Gate-Level Circuit Reliability Analysis: A Survey

<table>The relative error of circuit reliability <svg height="15.45" id="M114" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 20.0875 15.45" width="20.0875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117
t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.013,15.187)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
t325.5 101.5q114 0 204 -38z" id="x1D436"></path></g>
</svg> versus the number of simulation runs <svg height="15.4375" id="M115" style="vertical-align:-3.25792pt" version="1.1" viewbox="0 0 34.012501 15.4375" width="34.012501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M857 650l-6 -28q-44 -4 -61.5 -16.5t-29.5 -48.5q-11 -32 -37 -166l-78 -399h-29l-351 537h-4l-56 -276q-24 -120 -24 -164q0 -35 17.5 -46t75.5 -15l-6 -28h-245l7 28q41 2 62 14t31 44q10 30 41 171l53 245q8 44 6.5 60.5t-14.5 33.5q-10 15 -27 19.5t-64 6.5l6 28h153
l350 -516h5l48 257q25 131 25 171q0 34 -17.5 45t-77.5 15l7 28h240z" id="x1D441"></path></g>
<g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><path d="M861 0h-263v28q61 5 73 22t12 97l-4 408h-4l-244 -548h-20l-224 534h-2l-15 -285q-5 -98 -3 -166q1 -34 19.5 -45t72.5 -17v-28h-233v28q45 5 62.5 17t22.5 43q11 65 19 183l14 208q3 36 3.5 55t-2.5 37.5t-6.5 25t-16.5 13t-25.5 8t-39.5 4.5v28h164l228 -501l232 501
h170v-28q-68 -6 -81 -21.5t-11 -91.5l9 -362q2 -80 15 -97t78 -22v-28z" id="x4D"></path></g><g transform="matrix(.012,-0,0,-.012,25.42,15.187)"><path d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207
q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g>
</svg>/<svg height="15.4375" id="M116" style="vertical-align:-3.25792pt" version="1.1" viewbox="0 0 39.762501 15.4375" width="39.762501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M857 650l-6 -28q-44 -4 -61.5 -16.5t-29.5 -48.5q-11 -32 -37 -166l-78 -399h-29l-351 537h-4l-56 -276q-24 -120 -24 -164q0 -35 17.5 -46t75.5 -15l-6 -28h-245l7 28q41 2 62 14t31 44q10 30 41 171l53 245q8 44 6.5 60.5t-14.5 33.5q-10 15 -27 19.5t-64 6.5l6 28h153
l350 -516h5l48 257q25 131 25 171q0 34 -17.5 45t-77.5 15l7 28h240z" id="x1D441"></path></g>
<g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><path d="M409 504l-29 -5q-16 60 -44.5 96t-86.5 36q-54 0 -82.5 -32t-28.5 -77q0 -51 30.5 -82.5t96.5 -65.5l35.5 -18t33 -19.5t33.5 -23.5l27 -25.5t24.5 -32t13.5 -36.5t6 -45q0 -80 -62 -134.5t-160 -54.5q-47 0 -98 15q-22 7 -50 21q-8 23 -27 155l30 7q7 -27 18 -52
t30 -51.5t49 -42.5t67 -16q56 0 88 32.5t32 87.5q0 51 -31.5 82t-98.5 67q-80 44 -110 73q-55 53 -55 124q0 75 56 126.5t150 51.5q53 0 126 -23z" id="x53"></path></g><g transform="matrix(.012,-0,0,-.012,20.565,15.187)"><path d="M614 175l29 -10q-33 -109 -57 -154q-121 -26 -184 -26q-90 0 -160.5 29t-112.5 77t-63.5 105.5t-21.5 119.5q0 157 108 253t277 96q36 0 71.5 -5t69 -13.5t36.5 -8.5q15 -102 20 -150l-29 -8q-20 79 -66.5 114t-128.5 35q-119 0 -187.5 -86t-68.5 -207
q0 -140 73.5 -227.5t188.5 -87.5q73 0 119.5 37.5t86.5 116.5z" id="x43"></path></g><g transform="matrix(.012,-0,0,-.012,28.478,15.187)"><path d="M861 0h-263v28q61 5 73 22t12 97l-4 408h-4l-244 -548h-20l-224 534h-2l-15 -285q-5 -98 -3 -166q1 -34 19.5 -45t72.5 -17v-28h-233v28q45 5 62.5 17t22.5 43q11 65 19 183l14 208q3 36 3.5 55t-2.5 37.5t-6.5 25t-16.5 13t-25.5 8t-39.5 4.5v28h164l228 -501l232 501
h170v-28q-68 -6 -81 -21.5t-11 -91.5l9 -362q2 -80 15 -97t78 -22v-28z" id="x4D"></path></g>
</svg>.</table>

VLSI Design

Gate-Level Circuit Reliability Analysis: A Survey

Figure 5