Statistical analysis of accelerated life testing under Weibull distribution based on fuzzy theory

Abstract

Sometimes the accelerated life testing (ALT) of some products still take time and it is hard to implement real-time monitoring on samples to check whether the samples fail or not. Under this condition, periodic inspection is always conducted to monitor the sample performance, obtaining the failure time data in ALT. But periodic inspection may cause problems in some cases. When the failure is detected during the inspection, its timing point is recorded by estimation. So the failure time is not accurate since it may happen at any time in the adjacent inspection interval and cannot be detected immediately after the failure happen. The extreme case is that the sample fails immediately when the inspection is accomplished. Thus, there exists big uncertainty in failure time data if the interval is quite long which will affect the accuracy of evaluation results. However, there are some methods which may help to detect the failure happen indirectly. For example, the fluctuation or excursion of the output digital signal of samples may indicate the failure to some degree. Even so, the failure time cannot be recognized directly because the judging criteria of failure of different inspectors may slightly vary. This leads to the estimation of the exact failure time is not precise. Therefore, the failure time data of ALT is not precise and should be fuzzy data. The life estimation of ALT should be a fuzzy interval value rather than just a single number. Hence, in this paper, a statistical method for constant-stress ALT with Type II censored samples based on fuzzy theory is proposed which assumes that the life time of the product follows Weibull distribution.