Two new multi-phase reliability growth models from the perspective of time between failures and their applications

Aviation products would go through a multi-phase improvement in reliability performance during the research and development process.In the literature,most of the existing reliability growth models assume a constant failure intensity in each test phase,which inevitably limits the scope of the application.To address this problem,we propose two new models considering timevarying failure intensity in each stage.The proposed models borrow the idea from the accelerated failure-time models.It is assumed that time between failures follow the log-location-scale distribution and the scale parameters in each phase do not change,which forms the basis for integrating the data from all test stages.For the test-find-test scenario,an improvement factor is introduced to construct the relationship between two successive location parameters.Whereas for the test-fix-test scenario,the instantaneous cumulative time between failures is assumed to be consistent with Duane model and derive the formulation of location parameter.Likelihood ratio test is further utilized to test whether the assumption of constant failure intensity in each phase is suitable.Several applications with real reliability growth data show that the assumptions are reasonable and the proposed models outperform the existing models.

Bayesian Reliability Modeling and Assessment Solution for NC Machine Tools under Small-sample Data

Although Markov chain Monte Carlo（MCMC） algorithms are accurate, many factors may cause instability when they are utilized in reliability analysis; such instability makes these algorithms unsuitable for widespread engineering applications. Thus, a reliability modeling and assessment solution aimed at small-sample data of numerical control（NC） machine tools is proposed on the basis of Bayes theories. An expert-judgment process of fusing multi-source prior information is developed to obtain the Weibull parameters＇ prior distributions and reduce the subjective bias of usual expert-judgment methods. The grid approximation method is applied to two-parameter Weibull distribution to derive the formulas for the parameters＇ posterior distributions and solve the calculation difficulty of high-dimensional integration. The method is then applied to the real data of a type of NC machine tool to implement a reliability assessment and obtain the mean time between failures（MTBF）. The relative error of the proposed method is 5.8020×10-4 compared with the MTBF obtained by the MCMC algorithm. This result indicates that the proposed method is as accurate as MCMC. The newly developed solution for reliability modeling and assessment of NC machine tools under small-sample data is easy, practical, and highly suitable for widespread application in the engineering field; in addition, the solution does not reduce accuracy.

Reconstruction of Probability Density Function for Gamma Distribution

The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.

A Simple and Practical Algorithm for Calculating MTBF of Complex Systems

It is often difficult to calculate the failure rate of a complex system. For a complex system, therefore, the value of mean time between failures (MTBF) is also difficult to obtain with formula M=1/λ. The authors introduce a simple and practical algorithm, which can be easily used to obtain the value of MTBF of a complex system with M=∫∞0R(t)dt. The time axis is divided into lots of small intervals with step Δt, and lots of small trapezoids under the curve R(t) are obtained. By summing up all the areas of the trapezoids, a close approximation to MTBF of the system is obtained.