Double sampling plan by variables for distributions with increasing hazard rates (Q802271)

A double sampling plan by variables is proposed for the case that the items have a quality characteristic X with distribution function F with non-decreasing failure rate f/(1-F). An item is good if \(X\leq U\), the upper specification limit. The lot is accepted after inspection of the first sample of n ordered observations \(x_ 1,x_ 2,...,x_ n\) if \[ x_{n-k-j}+b_ 1(x_{n-k}-x_{n-k-j}) \leq U \] and rejected if \[ x_{n-k-j}+b_ 2(x_{n-k}-x_{n-k-j})\geq U. \] The lot is accepted after inspection of the second sample of size \(N-n\) if \[ x_{N-k- j}+b_ 2(x_{N-k}-x_{N-k-j})\leq U \] and otherwise rejected. For given n, N, k, j and a given portion of defectives p the constants \(b_ 1\) and \(b_ 2\) are determined such that the probability of acceptance on the basis of the first sample is equal to the probability of acceptance on the basis of the second sample and is equal to a given \(1-\nu\). Finally the operating characteristic and the average sample number are given.