A Central Limit Theorem for Assessing Average Quality

How to describe, reliably and effectively, the quality of a continuous stream is a problem facing many companies in the chemical industry. The average quality estimated from an average of individual test sample values is most useful if its distribution is known or can be estimated. A simple extension of the Central Limit Theorem is given that provides a means of estimating the distribution which, when coupled with the variogram method of variance estimation of Saunders et al. , enables the calculation of probabilities of closeness of lot mean to the nominal value. The result “sits well” with the current emphasis being placed on the importance of “conformance to target”.