Credit in Acceptance Sampling on Attributes

Credit is introduced in acceptance sampling on attributes and a Credit Based Acceptance sampling system is developed that is very easy to apply in practice.The credit of a producer is defined as the total number of items accepted since the last rejection.In our sampling system the sample size for a lot depends via a simple function on the lot size, the credit, and the chosen guaranteed upper limit on theoutgoing quality, and will be much smaller than in isolated lot inspection.Our Credit Based Acceptance sampling system also yields a simple continuous sampling plan

Credit-based accept-zero sampling schemes for the control of outgoing quality

A general procedure is presented for switching between accept-zero attributes or variables sampling plans to provide acceptance sampling schemes with a specified limit on the (suitably defined) average outgoing quality (AOQ). The switching procedure is based on credit, defined as the total number of items accepted since the last rejection. The limit on the AOQ is maintained by mandatory 100 % inspection of lots that are rejected when the credit is zero, with acceptance of all inspected items found to be conforming in such lots. The general procedure is developed and the application of the procedure to three situations is considered. Denoting the smallest value in a sample by $X_{(1)}$, a single, lower specification limit by $L$ and a constant by $c$, the method is applied to:- sampling by attributes, with acceptance criterion $X_{(1)}\geq L;$- sampling by variables from a normal distribution with unknown process mean $\mu$ and known process standard deviation $\sigma$, with acceptance criterion $X_{(1)}\geq L+c\sigma;$- sampling by variables from a normal distribution with unknown process mean $\mu$ and unknown process standard deviation $\sigma$, with acceptance criterion $X_{(1)}\geq L+cs$, where $s$ is the sample standard deviation.Finally it is shown that the guarantee on the upper limit to the AOQ remains valid when all rejected lots are submitted to 100 % inspection

Zero Information in the Two-Sample Mixed Proportional Hazards Model

The mixed proportional hazards model generalizes the Cox model by incorporating a random effect. In the case of two samples, it is chiefly determined by a triple consisting of a number representing the treatment effect, the integrated base-line hazard, and the distribution of the unobserved random effect. If the latter has expectation 1, then this triple is known to be identifiable, and the treatment effect is known to have a consistent estimator. We prove that estimators, however, cannot be uniformly square root n consistent, neither in a local nor in a global sense

Bayes Convolution

A general convolution theorem within a Bayesian framework is presented. Consider estimation of the Euclidean parameter θ by an estimator T within a parametric model. Let W be a prior distribution for θ and define G as the W-average of the distribution of T - θ under θ. In some cases, for any estimator T the distribution G can be written as a convolution G = K * L with K a distribution depending only on the model, i.e. on W and the distributions under θ of the observations. In such a Bayes convolution result optimal estimators exist, satisfying G = K. For location models we show that finite sample Bayes convolution results hold in the normal, loggamma and exponential case. Under regularity conditions we prove that normal and loggamma are the only smooth location cases. We also discuss relations with classical convolution theorems.

Spread, estimators and nuisance parameters

A general spread inequality for arbitrary estimators of a one-dimensional parameter is given. This finite-sample inequality yields bounds on the distribution of estimators in the presence of finite- or infinite-dimensional nuisance parameters.