Question 12.62

12.62 Monitoring rare events.

In certain SPC applications, we are concerned with monitoring the occurrence of events that can occur at any point within a continuous interval of time, such as the number of computer operator errors per day or plant injuries per month. However, for highly capable processes, the occurrence of events is rare. As a result, the data will plot as many strings of zeros with an occasional nonzero observation. Under such circumstances, a control chart will be fairly useless. In light of this issue, SPC practitioners monitor the time between successive events—for example, the time between accidental contaminated needle sticks in a health care setting. For this exercise, consider data on the time between fatal commercial airline accidents worldwide between January 1995 and August 2013.11

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  1. Construct an individuals chart for the time-between-fatalities data. If the lower control limit computes to a negative number, set it to 0 because negative data values are not possible. Report the lower and upper control limits. Identify any observations flagged as unusual.
  2. Time-between-events data tend to be non-Normal and most often are positively skewed. Construct a histogram for the fatalities data. Is that the case for these data?
  3. For time-between-events data, transforming the data by raising them to the 0.2777 power often Normalizes the data. Apply this transformation to the time-between-fatalities data, and construct a histogram for the transformed data. Is this histogram consistent with the Normal distribution?
  4. Construct an individuals chart for the transformed data. If the lower control limit computes to a negative number, set it to 0. Report the lower and upper control limits. Identify the points that are flagged as unusual. With what national tragedy are these observations associated? Are all the observations flagged in the transformed data the same as those flagged in part (a)?
  5. Remove the unusual observations found in part (d), and reestimate and report the control limits. What impressions do you have about the time-between-fatalities process when plotted with the revised limits? Is there evidence of improvement or worsening of the process over the almost 10-year time span?