tailieunhanh - The Microguide to Process Modeling in Bpmn 2.0 by MR Tom Debevoise and Rick Geneva_8

Tham khảo tài liệu 'the microguide to process modeling in bpmn by mr tom debevoise and rick geneva_8', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Single-Use Calibration Intervals Calibration Uncertainties As in prediction the data used to fit the process model can also be used to determine the uncertainty of the calibration. Both the variation in the average response and in the new observation of the response value need to be accounted for. This is similar to the uncertainty for the prediction of a new measurement. In fact approximate calibration confidence intervals are actually computed by solving for the predictor variable value in the formulas for prediction interval end points Graybill 1976 . Because the standard deviation of the prediction of a measured response is a function of the predictor variable like the regression function itself the inversion of the prediction interval endpoints is usually messy. However like the inversion of the regression function to obtain estimates of the predictor variable it can be easily solved numerically. The equations to be solved to obtain approximate lower and upper calibration confidence limits are respectively and Confidence Intervals for the Example Applications U - JI 3 I - h _ 2. r. Ởp z I Ũ with - denoting the estimated standard deviation of the prediction of a new measurement. 7 and - are both denoted as functions of the predictor variable here to make it clear that those terms must be written as functions of the unknown value of the predictor variable. The left-hand sides of the two equations above are used as arguments in the root-finding software just as the expression ờ - z 3i is used when computing the estimate of the predictor variable. Confidence intervals for the true predictor variable values associated with the observed values of pressure 178 and voltage 1522 are given in the table below for the Pressure Temperature example and the Thermocouple Calibration example respectively. The approximate confidence limits and estimated values of the predictor variables were obtained numerically in both cases. Example V Lower 95 Confidence Bound .