Random Variables

Many processes have outcomes that cannot be predicted given our current level of knowledge about the process. In such situations statistical analysis can be used to gain knowledge about a process from a set of data. Data is gathered by recording a specific random variable. Statistical analysis provides specific information about that random variable. In reliability engineering the primary random variable is time to failure, the successful operating time interval until a failure occurs.

Statistical analysis is quite useful because data, when gathered, is often hard to understand. Consider a set of data shown in Table A-1. This set of data is a record of failure times for thirty systems. Assume that all thirty systems are installed, commissioned and operating successfully. The units are checked every hour and the total number of hours of successful operating time is incremented. When a particular system fails, the successful operating time is no longer incremented. For example in this data set, system one failed after 96 hours. System two failed after 3091 hours. System thirty failed after a successful operating time interval of 409 hours. A set of data exists, but often the useful information hides inside the data.