Stratified Sampling

In many cases an improved method of estimating population parameters can be obtain using stratified random sampling [1]. A stratified sample is generated by separating the population into a number of non-overlapping regions, called strata. A simple random sample, as described above, is then selected from each region. Stratified sampling can increase the accuracy of population estimates where the selected strata have less variance than the population as a whole.

The estimator of the whole population mean, ${\mu}$ for a stratified survey is given by the stratified sample average $\overline{y}_{st}$,

$$\hat{\mu}=\overline{y}_{st}=\frac{1}{N}\displaystyle \sum_{ i=1}^{L} N_{i} \overline{y}_{i}$$ (4)

the estimated variance of $\overline{y}_{st}$:

$$\hat{V}(\overline{y}_{st})=\frac{1}{N^2} \displaystyle \sum_{ i=1}^{L} N_{i}^2 \hat{V}(\overline{y}_{i})$$ (5)

where N_i is the population size of the ith of L strata.

This technique can be usefully applied to the estimation of IC device critical areas by dividing up the device into a number regions (strata) for which the critical area is estimated using either simple random sampling or systematic sampling [1]. IC devices are usually made up of circuit blocks for which the defect sensitivity is less variable than the device as a whole. Consequently stratification will nearly always result in a more accurate estimate of total device critical area with smaller bounds on the error of estimation than an equivalent simple random sample.