Sensitivity analysis

In this section, the performance of the VSSI, VSS, VSI, and FSSI sampling schemes will be calculated and compared with the ANF, ANS, ANI, and AATS measures for the U control chart by using various numerical examples. The values of b, h, n, s, and f that used to calculate the statistical criteria are based on the references in Section 2, which can be referred for more information. The method used for calculating the control limits (UCLi), the warning limits (WLi), and the solution to determine the optimal values of the measures and parameters of the control chart are based on Shojaie-Navokh et al. [15]. In schemes that used two sample sizes (n1, n2), the range for choosing values equal;\(n_{1}=\left(1,\ldots,n_{0}\right)\ ,\ n_{2}=(n_{0},\ldots,50)\)and in schemes that used two sampling intervals (h1, h2), the range for choosing values are\(h_{2}=\left(0.1,\ldots,h_{0}\right)\ ,\ h_{1}=(h_{0},\ldots,8)\). Therefore, after determining the different levels for u0, u+, λ, n0, and h0, the results of calculating the statistical measures for the sampling schemes are presented in Tables 1-12 (Tables 2-12 is given in Appendix of this paper). Also, the values of obtained parameters in each table for the VSSI, VSS, VSI, and FSSI sampling schemes respectively are shown as follows: (n1, n2, h1, h2, WL1, WL2, UCL1, UCL2), (n1, n2, h0, WL1, WL2, UCL1, UCL2), (n0, h1, h2, WL, UCL), (n0, h0, UCL).
Table 1 The results of applying the VSSI sampling scheme when u+=3.2 and λ=0.04