Economical Sampling Plans with Warranty

Abstract

Designing a proper life test plan to evaluate the quality of a lot of products in order to decide on accepting or rejecting the lot between the manufacturer and customers is an important objective in quality control studies. Most existing life test plans are developed based on the mean time to failure (MTTF) of the products in which a lot is acceptable if the MTTF of products is higher than a given threshold and is rejected otherwise. To save the time and cost of a life test, truncated life test with a prefixed upper limit of the test time can be used in acceptance sampling plan. Instead of life test plans based on MTTF, we consider here life test plans simply based on the number of product failures. Nowadays, to make products more competitive in the market, providing product warranty is a common strategy for manufacturers. Therefore, the development of acceptance sampling plans with warranty considerations is desired. In this chapter, the general structure of an economical design of acceptance sampling plan with warranty using truncated life test is studied. To take into account the uncertainty of the underlying model of the product lifetimes, Bayesian approach using prior information and/or preliminary samples is used to design acceptance sampling plan. Methodologies and algorithms to obtain the optimal sampling plan that minimizes the expected total cost with warranty considerations are discussed. The proposed methodologies are illustrated with two flexible lifetime distributions, the Burr type XII and the generalized exponential distributions, along with real data examples.