BLUEs and Reliability Analysis for General Censored Data Subject to Inverse Gaussian Distribution

Working on product lifetime data is of significant importance for evaluating safety and reliability, predicting remaining useful life and formulating maintenance strategy or replacement policy. In practical applications, observed datasets often consist of failure data and randomly censored data, which are referred as general censored data. Meanwhile, inverse Gaussian (IG) distribution has been widely adopted to depict lifetime data because it not only can possess flexible expression formats but also can explain the mechanism of first hitting time from a soft failure viewpoint. Motivated by these two regards, this paper develops a novel method on best linear unbiased estimations (BLUEs) for general censored data. A three-parameter IG distribution type is adopted. A novel method is established to optimize the skewness parameter. Then, BLUEs of mean and standard deviation can be obtained. The proposed method can construct closed-form parameter estimations in linear functions of order statistics. The computation process has been further simplified for flexible applications. The frequently utilized maximum likelihood estimation method is also introduced as a reference for a better understanding. Comparative results of both comprehensive simulation study and empirical application illustrate that the proposed method can significantly enhance the estimation accuracy and keep a stable performance, because more life information can be extracted and adopted from the censored datasets.