Author(s)

Bo Qin, Ningxiang Wu, Liyang Xie

Department of Mechanical Engineering, Northeastern University, Shenyang, China.

Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This paper presents a stochastic simulation method to estimate the Weibull location parameters according to a small size of sample of product life observations and a large amount of statistically simulated life date. Big data technique is applied to find the relationship between the minimal observation in a product life sample of size n (n ≥ 3) and the Weibull location parameter. An example is presented to demonstrate the applicability and the value of the big data based stochastic simulation method. Comparing with other methods, the stochastic simulation method can be applied to very small size of sample such as the sample size of three, and it is easy to apply.

Three-Parameter Weibull Distribution, Location Parameter, Monte Carlo Sampling, Big Data

Qin, B. , Wu, N. and Xie, L. (2021) Characterizing the Relationship between Weibull Location Parameter and the Minimal Observation in a Small Size of Sample Based on Stochastic Simulation. Journal of Applied Mathematics and Physics, 9, 2345-2354. doi: 10.4236/jamp.2021.99149.