These data define an envelope that contains the expected range of data based on historical information. By statistically analyzing these data we can compute the central line and a set of control limits for the type of control chart that is appropriate for the data being analyzed: p chart, np chart, c chart, or u chart.
The CMMI definition of PPM is a description of the relationships among attributes of a process and its work products that are developed from historical process-performance data and calibrated using collected process and product measures from the project and that are used to predict results to be achieved by following a process. So by further analyzing the historical data, it is possible to derive PPMs that can be used to predict future process performance based on current process performance. The model may be as simple as merely extrapolating a straight line, or as sophisticated as running Monte Carlo simulations of the process if your model is based on a number of independent variables. Going back to the hurricane analogy there are a number of predictive hurricane models that the weather service uses to predict the ground track of the eye and where it might make landfall. Whereas the hurricane PPB is based on the statistics of ground track data from past hurricanes, the hurricane PPMs use that information plus additional parameters such as speed, barometric pressure, other nearby weather systems, high pressures, and fronts to predict the storm’s ground track. Every time there is a new set of storm data collected, the meteorologists revise their predictions by running the data through the PPMs. In addition, like the hurricane example, you may have more than one PPM because of the inherent complexity of the process you are trying to model. Sometimes the models agree fairly closely, as in the example shown. Other times there may be a big variance.
So, to answer your question, the PPB is the control chart, central line and the two control limits UCL and LCL. When you start plotting the actual data on the control chart, you can use the PPM to predict if the current data will violate the control limits in the future.
To gain a better understanding of a PPM you have to also understand what is meant by dependent and independent variables. In mathematical terms, an independent variable is an input to a function and a dependent variable is an output of the function. Thus if we have a function f(x), then x is the independent variable, and f(x) is the dependent variable. The dependent variable depends on the independent variables; hence the names.
In the design of experiments, independent variables are those whose values are controlled or selected by the person experimenting (experimenter) to determine its relationship to an observed phenomenon (the dependent variable). In such an experiment, an attempt is made to find evidence that the values of the independent variable determine the values of the dependent variable (that which is being measured). The independent variable can be changed as required, and its values do not represent a problem requiring explanation in an analysis, but are taken simply as given. The dependent variable on the other hand, usually cannot be directly controlled.
Controlled variables are also important to identify in experiments. They are the variables that are kept constant to prevent their influence on the effect of the independent variable on the dependent. Every experiment has a controlling variable, and it is necessary to not change it, or the results of the experiment won't be valid.
In other words:
The independent variable answers the question "What do I change?"
The dependent variable answers the question "What do I observe?"
The controlled variable answers the question "What do I keep the same?"
Back to the hurricane analogy, the independent variable is the storm’s current position. The dependent variable is the predicted ground track. The controlled variables are the current storm attributes that are assumed to remain constant for the next period of time between observations.
Therefore, a PPM is a predictive model based on one or more independent variables that can be used to predict an outcome (dependent variable). It is a mathematical model built using empirical process performance data.
In order to build a PPM, you have to use statistical and other analytic techniques to examine the historical data to construct a model that you can use to predict future states. Initially the PPM may not be very accurate. But each time you use a process you should incorporate the resulting process data into the model to improve its accuracy for its next use. A simple example is the estimation model used by the project manager. When first starting to use a project estimation model, the predicted results probably will not be very accurate. But collecting the project estimates and incorporating them into the model, the ability to predict accurately will improve over time.