A novel MTTF estimator and associated parameter estimation method on heavily censoring data

Abstract

Many reliability and maintenance decision problems need to estimate mean‐time‐to‐failure (MTTF) of a particular product component and/or build its life distribution model as early as possible based on field failure data. The field failure data are often heavily censored. In this case, the exponential‐assumption–based method can considerably overestimate the MTTF, and the classical parameter estimation methods such as the maximum likelihood method (MLM) cannot provide robust estimates. This paper aims to address this issue through proposing a novel method to estimate the MTTF and life distribution parameters. The proposed method first derives a nonparametric estimator of MTTF based on the decomposition of the integral expression of the theoretical MTTF and sample statistical characteristics. The estimated MTTF is then combined with a two‐step single‐parameter MLM to estimate the distribution parameters. A numerical experiment is carried out, and a real‐world dataset is analyzed. The results show that the proposed method can provide accurate and robust estimates for the MTTF and distribution parameters. The method is applicable for any life distribution and offers practitioners an efficient tool for reliability analysis.

An aging‐intensity‐function‐based parameter estimation method on heavily censored data

“…From Tables 6 and 9, we have the following observations: As a whole, the point estimates are fairly accurate, e.g., the estimated MTTFs range from 81.9 to 138.5, which are close to their true value (i.e., 100). However, the accuracy is slightly poorer than the ones of 15 and 16 in terms of $$\bar \varepsilon $$. All the confidence intervals cover their true values; and the averages of relative widths of β and MTTF are 0.5223 and 0.3791, respectively, which are smaller than ω 0 . That is, the confidence intervals are narrow and this is particularly true for the confidence intervals of MTTF. The γ value of the proposed approach equals to 0.0509, which is much smaller than those γ values shown in Table 6, implying that the proposed approach has the best unbiasedness.…”

“…Recently, Jiang proposes three such approaches 14–16 . The approaches first estimate the MTTF using an empirical relation or fitting the data to a one‐parameter auxiliary distribution, then fix the MTTF estimate and use a single‐parameter MLE to estimate the shape parameter.…”

Two bias‐corrected Kaplan‐Meier estimators

“…This will be beneficial for the parameter estimation on heavily censored data since more information generally results in more stable estimates. 20,21 This will be illustrated in Section 5.…”

“…The data shown in Table 5 are randomly generated from the Weibull distribution with shape parameter β = 2.5 and MTTF = μ = 100, 20 where "50 ( 27)" means 27 observations at t = 50.…”

“…In other words, the number of data points will increase from m to 2 m when merging the WKME and the MP‐KME. This will be beneficial for the parameter estimation on heavily censored data since more information generally results in more stable estimates 20,21 . This will be illustrated in Section 5.…”