The JMP subdivides the population using improved sources into three groups according to the level of service provided. Improved drinking water sources are those which, by nature of their design and construction, have the potential to deliver safe water. The new ladders build on the established improved/unimproved facility type classification, thereby providing continuity with past monitoring, and introduce new rungs with additional criteria relating to service levels. These have been updated and expanded to facilitate enhanced global monitoring of drinking water, sanitation and hygiene. The JMP service ladders are used to benchmark and compare service levels across countries.
The method used for optimization of the overall desirability function, or of the single desirability function if there is only one response, depends on the factor types. Then the overall desirability is defined as a weighted geometric mean of the individual desirability functions: Denote the scaled importance values by w 1, w 2., w k. The Importance values are scaled so that they sum to 1. If Importance values are defined as part of the Response Limits column property or are defined in the Response Goal window, they are integrated into the overall desirability function. Then the overall desirability function is the geometric mean of the individual desirability functions: The overall desirability for all responses is defined as the geometric mean of the desirability functions for the individual responses.ĭenote the individual desirability functions for k responses by d 1, d 2., d k. When multiple responses are to be optimized, an overall desirability function is constructed and optimized. Desirability Function for Multiple Optimization Because they are not smooth, they do not always work well with JMP’s optimization algorithm. Note: JMP does not use the Derringer and Suich ( 1980) functional forms. This approach to constructing the desirability functions results in good behavior as the desirability values switch between the maximize, target, and minimize values.
The Low and High control points are not allowed to reach all the way to zero or one. You can also construct custom desirability functions using formulas. In particular, you can specify desirability to be lower at the Middle value than at the Low and High values. The None function enables you to specify an arbitrary desirability function.Exponential functions are fit to the tails. The Target function is a piecewise function that is a scale multiple of a normal density on either side of the Middle value (with different curves on each side), which is also piecewise smooth and fit to the control points.The Minimize and Maximize functions are three-part piecewise smooth functions that consist of interpolating cubics between the control points and exponentials in the tails.These points are called control points (Low, Middle, High) and can be used to interactively control the shape of the desirability function. The individual desirability functions that are added to the Prediction Profiler are smooth piecewise functions that pass through three defining points.
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