Purified water is used in one step in the production of a medical device. The water is tested daily for bacteria. The results of 50 days of testing are contained in bacteria .txt. The values are the count of a particular strain of bacteria in a 100 ml sample of water. The process engineers would like to set up a warning limit and an action limit for future testing based on this data. If a sample were to test above the warning limit, then the engineers would be aware of potential system problems, such as a filter that might need changing. An action limit would indicate that the process should be stopped. Although there are regulatory limits on the bacteria level (which all of the samples fell below), the engineers wanted data-based warning and action limits on the bacteria level. They felt that a warning limit which 80% of the data fell below and an action limit which 95% of the data fell below would be reasonable.
(a) The data here are counts, so they are discrete, however, one might try to approximate the distribution with a continuous distribution. What distribution(s) might approximate the distribution of the data? What distribution(s) would not approximate the distribution of this data?
(b) Using quantiles, set up warning and action limits for the engineers.
(c) Examine these limits on a runs chart of the data (it is in the order in which it was collected).
(d) Do you think that the engineers could reduce their sampling from every day to every other day, or once a week? What information should you take into account in making such a decision?