Interval estimation for Wiener processes based on accelerated degradation test data

The evidential variable shows the powerful ability on the parameter description, so we have cooperated it with the linear Wiener process to model linear degradation processes. However, the degradation paths of some products exhibit two-phase patterns over the running time, which cannot be modeled by the linear Wiener process. Hence, it is developed into an associated evidential variable-based two-phase Wiener process. In order to utilize the proposed model, the related evidence obtaining, evidence fusion and performance inference approaches are constructed. A simulation study and an actual case are performed to verify the superiorities of the proposed method. The proposed method provides higher accuracies of the useful life, degradation, and reliability evaluations, due to utilizing the evidential variable and considering the two-phase degradation conditions.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A reliability estimation method based on two‐phase Wiener process with evidential variable using two types of testing data

Shi

Qiao

Wang

et al. 2022

“…Efron 32 introduced a computer‐based resampling technique called the

bootstrap

method, which is extensively applied to obtain the confidence intervals of PCIs for non‐normal distributions, see Erfanian and Gildeh, 7 Kashif et al, 33 and Kashif et al 34 . However, the

bootstrap

method is time‐consuming, and the actual coverage probability (CP) of the

bootstrap

confidence interval (BCI) is often not close enough to the nominal value (see Hong et al 35 …”

Section: Introductionmentioning

confidence: 99%

Generalized interval estimation of process capability indices for the Birnbaum–Saunders distribution

Bao-cai

Xia

et al. 2022

Since sampling variation would lead to the inaccurate assessment of process capability indices (PCIs), the interval estimation of PCIs has received considerable attention recently. The coverage probabilities (CPs) of the widely used bootstrap confidence intervals (BCIs) of PCIs are not sufficiently close to their nominal confidence level. Moreover, the bootstrap method is time-consuming. This paper develops a procedure for constructing generalized confidence intervals (GCIs) of two widely used percentile-based PCIs for the Birnbaum-Saunders (BS) distribution. A simulation study is conducted and the results indicate that the proposed GCI outperforms its bootstrap counterparts in terms of the CPs, the average widths (AWs) of the confidence intervals, and the variability of the interval widths. Finally, two real examples are used to illustrate the implementation of the proposed procedure.

“…After obtaining the GPQs of the model parameters, through simple plug‐in method, the GPQ of the real‐valued function of the model parameters can be obtained (Hannig et al 34 ). The literature on constructing CIs based on the GPQ method can refer to Wang and Iyer, 35 Wang and Wu, 36 Xu et al, 37 Hong et al, 38 Chen and Ye, 39 Wang et al, 40 Kong and Ye, 41 Wang et al, 42 Wu and Hsieh 43 …”

Section: Introductionmentioning

confidence: 99%

Interval estimation for inverse Gaussian distribution

Wang

Pan

et al. 2021

In this paper, we consider interval estimation for the inverse Gaussian (IG) distribution. Using generalized pivotal quantity method, we derive the generalized confidence intervals (GCIs) for the model parameters and some quantities such as the quantile, the reliability function of the lifetime, the failure rate function, and the mean residual lifetime. We verify that the GCI of the scale parameter is the same as its commonly used exact CI. We also obtain the generalized prediction intervals (GPIs) for future failure times based on the observed failure data set. In addition, we get the GCI for the reliability of the stress–strength model when the stress and strength variables follow the IG distributions with different parameters. We compare the proposed GCIs and GPIs with the Wald CIs and bootstrap‐p CIs by simulation. The simulation results show that the proposed GCIs and GPIs are superior to the Wald CIs and the bootstrap‐p CIs in terms of the coverage probability. Finally, two examples are used to illustrate the proposed procedures.