This simple graph shows the various Weibull Parameters.
Beta is extremely important because it describes the shape of the failure rate curve. The shape determines what asset management strategy is required to improve performance.
Beta values less than one indicate that we have problems with the way we perform maintenance and operating tasks. Root Cause Analysis is required to remove the high beginning failure rate so that the component will seek its natural failure mechanism. Time based replacement strategies on these will only lead to more failures.
Beta equal to one indicates random failures that have a constant failure rate. Time based replacement will not change the failure rate so we have to either monitor the components condition or allow it to run to failure. We may need a component with higher reliability if we can't achieve a desirable failure rate otherwise.
Beta greater than one indicates wear-out failures that MAY lend themselves to time based replacement strategies.
Remember, the goal is to manage failure modes in a way that generates the most profit at the least risk for safety, environmental, or operational problems.