A manufacturing company produces light bulbs, and they want to assess the quality of their production process. The company randomly selects a sample of 100 light bulbs from a large batch and measures their lifetimes. The mean lifetime of the sample is found to be 1500 hours with a standard deviation of 100 hours.

a) The company has set a specification limit for the light bulbs' lifetime at 1600 hours.

Determine the percentage of light bulbs produced by the company that would be expected to fail to meet this specification.

b) The manufacturing company decides to implement a control chart to monitor the light bulb production process continuously. Briefly explain the concept of a control chart, different types of control charts and discuss their importance in statistical quality control.