TY - JOUR
T1 - Distribution-free cumulative sum control charts using bootstrap-based control limits
AU - Chatterjee, Singdhansu B
AU - Qiu, Peihua
PY - 2009/3
Y1 - 2009/3
N2 - This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.
AB - This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.
KW - Cumulative sum control charts
KW - Distribution-free procedures
KW - Nonparametric model
KW - Resampling
KW - Robustness
KW - Statistical process control
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U2 - 10.1214/08-AOAS197
DO - 10.1214/08-AOAS197
M3 - Article
AN - SCOPUS:80052933187
SN - 1932-6157
VL - 3
SP - 349
EP - 369
JO - Annals of Applied Statistics
JF - Annals of Applied Statistics
IS - 1
ER -