## SPM Based on Univariate Techniques

Traditional statistical monitoring techniques for quality control of batch products relied on the use of univariate SPC tools on product quality variables. In this framework, each quality variable is treated as a single independent variable. The SPM techniques used for monitoring a single variable include Shewhart, cumulative sum (CUSUM), moving average (MA), and exponentially weighted moving average (EWMA) charts (Figure 6.1). For end-of-batch product quality control Shewhart and CUSUM charts are useful. MA and EWMA charts use time series data. Consequently, their use with end-of-batch product data is limited. However, they are discussed in this section for the sake of providing an overview of all popular univariate SPM techniques.

### Hypothesis Testing

Often decisions have to be made about populations on the basis of sample information. A statistical hypothesis is an assumption or a guess about the population. It is expressed as a statement about the parameters of the probability distributions of the populations. Procedures that enable decision making whether to accept or reject a hypothesis are called tests of hypotheses. For example, if the equality of the mean of a variable (p) to a value a is to be tested, the hypotheses are:

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