PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly; results from the past 30 days are given in the worksheet Mower Test. In addition, many in-process measurements are taken to ensure that manufacturing processes remain in control and can produce according to design specifications. The worksheet Blade Weight shows 350 measurements of blade weights taken from the manufacturing process that produces mower blades during the most recent shift. Elizabeth Burke has asked you to study these data from an analytics perspective. Drawing upon your experience, you have developed a number of questions.
- For the mower test data, what distribution might be appropriate to model the failure of an individual mower?
- What fraction of mowers fails the functional performance test using all the mower test data?
- What is the probability of having x failures in the next 100 mowers tested, for x from 0 to 20?
- What is the average blade weight and how much variability is occurring in the measurements of blade weights?
- Assuming that the data are normal, what is the probability that blade weights from this process will exceed 5.20?
- What is the probability that weights will be less than 4.80?
- What is the actual percent of weights that exceed 5.20 or are less than 4.80 from the data in the worksheet?
- Is the process that makes the blades stable over time? That is, are there any apparent changes in the pattern of the blade weights?
- Could any of the blade weights be considered outliers, which might indicate a problem with the manufacturing process or materials?
- Was the assumption that blade weights are normally distributed justified? What is the best-fitting probability distribution for the data?
Summarize all your findings to these questions in a well-written report.