Enhanced reliability sampling inspection plans for two-parameter Lindley distribution based on prior information

The probability <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> of observing defectives in a production process or lot inspection is usually assumed to be constant. A methodology to determine optimal sampling plans for Lindley distribution is presented by limiting the expected producer and consumer risks. The proposed approach generalizes the traditional single sampling plans when exists prior information on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> that is modeled under a prior model. In this case, the beta distribution is used to describe the random variation in the proportion defective. The suggested procedure may provide a significant reduction in sample size, as well as a better evaluation of the real producer and consumer risks. Two examples related to the lot acceptability with real lifetime data are shown for illustrative purposes.