In Hypothesis Testing the null hypothesis will be rejected if the p-value is below a threshold probability level, known as the alpha value. It is possible that the test will give misleading results and the wrong conclusion will be drawn. There are two types of error:
|Type I Error
||The probability of wrongly rejecting the null hypothesis, that is the null hypothesis is correct, at least to the level imposed by the power of the test, but the p-value is never-the-less smaller than the alpha level.
|Type II Error
||The probability of failing to reject the null hypothesis when it is false. That is the alternative hypothesis is correct, but the p-value is never-the-less larger than the alpha level. This is associated with the beta risk.
Note that in Statistical Process Control the p-value is not normally explicitly defined but it is equivalent to a sample plotting inside or outside the control limits of a control chart.