The Evaluation of Uncertainty in Engineering Calculations by Use of Non-Distributional Methods
Authors: Springer F. P. 
Published: December 2007

This paper was prepared for the SPE-European Spring Meeting 1974 of the Society of Petroleum Engineers of AIME, held in Amsterdam, the Netherlands, May 29–30, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Netherland Section of the Society of Petroleum Engineers, P. O. Box 228, The Hague, the Netherlands. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
As an alternative concept to probabilistic approaches to problems of probabilistic approaches to problems of uncertainty the concept of credibility is described. This concept expresses uncertainty in degrees of belief or credibility a particular individual has in certain propositions. The rules for manipulation propositions. The rules for manipulation of credibilities are selective. Major emphasis in decision making is put on extreme outcomes of possible actions. The method is illustrated by reserve calculations, production forecasting and setting-up of cash-flows.

Introduction
The systematic and consistent treatment of decisions under uncertainty with help of probabilistic approaches became prominent in the early sixties. prominent in the early sixties. Especially the findings of Grayson and Kaufmann based upon more or less theoretical work can be considered the starting point of various investigations point of various investigations concerning the application of probabilities in the field of petroleum engineering Nevertheless the idea of using probabilities in this industry goes back probabilities in this industry goes back to the thirties and forties. Grayson drew attention towards drilling decision problems in which probabilities interpreted from a personalistic probabilities interpreted from a personalistic point of view can be applied. This view point of view can be applied. This view holds that probability measures the confidence a particular individual has in the truth of a particular proposition. Following this interpretation one can conclude that all probabilities are known to the person concerned. Holders of this view stress that it is the very nature of probability to deal with decisions under probability to deal with decisions under uncertainty. Probabilities which can be determined by measuring - the so-called objectivistic probabilities - are to be considered as knowledge, and decision problems in which these probabilities problems in which these probabilities can be applied are not decisions under uncertainty as long as repeatability is given. Personalistic probabilities are subjected to the concept of mathematical probability which is commonly ascribed probability which is commonly ascribed to Kolmogoroff.