Statistics for Environmental Engineers

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Engineering professional societies have invested millions of dollars to develop, validate, and standardize measurement methods. Government agencies have made similar investments. Universities, technical institutes, and industries train engineers, chemists, and technicians in correct measurement techniques. Even so, it is unrealistic to assume that all measurements produced are accurate and precise. Testing machines wear out, technicians come and go, and sometimes they modify the test procedure in small ways. Chemical reagents age and laboratory conditions change; some people who handle the test specimens are careful and others are not. These are just some of the reasons why systematic checks on data quality are needed.


It is the laboratory’s burden to show that measurement accuracy and precision fall consistently within acceptable limits. It is the data user’s obligation to evaluate the quality of the data produced and to insist that the proper quality control checks are done. This chapter reviews how X and Range charts are used to check the accuracy and precision of laboratory measurements. This process is called quality control or quality assurance.


X and Range charts are graphs that show the consistency of the measurement process. Part of their value and appeal is that they are graphical. Their value is enhanced if they can be seen by all lab workers. New data are plotted on the control chart and compared against recent past performance and against the expected (or desired) performance.

Constructing X-Bar and Range Charts


The scheme to be demonstrated is based on multiple copies of prepared control specimens being inserted into the routine work. As a minimum, duplicates (two replicates) are needed. Many labs will work with this minimum number.

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