Economical sampling plans with warranty based on truncated data from Burr type XII distribution

Abstract

Economical sampling plans to ensure the qualities of Burr type XII distributed lifetimes were established using a truncated life test. The Bayesian inference method was used to address the lot-to-lot variation of products. The sampling plan was characterized by the sample size and the acceptance number to minimize the expected total cost. A simple empirical Bayesian estimation method was provided to estimate the hyperparameters of prior distribution, and simulation studies were conducted to validate the proposed empirical Bayesian estimation method. Lastly, the application of this proposed method was illustrated using two examples.

Keywords:

• quality control
• reliability
• statistics

Acknowledgements

The authors thank the editor, associate editor, and anonymous reviewers for their suggestions and comments on an earlier version of this manuscript, which led to this improved version. The authors also thank Michelle Rogge Gannon, Writing Center Director and Dakota Writing Project Director at the University of South Dakota, for copyediting.

Notes

1 R is a free software environment for statistical computing and graphics and can be downloaded at http://www.r-project.org.