diameter, area, or thickness of pilings. In sampling by attributes, each 

 of the sampled elements is classified as good (acceptable) or bad (defec- 

 tive) after inspection. This type of sampling plan would be used to 

 determine the percentage of piles infested by marine borers or to estimate 

 the number of piles falling within a certain maintenance category. 



Sampling by Variables 



Assuming that the variation of measurements within the critical 

 section of a structural element is purely random, the mean value of n 



measurements x, , x„, x is: 



11 n 



1 n 

 x = ± 5 x, (1) 



n 1=1 x 

 where: , - measurement taken on the ± * element of the sample 



x = mean or average value of all the samples 



n = number of samples 

 and the variance of the sample is 



2 1 n - 2 



(x - x.r (2) 



x n - 1 . , 

 1=1 



where s is the standard deviation of the sample and s 2 is the variance 

 of the sample. 



From the Central Limit Theorem, the error in estimating the mean 

 value of the measurement parameter using a statistical sample rather than 

 the entire population can be estimated from: 



(3) 



where s- is the standard deviation of calculating the mean from the sample 

 size (nj. From this it can be observed that the sampling error is a 

 function of the standard deviation of the sample data and the number of 

 samples . 



Since the standard deviation of the data sample is a function of the 

 deterioration of the facility being inspected, the tolerable sampling 

 error can be controlled only by the number of samples taken. The Central 

 Limit Theorem shows that the distribution of the sample means is normally 

 distributed regardless of the distribution of the population sample. 

 Therefore, the expected error in estimating the mean value of the sample 

 can be predicted by: 



