Non-Strict hierarchy has one similarity and one non-similarity with strict hierarchies. A non-strict hierarchy has one level in a hierarchy path to be having only one parent level. However, an instance (OR member OR value) in a level could belong to multiple instances in the parent level. In strict hierarchy, an instance in a child level can belong to only one instance in the parent level.
For example- as taken from previous topic on simple hierarchy:Sales executive—>direct Channel--Sales Manager—>Direct Channel-Sales Area manager—>Sales Zone head—>Sales Region head
The above can be made more complex by an example of non-strict and non-covering hierarchy, whereby a sales executive is reporting to direct channel-sales manager (say for sales of certain set of products) and also directly reporting to a direct-channel area manager (for sales of special set of products).
If we have a sales executive working only for a single direct channel- sales manager, it will be called a strict hierarchy. However, if we have a sales executive working for more than one manager, it will be a non-strict hierarchy.
As you go to the additivity of measures chapter within OLAP, you will see that unlike strict and simple hierarchies, you cannot have simple summarization of measures. For example, you cannot have the sales revenue achieved by a sales executive and roll it up through two sales managers he is reporting to. If you do this, you will be double counting.