# Multi-Phase - Mixed Data

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*This example appears in the Reliability Growth and Repairable System Analysis Reference*.

A one-shot system underwent reliability growth development for a total of 20 trials. The test was performed as a combination of configuration in groups and individual trial-by-trial. The following table shows the obtained data set. The **Failures in Interval** column specifies the number of failures that occurred in each interval, and the **Cumulative Trials** column specifies the cumulative number of trials at the end of that interval.

Mixed Data
| ||||

Event | Failures in Interval | Cumulative Trials | Classification | Mode |
---|---|---|---|---|

F | 1 | 8 | BD | 1 |

F | 1 | 8 | BD | 2 |

F | 1 | 8 | BD | 3 |

F | 0 | 10 | A | |

F | 0 | 11 | A | |

F | 0 | 12 | A | |

F | 1 | 13 | BD | 2 |

F | 0 | 14 | A | |

F | 0 | 15 | A | |

I | 0 | 15 | BD | 3 |

F | 1 | 16 | BD | 4 |

F | 0 | 17 | A | |

I | 0 | 17 | BD | 4 |

F | 0 | 18 | A | |

F | 0 | 18 | A | |

F | 1 | 20 | BD | 5 |

The table also gives the classifications of the failure modes. There are 5 BD modes. Of these 5 modes, 2 are corrected during the test (BD3 and BD4) and 3 have not been corrected by time (BD1, BD2 and BD5). Do the following:

- Calculate the parameters of the Crow Extended - Continuous Evaluation model.
- Calculated the demonstrated reliability at the end of the test.
- Calculate parameter .
- Calculate the unfixed BD mode failure probability.
- Calculate the nominal growth potential factor.
- Calculate the nominal average effectiveness factor.
- Calculate the discovery failure intensity function at the end of the test.
- Calculate the nominal projected reliability at the end of the test.
- Calculate the nominal growth potential reliability at the end of the test.

**Solution**

- The next figure shows the data entered in the RGA software.
The parameters and are calculated as follows (the calculations for these parameters are presented in detail in the Crow-AMSAA (NHPP) chapter):

and:

- The corresponding demonstrated unreliability is calculated as:
- Assume that the following effectiveness factors are assigned to the unfixed BD modes:
Classification Mode Effectiveness Factor Implemented at End of Phase BD 1 0.65 Phase 1 BD 2 0.70 Phase 1 BD 5 0.75 Phase 1 The parameter is the total number of distinct unfixed BD modes at time divided by the total number of distinct BD (fixed and unfixed) modes.

In this example:

- The unfixed BD mode failure probability at time is the total number of unfixed BD failures (classified at time ) divided by the total trials. Based on the table at the beginning of the example, we have:
- The nominal growth potential factor is:
- The nominal average effectiveness factor is:
- The discovery function at time is calculated using all the first occurrences of all the BD modes, both fixed and unfixed. In our example, we calculate and using only the unfixed BD modes and excluding the second occurrence of BD2, which results in the following:
- The nominal projected failure probability at time is:
- The nominal growth potential unreliability is: