This thesis is focused on investigating the Selection Function (SF) of the Arcminute Microkelvin Imager (AMI), a dual-array interferometer at Lord’s Bridge, located 8 kilometers away from central Cambridge. AMI observes and studies the Sunyaev- Zel’dovich (SZ) effect of galaxy clusters by using the Large and Small Arrays (LA & SA) in essentially simultaneously observations. The analysis uses a spherically- symmetric Navarro, Frenk and White (NFW) model for non-baryonic matter and a generalised (GNFW) model for gas and is analysed with a Bayesian methodology for parameter estimation. A modified multidimensional Kolmogorov-Smirnov (mK-S) test is used to study the coherence of idealised cluster simulations with two toy models. A frequentist and Bayesian approach are modelled and then analysed with MULTINEST. PROFILE was then used to create simulated AMI observations with varying noise realizations (thermal, cosmic microwave background (CMB) and source confusion) and then analysed with McAdam. A pipeline was developed to allow the application of the mK-S test on the posterior distribution functions (PDFs) and evidences of cluster simulations with varying physical and observational properties such as mass and redshift. This way, the statistical reliability of simulated AMI observations can be investigated. It is possible to extend the mK-S test by implementing additional measurements to constrain the accuracy data which allows the estimation of a AMI SF which is further discussed. A consequence of studying the SF is being able to obtain the interferometric efficiency of AMI by comparing the zero spacing flux to the amplitude of simulated integrated flux densities of different combinations of cluster properties at given lambdas. Contaminating radio sources of varying flux densities, spectral indices, position and size are then introduced to the simulations to extend the robustness of the basic SF analysis. By studying the peak flux density of clusters, it is possible to approximate the SF for that of contaminating sources. The same is applied to the cluster position, moving the primary beam away from the cluster centre to further test AMI’s ability to constrain cluster parameters extending the basic SF. N-body simulations, namely the MUSIC cluster simulation set, are used to analyse the robustness of the mK-S test. MUSIC clusters are generated externally and hence can be analysed as an independent source with AMI using simulated observations by replacing the original PROFILE generated y-maps. With differently generated y-map, it is then possible to apply the mK-S statistic directly onto MUSIC clusters allowing a study specific to a particular parameter set determined by the user much like the SF. For example, it allows one to approximate the mass boundary for cluster detection and better understand the coherence of AMI data with simulations for the AMI parametric model. MUSIC analysis is completed for four different noise injections, namely: all sources, CMB, source confusion and thermal simulations. It is possible to add additional radio sources much like with standardised SF studies with AMI into the observing field. This allows the observing field to simulate a more accurate source environment. Generally, N-body simulations evolve through time (redshift) but with lesser limitations when compared to parametric models. In this case, y-map clusters are specifically created for the purpose of an independent SF to test with AMI simulated observations. These mK-S results are then compared and applied to real AMI observations. SZ measurements of six galaxy clusters from the 400d catalogue are observed and analysed with AMI and then compared to both X-ray and optical data. They are then re-simulated using PROFILE and analysed using the mK-S test to better understand error estimates in a more realistic observing environment. This demonstrates that the simulated clusters, independently generated y-maps and real-life observing robustness of the AMI telescope.