By John P. Bentley
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4). 4 + and σE for system of elements described by error bands. /i = Ki -i / = K1K2 . . Ki . . Kn + = / − - [= 0, if K1K2 . . Kn = 1] σ I21 = 0 σ I22 = σO2 1 = h12 3 σ I23 = σO2 2 = K 22σ I22 + 7 7 σ I2i+1 = σO2 i = K 2i σ I2i + 7 h 22 3 h2i 3 7 σ O2 = σO2 n = K 2n σ I2n + h2n 3 σE = σ0 combining n rectangular distributions, each of width 2hi, i = 1, 2, . . , n. If n > 3, then the resultant distribution p(E) approximates to a normal distribution; the larger the value of n the closer the distribution is to normal.
21] where b is any residual zero error and k speciﬁes any residual scale error. There is little point in attempting a polynomial ﬁt at this stage. 8 Computer estimation of measured value using inverse model equation: (a) Principles (b) Example of displacement measurement system. 7. The correlation coefﬁcient: i= n r= 8. 22] between E and O data should now be evaluated. 7] is present and we can proceed to stage 8 to correct for it. 5, then there is no correlation between the E and O data; this means that the errors E are purely random and no correction can be made.
If every element in the system is described in this way, then the mean output value /i will have the ideal value /i = Ki -i + ai for each element in the system. In the special case ai = 0 for all i, /i = Ki -i, the mean value of system output is given by / = K1K2 . . Ki . . Kn and the mean value of error + = / − -. In the special case K1K2 . . Ki . . 4). 4 + and σE for system of elements described by error bands. /i = Ki -i / = K1K2 . . Ki . . Kn + = / − - [= 0, if K1K2 . . Kn = 1] σ I21 = 0 σ I22 = σO2 1 = h12 3 σ I23 = σO2 2 = K 22σ I22 + 7 7 σ I2i+1 = σO2 i = K 2i σ I2i + 7 h 22 3 h2i 3 7 σ O2 = σO2 n = K 2n σ I2n + h2n 3 σE = σ0 combining n rectangular distributions, each of width 2hi, i = 1, 2, .
Principles of measurement systems by John P. Bentley