In a nuclear reactor, e.g. Advanced Heavy Water Reactor, a large number of neutron flux detectors are used for measurement of core flux based on which different monitoring, control and protection functions are performed. Changes in ambient and operating conditions of these detectors result in deviations from the nominal signals. These deviations, termed as faults, lead to erroneous inferences about the operation of the reactor. In order to ensure that such faults do not hamper the intended functionality, adequate degree of redundancy is provided in the detectors and the signal that deviates considerably from the signals of other detectors is rejected. However, it would be desirable to develop a method to continuously monitor the detectors for occurrence of faults and isolate the faulty reading based on more formal and systematic approach. In addition to occasional faults, there might also be random errors resulting from various sources. This paper aims at detection and isolation of faults in Ion Chambers of Advanced Heavy Water Reactor and minimization of random errors in the signal data with the help of a Data Reconciliation based scheme. This scheme makes use of the process constraint models developed from the multivariate statistical techniques, viz., Principal Component Analysis and Iterative Principal Component Analysis combined with Iterative Measurement Test method of Fault Detection and Isolation. Development of constraint models relies on data from Ion Chambers in the form of current signals from their amplifiers. These signals are functions of the neutron fluxes at their respective locations. Such data were generated for four representative situations of the reactor operation with the help of the mathematical model of the reactor and the amplifier models associated with the Ion Chambers. To these data, various additive biases were applied, subsequently, Data Reconciliation and Fault Detection and Isolation are attempted within the ambit of linear steady-state Data Reconciliation and the results are presented. The study establishes the efficacy of Iterative Principal Component Analysis and Iterative Measurement Test for Data Reconciliation and Fault Detection and Isolation of Ion Chamber signals in a nuclear reactor.