Uncompleted developments in the fields of measurement sciences are categorically agreed on the fact that measurements obtained from continuous phenomena cannot be measured precisely. Therefore, these measurements cannot be considered precise numbers but are nonprecise or fuzzy. For this purpose, it is compulsion of the time that such estimators need to be developed to cover both the uncertainties. The classical accelerated life testing (ALT) approaches are based on precise life times and precise stress levels, but in fact, these are not precise numbers but fuzzy. In this study, the nonparametric procedure of ALT is generalized in such a manner that in addition to random variation, fuzziness of the lifetime observations and stress levels are integrated in the developed estimators. The developed generalized nonparametric estimators for accelerated life time analysis utilize all the obtainable information that is present in the form of fuzziness in single observations and random variation among the observations to make suitable inferences. On the other hand, classical estimators only deal with random variation, which is a strong reason to conclude that the developed estimators should be preferred over classical estimators.

It is often desired for practical reasons to cease a life test at a predetermined period ${𝓽}_0$. In this study, we provide sequential inspection sampling plan (SISP) for amputated life tests underlying the Burr Ⅻ (BTXII) distribution. We considered the ${\rho }^{\mathrm{t}\mathrm{h}}$ percentile lifetime of a product as the quality parameter. The sequential sampling plan is a dynamic and efficient technique to quality control and statistical decision-making. Unlike fixed sample plans, which require a predetermined number of samples before deciding, sequential plan enables ongoing analysis as a batch is examined. This flexible plan enables decisions- such as rejecting, accepting or continuing the sampling process - to be made after each sample, which is cumulative data for the number of nonconforming items. Acceptance, rejection limit lines, and optimal sample size at levels of manufacturer and customer errors were analyzed. A technique is provided for calculating the operation characteristic (OC) function and average sample number (ASN) in the suggested SISP. The effectiveness of the SISP was compared to the single, double, and repeating sampling strategies. In comparison to the single, double, and repetitive acceptance sampling plans (RASPs) the proposed sequential sampling acceptance strategy requires fewer sample resources on average for amputated life testing. The suggested method's uses are demonstrated with illustrated instances. In industrial applications, two actual sets of data are employed to demonstrate the SISP's flexibility.