A note on some modified Pulak and Al-Sultan's model

Pulak and Al-Sultan presented a rectifying inspection plan applying in the determination of optimum process mean. However, they did not point out whether the non-conforming items in the sample of accepted lot are replaced or eliminated from the lot and neglected the quality loss within specification limits. In this paper, we further propose the modified Pulak and Al-Sultan model with quadratic quality loss function. There are four cases considered in the modified model: (1) the non-conforming items in the sample of accepted lot are neither replaced nor eliminated from the lot; (2) the non-conforming items in the sample of accepted lot are not replaced but are eliminated from the lot; (3) the non-conforming items in the sample of accepted lot are replaced by conforming ones; (4) the non-conforming items in the sample of accepted lot are replaced by non-inspected items. The numerical results and sensitivity analysis of parameters show that their solutions are slightly different.     

Multiple Sampling Inspection Plans for Attributes

A set of tables is presented enabling one to design multiple (Group sequential) sampling plans when various entry parameters are given. Table yielding item by item sequential sampling plans indexed by (AQL, AOQL) is also presented.     

The Optimal Allocation Combination for the One-Sided Sequential Screening Procedure Based on the Individual Misclassification Error

In this article, the expected total costs of three kinds of quality cost functions for the one-sided sequential screening procedure based on the individual misclassification error are obtained, where the expected total cost is the sum of the expected cost of inspection, the expected cost of rejection, and the expected cost of quality. The computational formulas for three kinds of expected total costs are derived when k screening variables are allocated into r stages. The optimal allocation combination is determined based on the criterion of minimum expected total cost. At last, we give one example to illustrate the selection of the optimal allocation combination for the sequential screening procedure.     

Corrigendum for: The Distribution of Family Sizes Under a Time-Homogeneous Birth and Death Process

Regretably, there are a number of significant errors in Moschopoulos and Shpak, (2010). Communications in Statistics—Theory and Methods 39:1761–1775. Most are typographic errors that have the potential to cause confusion, and in some instances, have carried through to several equations.     

Phase II monitoring of binary profiles in the presence of within-profile autocorrelation based on Markov Model

This paper introduces a Markov model in Phase II profile monitoring with autocorrelated binary response variable. In the proposed approach, a logistic regression model is extended to describe the within-profile autocorrelation. The likelihood function is constructed and then a particle swarm optimization algorithm (PSO) is tuned and utilized to estimate the model parameters. Furthermore, two control charts are extended in which the covariance matrix is derived based on the Fisher information matrix. Simulation studies are conducted to evaluate the detecting capability of the proposed control charts. A numerical example is also given to illustrate the application of the proposed method.     

Modified Group Runs Control Charts to Detect Increases in Fraction Non Conforming and Shifts in the Process Mean

The nonparametric two-sample bootstrap is employed to compute uncertainties of measures in receiver operating characteristic (ROC) analysis on large datasets in areas such as biometrics, and so on. In this framework, the bootstrap variability was empirically studied without a normality assumption, exhaustively in five scenarios involving both high- and low-accuracy matching algorithms. With a tolerance 0.02 of the coefficient of variation, it was found that 2000 bootstrap replications were appropriate for ROC analysis on large datasets in order to reduce the bootstrap variance and ensure the accuracy of the computation.     

Exact Bayesian Variable Sampling Plans for the Exponential Distribution Based on Type-I and Type-II Hybrid Censored Samples

A sampling plan with a polynomial loss function for the exponential distribution is considered. From the distribution of the maximum likelihood estimator of the mean of an exponential distribution based on Type-I and Type-II hybrid censored samples, we obtain an explicit expression for the Bayes risk of a sampling plan with a quadratic loss function. Some numerical examples and comparisons are given to illustrate the effectiveness of the proposed method, and a robustness study reveals that the proposed optimal sampling plans are quite robust.