New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions

Abstract

In this paper, we consider the Birnbaum-Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.

Improved double acceptance sampling plan based on truncated life test for some popular statistical distributions

“…( 1 1 ) As suggested by Aslam et al, [18] it more convenient for life test to write t 0 as t 0 = aθ 0 for a constant termination ratio a. Therefore, Equation (11) can be rewritten as…”

Bayesian inference for the Birnbaum–Saunders nonlinear regression model

“…Some generalizations and extensions of the BS distribution are presented in Díaz-García and Leiva (2005), Gómes et al (2009), Guiraud et al (2009) and Cordeiro and Lemonte (2011. Bhatti (2010) introduced the BS autoregressive conditional duration model and Aslam et al (2011) developed various acceptance sampling schemes based on the truncated life tests. This distribution has been applied in reliability studies (Balakrishnan et al 2007) and outside this field (Leiva et al 2008).…”

Sampling Plans Based on Truncated Life Test for a Generalized Inverted Exponential Distribution

“…A generalization of the single acceptance sampling plan is known as the double acceptance sampling plan. Such plans have also found wide applications in the area of quality control and reliability analysis and one may refer to Aslam and Jun (2010) and Aslam et al (2011a) for some related results. Balasooriya (1995) suggested that when the test units are highly reliable but relatively cheap and the test facilities are scarce, a life test experiment can be conducted by placing g independent groups on the test where each group contains r number of units.…”

“…Note that g, r and c are the design parameters of the associated group acceptance sampling plan. In literature, group acceptance sampling plans have been discussed by Aslam et al (2009) for gamma distribution, Aslam and Jun (2009a) for Weibull distribution, Aslam and Jun (2009b) for inverse Rayleigh and log-logistic distributions, Rao (2010) for generalized exponential distribution and Aslam et al (2011a) for Birnbaum-Saunders distribution. It is to be noticed that two-stage group acceptance sampling plan is a further generalization of the group acceptance sampling plan.…”