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Module 17C

Module 17C - IE 361 Module 17 Process Capability Analysis...

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IE 361 Module 17 Process Capability Analysis: Part 1 Reading: Sections 5.1, 5.2 Statistical Quality Assurance Methods for Engineers Prof. Steve Vardeman and Prof. Max Morris Iowa State University Vardeman and Morris (Iowa State University) IE 361 Module 17 1 / 23

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Normal Plotting and Quantiles If (by virtue of process monitoring and wise intervention) one is willing to say that a data set represents a stable process , it may be used to characterize process output. Section 5.1 of SQAME discusses several graphical techniques for summarizing a sample and therefore representing the process that stands behind it. Here we emphasize one of these, so called "normal plotting," a tool for investigating the extent to which a data set (and thus the process that produced it) can be described using a normal distribution. Normal plots are made using so called quantiles . The p quantile (or 100 p th percentile) of a distribution is a number such that a fraction p of the distribution lies to the left and a fraction 1 ± p lies to the right. If one scores at the .8 quantile (80th percentile) on an exam, 80% of those taking the exam had lower marks and 20% had higher marks. Or, since 95% of the standard normal distribution is to the left of 1.645, 1.645 is the .95 quantile of that distribution. We will use the notation Q ( p ) to stand for the p quantile of any distribution. Vardeman and Morris (Iowa State University) IE 361 Module 17 2 / 23
Normal Plots For a data set consisting of n values x 1 x 2 x n ( x i is the i th ll adopt the convention that x i is the p = ( i ² . 5 ) / n quantile of the data set, that is Q data i ² . 5 n ± = x i For Q z ( p ) the standard normal quantile function, a normal plot is then made by plotting ordered pairs Q data i ² . 5 n ± , Q z i ² . 5 n ±± i.e. x i , Q z i ² . 5 n ±± Vardeman and Morris (Iowa State University) IE 361 Module 17 3 / 23

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Normal Plots (Operational Details and Interpretation) Standard normal quantiles Q z ( p ) can be found by locating values of p in the body of a typical cumulative normal probability table and then reading like JMP provide "inverse cumulative probability" functions and "normal plotting" functions that can be used to automate this. This plot allows comparison of data quantiles and (standard) normal ones. A "straight line" normal plot indicates that a data set has the same shape as the normal distributions, and suggests that the process that stands behind the data set can be modeled as producing normally distributed observations. (Section 5.1 of SQAME has a careful discussion of interpretation of such Q - Q plots for those who need a review of this Stat 231 material.) Vardeman and Morris (Iowa State University) IE 361 Module 17 4 / 23
Normal Plots (Example 17-1) Table 5.7 of SQAME contains measured "tongue thickness" for n = 20 steel levers. Below is a normal plot for those data. It shows the largest

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Module 17C - IE 361 Module 17 Process Capability Analysis...

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