Statistical Inference for Burr Type X Distribution using Geometric Process in Accelerated Life Testing Design for Time censored data

Abstract

In accelerated life testing researcher generally use a life stress relationship between life characteristic and stress to estimate the parameters of failure time distributions at use condition which is just a re-parameterization of original parameters but from statistical point of view it is easy and reasonable to deal with original parameters of the distribution directly instead of developing inference for the parameters of the life stress relationship. So, an attempt is made here to estimate the parameters of Burr Type X life distribution directly in accelerated life testing by assuming that the lifetimes at increasing stress levels forms a geometric process. A mathematical model for the analysis of constant stress accelerated life testing for type-I censored data is developed and the estimates of parameters are obtained by using the maximum likelihood method. Also a Fisher information matrix is constructed in order to get the asymptotic variance and interval estimates of the parameters. Lastly, a simulation study is performed to illustrate the statistical properties of the parameters and the confidence intervals.

Reliability analysis incorporating exponentiated inverse Weibull distribution and inverse power law

“…For further discussion on distributions, see Ref. [21][22][23][24][25][26][27][28]. Figure 1 demonstrates the nonmonotonic behaviour of hazard rate function (hrf) of IWD.…”

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

“…According to [3], stress loading in ALT may be performed in a variety of ways, although the most commonly used stress loadings are constant, step, and progressive stress loadings. Many scholars so far have looked at the ALT models, including [4][5][6][7][8][9][10]. Assuming a lognormal lifetime distribution, Li et al [5] proposed two types of Bayesian accelerated acceptance sampling plans for illustrating product reliability based on the product's operating characteristic curve under Type-I censoring.…”

“…The first plan addresses both producer and customer risks at the same time, whereas the second exclusively considers consumer risk. Rahman et al [9] used MLE methods for estimating the parameters of Burr-X life distribution parameters assuming that failure under arithmetically increasing stress levels of CSALT forms a geometric process. Ma et al [10] proposed an optimum hybrid accelerated test plan under many experimental design restrictions by combining ALT with accelerated degradation testing and modeling the degradation process with an inverse Gaussian process.…”

Unsteady MHD Williamson Fluid Flow with the Effect of Bioconvection over Permeable Stretching Sheet

“…Sindhu and Atangana [32] discussed the framework to model the efficiency and functionality lifespan of electronic equipment with reliability analysis. Rehman et al [33] discussed time-censored data and statistical inference for the Burr type X distribution in an accelerated life testing design using a geometric process. Shafiq et al [34] simulated an effective statistical distribution to examine COVID-19 death rates in Canada and the Netherlands.…”