USL – LSL ie Total Tolerance 6 Sigma Process Spread Cpk = Min X bar - LSL , USL – X bar Cpk accounts for process centering and spread 3 sigma 3 sigma Cpk will always be equal to or less than Cp Standard Deviation, Sigma = R bar/ d2 d2 is a constant varying by sample size, n 2 3 4 5 6 7 8 9 10 d2 1.13 1.69 2.06 2.33 2.53 2.70 2.85 2.97 3.08