An Improvement of pn and p Control Charts

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  • pn管理図およびp管理図の改良
  • pn カンリズ オヨビ p カンリズ ノ カイリョウ

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Abstract

As attribute control charts, the pn control chart for controlling the number of defectives and p control chart for controlling the fraction defective are well known. However, by use of the three sigma limiting method, the lower control limits of these control charts are sometimes negative, and so have no meaning. This paper presents new pn control and p control charts which enable the user to control changes in the number of defectives and the fraction defective in the case that a process is improving and the number of defectives and fraction defective are declining as the result of quality circle activities. The design of the proposed control charts is based on the direct application of Patnaik's approximation to the number of defectives pn and the fraction defective p, and is easily done by using the probability limiting method based on x^2-distribution, so the lower control limits are always non-negative. Therefore, it is expected that the powers of the proposed control charts can be higher than those of the traditional pn control and p control charts in the case that the number of defectives and fraction defective are declining. The powers and average run length (ARL) using joint detection by a 7-length run of the proposed control charts are compared with those of the traditional pn control and p control charts, alternative charts designed by the probability limiting method and modified charts through computer simulations.

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