After reformatting the data with Pre-Process Warranty Data, the data are interval censored, grouped in intervals of the form (t_{0}, t_{1}), (t_{1}, t_{2}),...,(t_{k-1}, t_{k}) such that each interval (t_{i-1}, t_{i}) contains n_{i} failures (if t_{i} is finite) or n_{i} suspensions (if t_{i} is infinite), i = 1, 2,..., k.

Total number of units = the total number of units shipped up to the present time

Observed number of failures = the number of shipped units that failed during the warranty period

If you do not specify a length of warranty (L), the expected number of failures (ENF) is given by:
where I_{C} = 1 if condition C is met, I_{C} = 0 otherwise.

If you specify a length of warranty (L), the expected number of failures is given by:

Number of units at risk for future time periods = the total number of right censored units under warranty

Term | Description |
---|---|

R(t) | the reliability function |

For more information on the reliability function, go to Survival probabilities.

Calculations for the expected number of future failures are based only on "suspended units" (right-censored units). Units that have already failed have no impact on future failures.

The predicted number of failures (PNF) for an additional period of time Δ is given by:

If you specify production quantities d_{1}, d_{2},...,d_{r} for future time periods 1, 2,...,r, the PNF for any future time period Δ is given by:
where q = min{r, int(Δ)} and int(Δ) is the integer part of Δ.

If you specify a warranty limit L, then only units still within the warranty period contribute to PNF, which is given by:
where I_{C} = 1 if condition C is met, and I_{C} = 0 otherwise

If you specify a warranty limit L and production quantities d_{1}, d_{2},...,d_{r} for future time periods 1, 2,...,r, then the PNF for any future time period Δ is given by:
where q = min{r, int(Δ)} and int(Δ) is the integer part of (Δ).

Term | Description |
---|---|

t_{i} | the suspension times |

n_{i} | the number of units suspended at time t_{i}, i = 1, 2,...,m |

m | the number of distinct suspension times |

R(t) | the reliability function. For more information, go to Survival probabilities |

An approximate 100(1-α)% confidence interval for the predicted number of failures (x) is given by:

An approximate one-sided 100(1-α)% lower confidence bound is given by:

An approximate one-sided 100(1-α)% upper confidence bound is given by:

These confidence intervals and bounds are based on the assumption that failures occur according to an approximate Poisson process with a constant rate.

Term | Description |
---|---|

s | calculated predicted number of failures (the statistic) |

x | true predicted number of failures (the parameter) |

the 100(1-α)^{th} percentile of the chi-square distribution with f degrees of freedom | |

α | the level of significance (alpha) |

- Predicted Number of Failures Plot
- The predicted number of failures are plotted against future time periods. The range of the x-axis is the range of future time periods. If you do not specify future time periods (that is, if the PREDICT subcommand is not given), the range of the x-axis is (0, 5].
- Predicted Cost of Failures Plot
- If you specify an average cost per failure (that is, if you use the COST subcommand), the predicted cost of failures are plotted against future time periods. The range of the x-axis is the range of future time periods. If you do not specify future time periods (that is, if the PREDICT subcommand is not given), the range of the x-axis is (0, 5].