As an economically superior approach to uniform sampling scheme‎, the pioneering work of Rahim and ‎Banerjee on sampling procedure with non-uniform 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 constraints on choosing the length of sampling intervals and their effects on the optimal design of control charts‎,‎ ‎specifically for processes which deteriorate over time‎.‎ ‎‎Extensive numerical illustrations are prepared for monitoring univariate and multivariate quality characteristics in manufacturing and service sectors following an increasing failure rate Weibull shock model‎. The results obtained from proposed structures for sampling intervals could slightly improve the expected cost per unit time which illustrate Rahim-Banerjee model inducing constant integrated hazard over each sampling interval is a well-established near-optimal non-uniform approach‎. ‎However, further investigation on the mathematical problem of finding the sampling scheme by which the cost function is optimized ‎would be highly fruitful‎‎‎.