Estimation of distance error by fuzzy set theory required for strength determination of HDR (192)Ir brachytherapy sources

Verification of the strength of high dose rate (HDR) (192)Ir brachytherapy sources on receipt from the vendor is an important component of institutional quality assurance program. Either reference air-kerma rate (RAKR) or air-kerma strength (AKS) is the recommended quantity to specify the strength of gamma-emitting brachytherapy sources. The use of Farmer-type cylindrical ionization chamber of sensitive volume 0.6 cm(3) is one of the recommended methods for measuring RAKR of HDR (192)Ir brachytherapy sources. While using the cylindrical chamber method, it is required to determine the positioning error of the ionization chamber with respect to the source which is called the distance error. An attempt has been made to apply the fuzzy set theory to estimate the subjective uncertainty associated with the distance error. A simplified approach of applying this fuzzy set theory has been proposed in the quantification of uncertainty associated with the distance error. In order to express the uncertainty in the framework of fuzzy sets, the uncertainty index was estimated and was found to be within 2.5%, which further indicates that the possibility of error in measuring such distance may be of this order. It is observed that the relative distance l(i) estimated by analytical method and fuzzy set theoretic approach are consistent with each other. The crisp values of l(i) estimated using analytical method lie within the bounds computed using fuzzy set theory. This indicates that l(i) values estimated using analytical methods are within 2.5% uncertainty. This value of uncertainty in distance measurement should be incorporated in the uncertainty budget, while estimating the expanded uncertainty in HDR (192)Ir source strength measurement.