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In this paper, Bayesian estimation of log odds ratios over R × C and 2 × 2 × K contingency tables is considered, which is practically reasonable in the presence of prior information. Likelihood functions for log odds ratios are derived for each table structure. A prior specification strategy is proposed. Posterior inferences are drawn using Gibbs sampling and Metropolis-Hastings algorithm. Two numerical examples are given to illustrate the matters argued.

In this paper the control limits of \(\bar{X}\) and \(R\) control charts for skewed distributions are obtained by considering the classic, the weighted variance (\(\mathit{WV}\)), the weighted standard deviations (\(\mathit{WSD}\)) and the skewness correction (\(\mathit{SC}\)) methods. These methods are compared by using Monte Carlo simulation. Type I risk probabilities of these control charts are compared with respect to different subgroup sizes for skewed distributions which are Weibull, gamma and lognormal. Simulation results show that Type I risk of \(\mathit{SC}\) method is less than that of other methods. When the distribution is approximately symmetric, then the Type I risks of Shewhart, \(\mathit{WV}\) , \(\mathit{WSD}\), and \(\mathit{SC}\) \(\bar{X}\) charts are comparable, while the \(\mathit{SC}\) \(R\) chart has a noticeable smaller Type I risk.

This article deals with the construction of anX control chart using the Bayesian perspective. We obtain new control limits for theX chart for exponentially distributed data-generating processes through the sequential use of Bayes'theorem and credible intervals. Construction of the control chart is illustrated using a simulated data example. The performance of the proposed, standard, tolerance interval, exponential cumulative sum (CUSUM) and exponential exponentially weighted moving average (EWMA) control limits are examined and compared via a Monte Carlo simulation study. The proposed Bayesian control limits are found to perform better than standard, tolerance interval, exponential EWMA and exponential CUSUM control limits for exponentially distributed processes.

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