For attribute data with (very) small failure rates often control charts are used which decide whether to stop or to continue each time r failures have occurred, for some r ≥ 1. Because of the small probabilities involved, such charts are very sensitive to estimation effects. This is true in particular if the underlying failure rate varies and hence the distributions involved are not geometric. ...

There is a considerable amount of ongoing research on the use of Bayesian control charts for detecting a shift from a good quality distribution to a bad quality distribution in univariate and multivariate processes. It is widely claimed that Bayesian control charts are economically optimal; see, for example, Calabrese (1995) [Bayesian process control for attributes. Management Science, DOI: 10....

The basic control chart consists of sampling from a process over time and charting process measurements. For as long as the measurements fall inside control limits (L), the process is considered in-control. In feed production, it is customary to set the control limits at two standard deviations. This practice does not consider the probability of both Type I and Type II errors in addition to all...

For attribute data with (very) low rates of defectives, attractive control charts can be based on the maximum of subsequent groups of r failure times, for some suitable r ≥ 1, like r = 5. Such charts combine good performance with often highly needed robustness, as they allow a nonparametric adaptation already for Phase I samples of ordinary size. In the present paper we address the problem of e...

This paper presents the economic design of X control charts for monitoring a critical stage of the main production process at a tile manufacturer in Greece. Two types of X-charts are developed: a chart of the Shewhart type with fixed parameters and adaptive charts with variable sampling intervals and/or sample size. Our prime motivation was to improve the statistical control scheme employed for...

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