Design of an Adaptive (x^^-, s) Simultaneous Control Chart with Variable Sample Size and Sampling Intervals

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  • 可変サンプル・サイズと可変サンプリング間隔をもつ(x^^-, s)同時管理図の設計
  • カヘン サンプル サイズ ト カヘン サンプリング カンカク オ モツ x s ドウジ カンリズ ノ セッケイ

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Abstract

Recently, Kanagawa et al.(1993) proposed a (x^^-, s) simultaneous control chart with the control limit based on the probability limit method. Further, the results derived by Arizono et al.(1995) enable the user to evaluate the performance of the (x^^-, s) simultaneous control chart. On the othe hand, some innovations have been proposed to improve chart performance in the case of monitoring the shift in the process mean. Reynolds et al.(1988) considered the properties of the Shewhart x^^- control chart with variable sampling intervals. A Shewhart x^^- control chart with variable sample size was also considered by Prabhu et al.(1993) and Costa (1994). Additionally, Prabhu et al.(1994) and Costa (1997) investigated the Shewhart x^^- control chart where both the sampling interval and sample size are varied depending on the position of the current observations on the Shewhart x^^- control chart. Furthermore, the CUSUM x^^- control chart and EWMA x^^- control chart with variable sampl sizes and/or sampling intervals were also considered for the purpose of improving chart performance. However, in a physical environment, it is usual to employ jointly the x^^- chart for monitoring the shift in process mean and the R chart for monitoring the change in process variance. Recently, Costa (1998) has considered joint x^^- and R control charts with variable sample size and variable sampling intervals with this view. The variable sample size and sampling interval x^^--R control charts presented by Costa (1998) have twelve design parameters, since the statistic x^^- for monitoring the shift in process mean and statistic R for monitoring the change in process variance are jointly employed. The feature of the (x^^-, s) simultaneous control chart is, however, that in this control chart we can monitor the process condition to the in-control state described by the process mean and variance by using a single statistic. In this paper, we consider the variable sample size and sampling interval (x^^-, s) simultaneous control chart for monitoring both the shift in process mean and the change in process variance for the purpose of improving chart performance. The performance of the variable sample size and sampling interval (x^^-, s) simultaneous control chart is compared with the performance of the standard (x^^-, s) simultaneous control chart.

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