Gathering Data For A Control Chart DCOVA Collect samples from the output of a process over time Each sample is called a subgroup Often subgroups are equally spaced over time For each subgroup calculate a sample statistic associated with a Critical To Quality (CTQ) variable Frequently used sample statistics are: For a categorical CTQ--The proportion non- conforming or the number non-conforming For a numerical CTQ--The mean of the sample and the range of the sample Statistics for Managers Using Microsoft Excel
Statistics for Managers Using Microsoft Excel Gathering Data For A Control Chart Collect samples from the output of a process over time Each sample is called a subgroup Often subgroups are equally spaced over time For each subgroup calculate a sample statistic associated with a Critical To Quality (CTQ) variable Frequently used sample statistics are: For a categorical CTQ -- The proportion nonconforming or the number non-conforming For a numerical CTQ -- The mean of the sample and the range of the sample DCOVA
Control Limits DCOVA Forming the Upper control limit (UCL)and the Lower control limit(LCL): UCL Process Mean 3 Standard Deviations LCL Process Mean-3 Standard Deviations UCL +30 Process Mean -30 -LCL time Statistics for Managers Using Microsoft Excel
Statistics for Managers Using Microsoft Excel Process Mean Control Limits UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL +3σ -3σ time Forming the Upper control limit (UCL) and the Lower control limit (LCL): DCOVA
Control Chart Basics DCOVA Special Cause Variation: Range of unexpected variability UCL Common Cause +30 Variation:range of Process Mean expected variability -30 LCL time UCL Process Mean 3 Standard Deviations LCL Process Mean-3 Standard Deviations Statistics for Managers Using Microsoft Excel
Statistics for Managers Using Microsoft Excel Process Mean Control Chart Basics UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL +3σ -3σ Common Cause Variation: range of expected variability Special Cause Variation: Range of unexpected variability time DCOVA
Process Variability DCOVA Special Cause of Variation: A measurement this far from the process mean is very unlikely if only expected variation is present UCL ±3σ→99.7%of process values Process Mean should be in this range LCL time UCL Process Mean 3 Standard Deviations LCL Process Mean-3 Standard Deviations Statistics for Managers Using Microsoft Excel
Statistics for Managers Using Microsoft Excel Process Mean Process Variability UCL = Process Mean + 3 Standard Deviations LCL = Process Mean – 3 Standard Deviations UCL LCL ±3σ → 99.7% of process values should be in this range time Special Cause of Variation: A measurement this far from the process mean is very unlikely if only expected variation is present DCOVA
Using Control Charts DCOVA Control Charts are used to check for process control Ho:The process is in control i.e.,variation is only due to common causes H,:The process is out of control i.e.,special cause variation exists If the process is found to be out of control, steps should be taken to find and eliminate the special causes of variation Statistics for Managers Using Microsoft Excel
Statistics for Managers Using Microsoft Excel Using Control Charts Control Charts are used to check for process control H0: The process is in control i.e., variation is only due to common causes H1: The process is out of control i.e., special cause variation exists If the process is found to be out of control, steps should be taken to find and eliminate the special causes of variation DCOVA