Dear Vidya,
Assuming that this is a study for process improvement and not for spying on colleagues, my best answer would be to tell you how I would appproach this myself. I would certaintly not start with dealing with this question only from a statistical point of view. I would start with going to the workplace, just observe the area and the operators, and chat with one or two of them. Then it is time to ask yourself a few questions:
1) Can you assume that the mix of percentages between the different tasks is stabile? For instance, is the operator working on a stabile process or in an ever changing environment? In case of the latter, sampling over longer time does not necessarily make the result better. And are the operators determining what the process does, or does the process determine what the operators do. If the operators determine the process, there can be more differences between operators than in the other case.
2) How many different tasks do you define? Almost every task can be divided into numerous subtasks, but the more tasks you define, the longer it will take before you are finished. It is a good idea to discuss this carefully with whoever ‘required’ you to do this work.
3) What resolution do you need for the proportion of time? Is your client interested in portions of 1%, or 10%, or …..? Without this question you will not know when enough is enough. Again, discuss with the client.
Next step is to start collecting data during a short period, calculate percentages, collect new data in a second short period, recalculate the percentages, and so on. I would start with at least ten samples. Then, make a plot of the sample number on the x-axis and the cumulative percentages on the y-axis.
Just look at the graph, and check if the percentages still show important changes with each new sample “Important” being defined as: judged against the question of how much resolution you need.
-If it doesn’t, it is now a good time to do a formal calculations of the percentages, with their confidence intervals and such. If these are not too large, you can start reporting.
-If changes have a random appearance that are large compared to your desired resolution, there is still too much noise in the data and more samples are needed.
-If changes show a trend, the percentages of time spent are not stabile, which is also usefull information that you can discuss with your client.
I hope this is helpfull for you!
.
