New Inference for Constant-Stress Accelerated Life Tests With Weibull Distribution and Progressively Type-II Censoring

Abstract

Constant-stress procedures based on parametric lifetime distributions and models are often used for accelerated life testing in product reliability experiments. Maximum likelihood estimation (MLE) is the typical statistical inference method. This paper presents a new inference method, named the random variable transformation (RVT) method, for Weibull constant-stress accelerated life tests with progressively Type-II right censoring (including ordinary Type-II right censoring). A two-parameter Weibull life distribution with a scale parameter that is a log-linear function of stress is used. RVT inference life distribution parameters and the log-linear function coefficientsare provided. Exact confidence intervals for these parameters are also explored. Numerical comparisons of RVT-based estimates to MLE show that the proposed RVT inference is promising, in particular for small sample sizes.

An imprecise statistical method for accelerated life testing using the power-Weibull model

“…We repeated this simulation several times, always leading to the same conclusion. It should be remarked that bias in parameter estimates for ALT models has been reported previously [20], we briefly discuss this further in Section 7.…”

“…Another issue is bias in statistical estimation methods for ALT models, which can particularly occur if one has relatively few items on test. One can study alternative estimation methods in order to reduce such bias [20], but again we consider the use of a widely available method like MLE together with some additional imprecision a simple and attractive alternative.…”

“…These include doubt about the model used at stage 1 and, related to this, the fact that the estimation of the Weibull parameters influences the estimate of the parameter p but is further neglected at stage 2. As mentioned in the example, there may also be some numerical instability in the estimation computations and it has been reported that maximum likelihood methods for such accelerated life test data can lead to bias in the estimates when relatively small sample sizes are used [20]. One could rebute all such issues by suggesting more detailed modelling, but particularly for ALT data there often remains an element of model-based extrapolation that is difficult, sometimes even impossible, to justify on the basis of available data.…”

“…For the example in Section 3, the point estimate for p was equal top = 15.09927, the NPI lower and upper survival functions corresponding to this value were presented in Figure 2. [13,17]; [10,20] shows that increased imprecision for the parameter p leads to increased differences between the NPI upper and lower survival functions. It is interesting to see that even for very substantial imprecision for p the imprecision between the lower and upper survival functions is mostly not too large.…”

Reliability Analysis of Multiple Causes of Failure in Presence of Independent Competing Risks

“…For clarity, the observed failure times and uncensored times can be used interchangeably . Since there are also some other reasons that may lead to right censoring, such as test time constraint, cost reduction, loss to track or any combination of these, right‐censored data is therefore a common lifetime data type in reliability experiments …”