Th e Non-Central Chi-Square Chart with Double Sampling
AbstractIn this article, we consider a non-central chi-square chart with double sampling (DS χ2 chart) to control the process mean and variance. As in the case of Shewhart control charts, samples of fi xed size are taken from the process at regular time intervals; however, the sampling is performed in two stages. Let X be the process quality variable being measured. During the fi rst stage, one item of the sample is inspected; if its X value is close
to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and a
non-central chi-square statistic, say T, is computed taking into account all n items of the sample, that is, their X values. A signal is triggered when the sample point given by the
T value falls above the upper control limit of the proposed chart. The DS χ2 chart performs better than the joint X and R charts, except when there is a large change in the process mean. Furthermore, if the DS χ2 chart is used for monitoring diameters, volumes, weights, etc., then the employment of appropriate devices, such as go-no-go gauges can reduce the effort to decide if the sampling should go to the second stage or not.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors must have a written permission from any third-party materials used in the article, such as figures and graphics. The permission must explicitly allow authors to use the materials. The permission should be submitted with the article, as a supplementary file.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after BJO&PM publishes it (See The Effect of Open Access).