ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 26 Nov 2022 08:51:21 GMT2022-11-26T08:51:21Z5041- On the performance of geometric charts with estimated control limitshttps://scholarbank.nus.edu.sg/handle/10635/51863Title: On the performance of geometric charts with estimated control limits
Authors: Yang, Z.; Xie, M.; Kuralmani, V.; Tsui, K.-L.
Abstract: The control chart based on the geometric distribution (geometric chart) has been shown to be competitive with p- or np-charts for monitoring the proportion nonconforming, especially for applications in high quality manufacturing environments. However, implementing a geometric chart is often based on the assumption that the in-control proportion nonconforming is known or accurately estimated. For a high quality process, an accurate parameter estimate may require a very large sample size that is seldom available. In this paper we investigate the sample size effect when the proportion nonconforming is estimated. An analytical approximation is derived to compute shift detection probabilities and run length distributions. It is found that the effect on the alarm probability can be significant even with sample sizes as large as 10,000. However, the average run length is only affected mildly unless the sample size is small and there is a large process improvement. In practice, the quantitative results of the paper can be used to determine the minimum number of items required for estimating the control limits of a geometric chart so that certain average run length requirements are met.
Tue, 01 Oct 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/518632002-10-01T00:00:00Z
- On the performance of geometric charts with estimated control limitshttps://scholarbank.nus.edu.sg/handle/10635/87123Title: On the performance of geometric charts with estimated control limits
Authors: Yang, Z.; Xie, M.; Kuralmani, V.; Tsui, K.-L.
Abstract: The control chart based on the geometric distribution (geometric chart) has been shown to be competitive with p- or np-charts for monitoring the proportion nonconforming, especially for applications in high quality manufacturing environments. However, implementing a geometric chart is often based on the assumption that the in-control proportion nonconforming is known or accurately estimated. For a high quality process, an accurate parameter estimate may require a very large sample size that is seldom available. In this paper we investigate the sample size effect when the proportion nonconforming is estimated. An analytical approximation is derived to compute shift detection probabilities and run length distributions. It is found that the effect on the alarm probability can be significant even with sample sizes as large as 10,000. However, the average run length is only affected mildly unless the sample size is small and there is a large process improvement. In practice, the quantitative results of the paper can be used to determine the minimum number of items required for estimating the control limits of a geometric chart so that certain average run length requirements are met.
Tue, 01 Oct 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/871232002-10-01T00:00:00Z
- On optimal setting of control limits for geometric charthttps://scholarbank.nus.edu.sg/handle/10635/87114Title: On optimal setting of control limits for geometric chart
Authors: Xie, M.; Goh, T.N.; Kuralmani, V.
Abstract: Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment. © World Scientific Publishing Company.
Wed, 01 Mar 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/871142000-03-01T00:00:00Z
- On optimal setting of control limits for geometric charthttps://scholarbank.nus.edu.sg/handle/10635/63214Title: On optimal setting of control limits for geometric chart
Authors: Xie, M.; Goh, T.N.; Kuralmani, V.
Abstract: Control charts based on geometric distribution have shown to be very useful in the monitoring of high yield manufacturing processes and other applications. It is well known that the traditional 3-sigma limits will give too many false alarms and the probability limits should be used. This paper shows that the average time to alarm may even increase at the beginning when the process is deteriorated. A new procedure is established for the setting of control limits so that the average run length is maximized when the process is at the normal level. Hence the chart sensitivity can be improved. For the derivation of the control limits in this new procedure, a simple adjustment factor is suggested so that the probability limits can be used after the adjustment. © World Scientific Publishing Company.
Wed, 01 Mar 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/632142000-03-01T00:00:00Z