Bayesian Sampling Plans With Progressive Censoring and Warranty Policy

Abstract

The paper investigates the design of Bayesian sampling plan for the exponential lifetime model under progressive type-II censoring, in which items are manufactured in batches and sold to consumers with a general rebate warranty policy. Assume that the mean lifetime of items is random and varies from lot to lot. A cost model consists of the cost per item on test, the cost per item of test time and the costs of rejecting and accepting an item is established, and an algorithm is provided to determine the optimal Bayesian sampling plan which minimizes the expected average cost per lot. The use of the proposed method is illustrated by numerical results and an example. A sensitivity study is conducted to evaluate the influences of the removal scheme and using incorrect estimates for the hyper-parameters on the proposed sampling plans. The proposed method can be extended to the Weibull lifetime model as its shape parameter is known.

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

“…Some of them were constructed with a truncated censoring scheme, for example, Aslam and Jun (2009), Aslam et al (2013), Lio et al (2009Lio et al ( , 2010, and Sobel and Tischendrof (1959). Acceptance sampling plans that were developed using a Bayesian framework can be found in Al-Hussaini and Jaheen (1992), Ali Mousa (1995), Kwon (1996), Tsai (2008), and Tsai et al (2008). At present, many products are highly reliable, for example relays and light emitting diodes.…”

“…The warranty policy, described in Equation (3), has been used by various authors (Kwon (1996), Huang et al (2008), Tsai (2008), and Tsai et al (2008)). The lot is acceptable if the number of failed items at τ does not exceed r b .…”

Economic design of the life test with a warranty policy

“…Therefore, it is necessary to consider a warranty policy in the construction of an optimal TLT plan, see Thomas and Rao [20], Murthy and Blischke [17], Menke [15], Blischke and Scheuer [2], Vintr [24], Kwon [12], Tsai [21] and Tsai et al [23].…”