MATERIALS ENGINEERING CONCEPTS - Materials for Civil and Construction Engineers - page 29

m Population mean

s Population

standard deviation

34.1% 34.1%

2.2% 2.2%

13.6% 13.6%

m 3 sm 2 s m 2 sm 3 s

m s m m s

FIGURE 1.19 A normal distribution .

where n is the sample size. The mean and standard deviation of random
samples are estimates of the mean and standard deviation, respectively, of
the population.

1.6.2 Normal Distribution
The normal distribution is a symmetrical function around the mean, as
shown in Figure 1.19. The normal distribution describes many populations
that occur in nature, research, and industry, including material properties.
The area under the curve between any two values represents the probabili-
ty of occurrence of an event of interest. Expressing the results in terms of
mean and standard deviation, it is possible to determine the probabilities of
an occurrence of an event. For example, the probability of occurrence of an
event between the mean and standard deviation is 68.3%, between the
mean and standard deviations is 95.5%, and between the mean and
standard deviations is 99.7%. If a materials engineer tests 20 specimens of
concrete and determines the average as 22 MPa and the standard deviation
as 3 MPa, the statistics will show that 95.5% of the time the true mean of the
population will be in the range of

; 1

; 2 ; 3

22 ; 1 2 * 3 2 , or 16 to 28 MPa.

1.6.3 Control Charts
Control charts have been used in manufacturing industry and construction
applications to verify that a process is in control. It is important to note that
control charts do not get or keep a process under control; they provide only
a visual warning mechanism to identify when a contractor or material sup-
plier should look for possible problems with the process. Control charts
have many benefits (Burati and Hughes 1990), such as

detect trouble early

■

decrease variability

■

establish process capability

■