1Process Control ChartsRef. “Engineering Statistics”Robert V. Hogg, and Johannes Ledolter1987 MacMillian Publishing2Process variation3Statistical Control MethodsStrategy:1. Determine Centerline, UCL, and LCL(from past data sampling when process is under control)2. Monitor stability of process3. Alert user of shifts (outside of UCL/LCL)4. Investigate and eliminate causes of shift4Statistical Control MethodsFactors that determine the appropriatesampling frequency:n Stability of process n Potential lossn Cost of sampling inspection5“x-bar charts”Mean and Standard DeviationMean∑==kjjxkx11RAxLCLUCL2, ±=Where, n = sample sizek = number of samplesA2= constant from Table C.1∑==niinxx16“R-charts” Range = high - low∑==kjjRkR11RDUCLRDLCL43==Where, n = sample sizek = number of samplesD3, D4= constants from Table C.1Standard Deviation),,min(),,max(11 nnxxxxR KK −=7Table C.18p-chartProportion of Defects (binary)nkdddpk+++=L21npppLCLUCL)1(3,−±=Where, d = number of defective samplesn = sample sizek = number of samplesNote: LCL is neglected because it is not possible for negative defects9c-chartCount of Defects (in each unit)∑==kiickc11ccLCLUCL 3, ±=Where, c = number of defects per samplek = number of samplesNote: LCL is neglected because it is not possible for a negative number of
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