Illustrative presentation of some basic concepts of network internal reliability with comments as regards engineering surveys <s> PTS S <s> An approach to internal reliability analysis is presented which, compared to existing approaches, offers further insight into the system responses to observation gross errors. The proposed reliability measures are defined on the diagonal and non-diagonal elements of the modified reliability matrix being an oblique projector. It maps the observations into the least squares residuals, both expressed as multiples of the a priori standard deviations of the observations. The system responses to a single gross error, such as the local, the quasi-global or the global response, are discussed and their consistency with non-correlation case is proved. Also, the reliability criteria interpretable in terms of those responses are proposed. They enable one to evaluate the observation systems with correlated and uncorrelated observations with respect to internal reliability. An attempt is also made to relate the global responses to reliability numbers that are the basis for determining the magnitude of the minimal detectable bias. Some differences of the new reliability measures in relation to existing measures are indicated. A numerical example is provided, showing the reliability analysis for a simulated horizontal network (distances, angles and GPS vectors), with given covariance matrix for GPS-vector components. In addition, a reliability analysis is presented for a simple leveling network being a study case for other authors referred to in this paper. <s> BIB001 </s> Illustrative presentation of some basic concepts of network internal reliability with comments as regards engineering surveys <s> PTS S <s> The concept of minimal detectable bias (MDB) as initiated by Baarda (Publ Geod New Ser 2(5), 1968) and later developed by Wang and Chen (Acta Geodaet et Cartograph Sin Engl Edn 42–51, 1994), Schaffrin (J Eng Surv 123:126–137, 1997), Teunissen (IEEE Aerosp Electron Syst Mag 5(7):35–41, 1990, J Geod 72:236–244 1998, Testing theory: an introduction. Delft University Press, Delft, 2000) and others, refers to the issue of outlier detectability. A supplementation of the concept is proposed for the case of correlated observations contaminated with a single gross error. The supplementation consists mainly of an outlier identifiability index assigned to each individual observation in a network and a mis-identifiability index being the maximum probability of identifying a wrong observation. To those indices there can also be added the MDB multiplying factor to increase the identifiability index to a satisfactory level. As auxiliary measures there are indices of partial identifiability concerning pairs of observations. The indices were derived assuming the generalized outlier identification procedure as in Knight et al. (J Geod. doi: 10.1007/s00190-010-0392-4, 2010), which with one outlier case being assumed is similar to Baarda’s w-test (Baarda in Publ Geod New Ser 2(5), 1968). The following two options of identifiability indices and partial identifiability indices are distinguished: I. the indices related to identification of a contaminated observation within a set of observations suspected of containing a gross error (identifiability), II. the indices related to identification of a contaminated observation within a whole set of observations (pseudo-identifiability). To characterize the proposed approach in the context of the existing solutions of similar topic being the separability testing, the properties of both types of identifiability indices are discussed with reference to the concept of Minimal Separable Bias (Wang and Knight in J Glob Position Syst 11(1):46–57, 2012) and a general approach in Yang et al. (J Geod 87(6):591–604, 2013). Numerical examples are provided to verify the proposed approach. <s> BIB002
with the It is of out or eliability etworks It should be noted that the global index of internal reliability can be termed equivalently the index of unit redundancy, i.e. the redundancy per single observation. We get it immediately, denoting the number of observations by n, the number of model parameters by u and the network defect by d, and expressing the global index of network internal reliability h ( 1 0   h ) as: Hence, the networks of low or high internal reliability can be understood as networks of low unit redundancy or high unit redundancy respectively. To simplify terminology we will be calling them here just low-redundancy and high-redundancy networks. First, the concepts of detection and identification are discussed as a basis for the concepts of detectability and identifiability. Further, the classification of possible types of gross errors is presented. In the present paper use is made of some earlier and the recent publication of the author, devoted to gross errors  BIB001 BIB002 . The presentation does not pretend to be an extensive study of all the properties of gross errors but is confined to those that are decisive for finding the outliers in the phase of data processing. Explanatory role of the paper comes to the fore.