As an economically superior approach to uniform sampling scheme, the pioneering work of Rahim and Banerjee on sampling procedure with non-uniform time intervals has been broadly employed in statistical process monitoring during the past three decades. However, since its consecutive times of inspection have to be determined through a function of the first sampling interval, it might make some kind of complexity in practical administration compare to uniform approach. In this paper, the intuitive companionship between the sampling frequencies and the failure rate of a process is discussed by investigating various functional costraints on choosing the length of sampling intervals and their effects on the optimal design of control charts, especifically for non-Markovian processes which deteriorate over time. Extensive numerical illustrations are prepared for monitoring both univariate and multivariate quality characteristics in manufacturing and service sectors following an increasing failure rate Weibull shock model. Although the proposed structures for sampling intervals could slightly improve the expected cost per unit time, the results illustrated that Rahim-Banerjee model of non-uniform inspection sheme which induces constant integrated hazard over each sampling interval is a well-established near-optimal approach.