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QQPLOT Statement |
You can use Q-Q plots to estimate shape, location, and scale parameters and to estimate percentiles. If you are working with a normal Q-Q plot, you can also estimate certain capability indices.
You can visually estimate a shape parameter by specifying a list of values for the shape parameter option. A separate plot is displayed for each value, and you can then select the value that linearizes the point pattern. Alternatively, you can request that the plot be created using an estimated shape parameter. See the entries for the distribution options in "Dictionary of Options" for details on specification of shape parameters. Example 10.2 and Example 10.3 illustrate shape parameter estimation with lognormal and Weibull Q-Q plots.
Note that for Q-Q plots requested with the WEIBULL2 option, you can estimate the shape parameter c from a linear pattern using the fact that the slope of the pattern is [1/c]. For an illustration, see Example 10.3.
Table 10.15: Shape Parameter Options for the QQPLOT StatementDistribution Keyword | Mandatory Shape Parameter Option | Range |
BETA | ALPHA=, BETA= | , |
EXPONENTIAL | None | |
GAMMA | ALPHA= | |
LOGNORMAL | SIGMA= | |
NORMAL | None | |
WEIBULL | C=c | c>0 |
WEIBULL2 | None |
Parameters | Linear Pattern | ||||
Distribution | Location | Scale | Shape | Intercept | Slope |
Beta | , | ||||
Exponential | |||||
Gamma | |||||
Lognormal | |||||
Normal | |||||
Weibull (3-parameter) | c | ||||
Weibull (2-parameter) | (known) | c | [1/c] |
You can enhance a Q-Q plot with a diagonal distribution reference line by specifying the parameters that determine the slope and intercept of the line; alternatively, you can request estimates for these parameters. This line is an aid to checking the linearity of the point pattern, and it facilitates parameter estimation. For instance, specifying MU=3 and SIGMA=2 with the NORMAL option requests a line with intercept 3 and slope 2. Specifying SIGMA=1 and C=2 with the WEIBULL2 option requests a line with intercept log(1) = 0 and slope (1/2).
With the LOGNORMAL and WEIBULL2 options, you can specify the slope directly with the SLOPE= option. That is, for the LOGNORMAL option, specifying THETA= and SLOPE=gives the same reference line as specifying THETA=and ZETA=. For the WEIBULL2 option, specifying SIGMA= and SLOPE=[1/(c_{0})] gives the same reference line as specifying SIGMA= and C=c_{0}.
For an example of parameter estimation using a normal Q-Q plot, see "Adding a Distribution Reference Line". Example 10.2 illustrates parameter estimation using a lognormal plot, and Example 10.3 illustrates estimation using two-parameter and three-parameter Weibull plots.
You can also estimate percentiles using probability plots created with the PROBPLOT statement. See Output 9.2.1 for an example.
In particular, one-third the standardized distance between an upper specification limit and the mean is the one-sided capability index CPU.
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