The field failure data is important in the reliability field. Component failure data, instead of system failure data, are usually collected by the system owners. However, in many cases the individual component time-to-failure data are not recorded. Instead, cumulative operation time and the number of failure times are recorded. This can be explained by the fact that exponential distribution is often used to fit the data. Unfortunately, the assumption of exponential distribution is not valid in many cases. In our paper, Gamma distribution and Inverse Gaussian (IG) distribution are used to fit the data. The point estimate for parameters of these two distributions can be obtained easily by general computer software. We then proposed methods to obtain the confidence interval (CI) for parameters of gamma distribution and IG distribution when the data are merged. In particular, for the rate parameter and mean of a gamma distribution, no efficient methods have been found to get the interval estimation. We borrow the idea of General Pivotal Quantity to obtain the interval estimation for the rate parameter and mean of a gamma distribution. The simulation study shows our method outperforms Wald method in terms of coverage probability. At last, an illustrative example is given to demonstrate the applicability of proposed models.
- Generalized pivotal quantity
- Grouped data
- Inverse Gaussian distribution
- Gamma distribution
- Confidence interval