Author:Jan-Philipp Hofmann,January 2011,Basic Statistics Quality Assurance Corporate,Basic Statistics,Why Statistics Population and Sample Variation and Distribution Normal Distribution Cp / Cpk Brgens, M.; Malerczyk, C.; Emmel, S.: Interaktive Mathematik - Beitrag zum World Mathematical Year 2000. http:/homepages.fh-friedberg.de/mlutz/MatheApplets/index.html,Basic Statistics,Content,Why Statistics Population and Sample Variation and Distribution Normal Distribution Process Capability Index ANOVA Attachments,Basic Statistics,Process Capability Index,Basic Statistics,Process Capability Index,Candy bar-Experiment Divide the candy bar into 3 equal pieces and weigh them,Basic Statistics,Process Capability Index,Candy bar-Experiment Note: Use data to calculate Cp and Cpk manually Compare results with Minitab Sixpack results and interprete,Basic Statistics,Process Capability Index,Pp, Ppk Cp, Cpk,Basic Statistics,Process Capability Index,Cp, Cpk, Pp, and Ppk Capability indices that measure whether a process is capable of meeting specifications by calculating a ratio between the specification limits and the process spread The higher your Cp and Pp values, the more capable your process To calculate Cp and Pp you must know the upper and lower specification limits,Once we know the capability of our process we add the customers requirements This means we set the specification limits in relation to our process window,Basic Statistics,Process Capability Index,Basic Statistics,About 68% of the observations fall within 1 standard deviation from the mean (-1 to +1) About 95% of the observations fall within 2 standard deviations of the mean (-2 to +2) shown by the blue shaded area About 99.7% of the observations would fall within 3 standard deviations of the mean (-3 to +3),Process Capability Index,Tells you how the data are spread in respect to the mean,Basic Statistics,Process Capability Index,Basic Statistics,Process Capability Index,In general the industry considers 1.33 as minimum acceptable value for process capability A value less than 1 indicates that your process variation is wider than the specification limits,Basic Statistics,Process Capability Index,Cp = process capability Distribution in comparison to the specification limits without regarding centering,Basic Statistics,Process Capability Index,Cp does not consider the location of the process mean in relation to the specification limits Calculate Cp (according to the candy bar experiment) USL: 12 LSL: 8 Sigma: ?,Basic Statistics,Process Capability Index,Does your car fit in the garage,Basic Statistics,Process Capability Index,Cpk = (k)ritical process capability Distribution in comparison to the nearest specification limits with regarding the centering,Basic Statistics,Process Capability Index,Cpk, Cpu, and Cpl Cpl how close the process mean is running to the lower specification limit Cpu how close the process mean is running to the upper specification limit Cpk distribution in comparison to the nearest specification limits with regarding the centering,Basic Statistics,Process Capability Index,Cpk is an index which measures how close a process is running to its specification limits in relation to the process spread Cpk is higher only when you are meeting the target Calculate Cpk (according to the candy bar experiment) USL: 12 LSL: 8 Xbar: ? Sigma: ?,Basic Statistics,Process Capability Index,Cpl Cpu not centered It is more likely to produce defective units that violate the upper specification limit.,Cpk = Cpu = Cpl process is centered at the exact midpoint of the specification limits,Cpl Cpu not centered It is more likely to produce defective units that violate the lower specification limit.,Does your car fit in the garage and on which side does it park,Basic Statistics,Process Capability Index,Cpk = CpL = CpU = 2.76,Cpk = min( CpL =0.96, CpU =4.56) = 0.96,Cpk = min( CpL = 4.56, CpU = 0.96) = 0.96,Cpk = min( CpL =0.96, CpU =4.56) = 0.96,Basic Statistics,Process Capability Index,Cpk = CpL = CpU = 0.96,To avoid mistakes, consider all indices along with a graphical summary to draw meaningful conclusions,A disadvantage of the Cpk index is that it only represents one side of the process curve, and tells you nothing about the other extreme. The two graphs display processes with identical Cpk values However, one violates both specification limits, and the other only violates the lower specification limit,Basic Statistics,Process Capability Index,How big is our process capability?,Process not centered,Variation too big,Decrease variation,Center process,Basic Statistics,Process Capability Index,Basic Statistics,Process Capability Index,Within (potential) and overall capability Most capability assessments can be grouped into Within- (Potential) and Overall- capability Within capability ignores differences between subgroups and represents how the process could perform if the shift and drift between subgroups were eliminated Overall capability accounts