Monte carlo simulation design methodology

Claim 1

A method of fabricating a multi-component assembly having components x, y, and z, to within a pre-set tolerance, F(x,y,z), each of said components, x,y,z, having parameters with a distribution of values thereof, said method comprising: a. generating by Monte Carlo simulation over the n individual components of each type, x, y, z, in the sample space, for i=1 to the sample size, n, (1) a mean, (2) a shifted, time variant mean, chosen from the group consisting of: i. the dynamic mean shift, μ.sub.adj =(USL-LSL)/6C.sub.pk, ii. the static mean shift, μ.sub.adj =Nominal+[V(C.sub.p -C.sub.pk)(USL-LSL)]/2C.sub.p where Nominal is the time invariant mean, C pk =C p (1-k), C p =(USL-LSL)/(6 Sigma), k=|Nominal-Mean|/[(USL-LSL)/2], μ adj is the adjusted standard deviation, and USL and LSL are the upper and lower limits of the distribution, V is a shift vector that indicates the direction of the mean shift; and (3) a deviation about the shifted, time variant mean, of each of the parameters of the individual components, x,y,z, between a lower limit thereof and an upper limit thereof, to determine the statistical distributions of the parameters of the ith sets of the individual components, x(i), y(i), and z(i); and b. generating a set of tolerances, F(x, y, z), of the multi-component assemblies by inputting for each individual component in the ith set of individual components, x(i), y(i), z(i), the parameters thereof, and thereafter for the ith assembly determining the fabrication tolerance, F(x(i), y(i), z(n)), of the ith set of individual components, x(i), y(i), and z(i), in the ith individual multi-component assembly based upon combining into the ith assembly said distributed parameters of the ith set of individual components, x(i), y(i), z(i), determined by Monte Carlo simulation, c. incrementing i and repeating steps (a) and (b) for each set of individual components, x(i), y(i), z(i), and each assembly in the sample space; d. thereafter determining the fraction of the tolerances of the set of n multi-component assemblies falling between a lower limit thereof and an upper limit thereof to determine the statistical distribution of the tolerances of the set of multi-component assemblies; and e. redesigning individual components of the multicomponent assembly to increase the fraction of the fabrication fit tolerances of the multi-component assemblies falling between a lower limit thereof and an upper limit thereof; and fabricating the multicomponent assembly.

Claim 2

A method of fabricating a multi-component assembly having components x, y, and z, to within a pre-set tolerance, F(x,y,z), each of said components, x,y,z, having parameters with a distribution of values thereof, said method comprising: a. generating by Monte Carlo simulation over the n individual components of each type, x, y, z, in the sample space, for i=1 to the sample size, n, (1) a mean, (2) a shifted, time variant mean, chosen from the group consisting of: i. the dynamic mean shift, μ.sub.adj =(USL-LSL)/6C.sub.pk, ii. the static mean shift, μ.sub.adj =Nominal+[V(C.sub.p -C.sub.pk)(USL-LSL)]/2C.sub.p where Nominal is the time invariant mean, C pk =C p (1-k), C p =(USL-LSL)/(6 Sigma), k=|Nominal-Mean|/[(USL-LSL)/2], μ adj is the adjusted standard deviation, and USL and LSL are the upper and lower limits of the distribution, V is a shift vector that indicates the direction of the mean shift; and (3) a deviation about the shifted, time variant mean, of each of the parameters of the individual components, x,y,z, between a lower limit thereof and an upper limit thereof, to determine the statistical distributions of the parameters of the ith sets of the individual components, x(i), y(i), and z(i); and b. generating a set of tolerances, F(x, y, z), of the multi-component assemblies by inputting for each individual component in the ith set of individual components, x(i), y(i), z(i), the parameters thereof, and thereafter for the ith assembly determining the fabrication tolerance, F(x(i), y(i), z(n)), of the ith set of individual components, x(i), y(i), and z(i), in the ith individual multi-component assembly based upon combining into the ith assembly said distributed parameters of the ith set of individual components, x(i), y(i), z(i), determined by Monte Carlo simulation, c. incrementing i and repeating steps (a) and (b) for each set of individual components, x(i), y(i), z(i), and each assembly in the sample space; d. thereafter determining the fraction of the tolerances of the set of n multi-component assemblies falling between a lower limit thereof and an upper limit thereof to determine the statistical distribution of the tolerances of the set of multi-component assemblies; and e. redesigning individual components of the multicomponent assembly to increase the fraction of the fabrication fit tolerances of the multi-component assemblies falling between a lower limit thereof and an upper limit thereof; and fabricating the multicomponent assembly.