Dear Mohana,
Analytical skills are just a medium and not an end. What happens when you use these skills is important. Therefore, focus on the end result rather than the medium.
Analytical skills are required to improve quality and productivity, Therefore, if you wish to improve productivity, learn "7 QC Tools For Quality Improvement and Customer Satisfaction". However, merely you learning these tools is not sufficient. Those who are from operations need to learn and implement these tools. Once your organisation is thorough with the implementation of the basic tools, you can upscale to the advanced tools.
If your management is really interested in improving productivity, then nothing beats the implementation of Operations Research techniques. However, the OR techniques are very complex and contain a very high level of mathematics. 99.9% of people are not properly aware of their implementation. As far as a hospital is concerned, I can say that linear programming and the theory of queuing (or the theory of waiting lines) are the two OR techniques that can be used effectively.
Thanks,
Dinesh Divekar