## Measurement Uncertainties: Physical Parameters and Calibration of InstrumentsThis book fulfills the global need to evaluate measurement results along with the associated uncertainty. In the book, together with the details of uncertainty calculations for many physical parameters, probability distributions and their properties are discussed. Definitions of various terms are given and will help the practicing metrologists to grasp the subject. The book helps to establish international standards for the evaluation of the quality of raw data obtained from various laboratories for interpreting the results of various national metrology institutes in an international inter-comparisons. For the routine calibration of instruments, a new idea for the use of pooled variance is introduced. The uncertainty calculations are explained for (i) independent linear inputs, (ii) non-linear inputs and (iii) correlated inputs. The merits and limitations of the Guide to the Expression of Uncertainty in Measurement (GUM) are discussed. Monte Carlo methods for the derivation of the output distribution from the input distributions are introduced. The Bayesian alternative for calculation of expanded uncertainty is included. A large number of numerical examples is included. |

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### Contents

Some Important Definitions | 1 |

Distribution Functions | 31 |

Other Probability Functions | 53 |

Evaluation of Measurement Data | 75 |

Propagation of Uncertainty | 109 |

Uncertainty and Calibration of Instruments | 131 |

Calculation of Uncertainty | 153 |

Uncertainty in Calibration of a Surface Plate Fitting a Plane | 177 |

### Other editions - View all

Measurement Uncertainties: Physical Parameters and Calibration of Instruments S. V. Gupta No preview available - 2014 |

Measurement Uncertainties: Physical Parameters and Calibration of Instruments S. V. Gupta No preview available - 2012 |

### Common terms and phrases

ˆ ˆ arithmetic mean BIPM buoyancy correction coefficient combined standard uncertainty confidence level coverage factor degrees of freedom diagonal effective degrees equal equation evaluation of uncertainty example expanded uncertainty F-test giving Hence hydrometer independent variable indication input quantities ISO Gum kmax laboratory mass value maximum permissible error measurand measured value Measurement Uncertainties measuring instruments Metrologia normal distribution number of observations obtained OIML parameter pD1 xp pDnP pDnqP pDnX pD1 piston plane pooled variance probability density function probability distribution probability function propagation of uncertainty proving rings pth point q=m p=ng qD1 pD1 qDmP qD1 qDmX random variable rectangular distribution relative uncertainty repeatability S.V. Gupta sample semi-range standard deviation standard uncertainty standard weights statistical Student’s systematic uncertainty taken tank temperature true value Type B evaluation uncertainty components uncertainty due Uncertainty in Calibration uncertainty in measurement under-test zero