Mathematical Problems in Engineering

Research Article

An Analytical Framework for Error Propagation Effects in Multiprocess Manufacturing

Table 6

Link matrix of error propagation for the example analysis.
Manufacturing featuresk = 1k = 2k = 3k = 4k = 5
MF1[1, 1, 0, 0, 1, 1, X1(0), X1(1)][0, 0, 0, 0, 0, 0, X1(1), X1(2)][0, 0, 0, 0, 0, 0, X1(2), X1(3)][0, 0, 0, 0, 0, 0, X1(3), X1(4)][0, 0, 0, 0, 0, 0, X1(4), X1(5)]
MF2[1, 1, 0, 0, 1, 1, X2(0), X2(1)][0, 0, 0, 0, 0, 0, X2(1), X2(2)][0, 0, 0, 0, 0, 0, X2(2), X2(3)][0, 0, 0, 0, 0, 0, X2(3), X2(4)][0, 0, 0, 0, 0, 0, X2(4), X2(5)]
MF3[0, 0, 0, 0, 0, 0, X3(0), X3(1)][1, 1, 1, X1(1) + X2(1), 1, 1, X3(1), X3(2)][0, 0, 0, 0, 0, 0, X3(2), X3(3)][0, 0, 0, 0, 0, 0, X3(3), X3(4)][0, 0, 0, 0, 0, 0, X3(4), X3(5)]
MF4[0, 0, 0, 0, 0, 0, X4(0), X4(1)][1, 1, 1, X1(1) + X2(1), 1, 1, X4(1), X4(2)][0, 0, 0, 0, 0, 0, X4(2), X4(3)][0, 0, 0, 0, 0, 0, X4(3), X4(4)][0, 0, 0, 0, 0, 0, X4(4), X4(5)]
MF5[0, 0, 0, 0, 0, 0, X5(0), X5(1)][0, 0, 0, 0, 0, 0, X5(1), X5(2)][1, 1, 1, X1(1) + X2(1), 1, 1, X5(2), X5(3)][0, 0, 0, 0, 0, 0, X5(3), X5(4)][0, 0, 0, 0, 0, 0, X5(4), X5(5)]
MF6[0, 0, 0, 0, 0, 0, X6(0), X6(1)][0, 0, 0, 0, 0, 0, X6(1), X6(2)][1, 1, 1, X1(1) + X2(1), 1, 1, X6(2), X6(3)][0, 0, 0, 0, 0, 0, X6(3), X6(4)][0, 0, 0, 0, 0, 0, X6(4), X6(5)]
MF7[0, 0, 0, 0, 0, 0, X7(0), X7(1)][0, 0, 0, 0, 0, 0, X7(1), X7(2)][0, 0, 0, 0, 0, 0, X7(2), X7(3)][1, 1, 1, X2(1) + X4(2) + X6(3), 1, 1, X7(3), X7(4)][0, 0, 0, 0, 0, 0, X7(4), X7(5)]
MF8[0, 0, 0, 0, 0, 0, X8(0), X8(1)][0, 0, 0, 0, 0, 0, X8(1), X8(2)][0, 0, 0, 0, 0, 0, X8(2), X8(3)][1, 1, 1, X2(1) + X4(2) + X6(3), 1, 1, X8(3), X8(4)][0, 0, 0, 0, 0, 0, X8(4), X8(5)]
MF9[0, 0, 0, 0, 0, 0, X9(0), X9(1)][0, 0, 0, 0, 0, 0, X9(1), X9(2)][0, 0, 0, 0, 0, 0, X9(2), X9(3)][0, 0, 0, 0, 0, 0, X9(3), X9(4)][1, 1, 1, X4(2) + X6(3) + X7(4), 1, 1, X9(4), X9(5)]
MF10[0, 0, 0, 0, 0, 0, X10(0), X10(1)][0, 0, 0, 0, 0, 0, X10(1), X10(2)][0, 0, 0, 0, 0, 0, X10(2), X10(3)][0, 0, 0, 0, 0, 0, X10(3), X10(4)][1, 1, 1, X4(2) + X6(3) + X7(4), 1, 1, X10(4), X10(5)]
MF11[0, 0, 0, 0, 0, 0, X11(0), X11(1)][0, 0, 0, 0, 0, 0, X11(1), X11(2)][0, 0, 0, 0, 0, 0, X11(2), X11(3)][0, 0, 0, 0, 0, 0, X11(3), X11(4)][1, 1, 1, X4(2) + X6(3) + X7(4), 1, 1, X11(4), X11(5)]
MF12[0, 0, 0, 0, 0, 0, X12(0), X12(1)][0, 0, 0, 0, 0, 0, X12(1), X12(2)][0, 0, 0, 0, 0, 0, X12(2), X12(3)][0, 0, 0, 0, 0, 0, X12(3), X12(4)][1, 1, 1, X4(2) + X6(3) + X7(4), 1, 1, X12(4), X12(5)]