Estimation of \(C_p\) for autocorrelated data and measurement errors. (English) Zbl 1009.62110
Summary: The properties of the estimator of \(C_p\) for autocorrelated data in presence of measurement errors are discussed. This work is motivated by the fact that while some efforts have been dedicated in the literature to the statistical properties of the capability index estimator when the data are autocorrelated, scarce attention has been given to the evaluation of these properties when sample data are affected by measurement errors.
In this paper, for a first order stationary autoregressive process, the performance of the estimator of \(C_p\) in the case of measurement errors is derived and compared with those obtained in the error free case.
In this paper, for a first order stationary autoregressive process, the performance of the estimator of \(C_p\) in the case of measurement errors is derived and compared with those obtained in the error free case.
MSC:
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
tablesReferences:
| [1] | Kotz S., Process Capability Indices in Theory and Practice (1998) |
| [2] | Bissel A.F., Applied Statistics (1990) |
| [3] | DOI: 10.1080/03610929008830183 · Zbl 0900.62539 · doi:10.1080/03610929008830183 |
| [4] | DOI: 10.1080/03610928908830174 · Zbl 0707.62030 · doi:10.1080/03610928908830174 |
| [5] | Gunter B.H., Quality Progress 22 pp 72– (1989) |
| [6] | DOI: 10.1080/02664769823025 · Zbl 0934.62128 · doi:10.1080/02664769823025 |
| [7] | DOI: 10.1007/978-3-642-59239-3_15 · doi:10.1007/978-3-642-59239-3_15 |
| [8] | Bordignon S., Quality and Reliability Engineering International (2002) |
| [9] | Kotz S., Process Capability Indices (1993) · Zbl 0860.62075 · doi:10.1007/978-1-4899-4465-8 |
| [10] | Montgomery D.C., Introduction to Statistical Quality Control,, 4. ed. (2001) · Zbl 0997.62503 |
| [11] | Ryan T.P., Statistical Methods for Quality Improvement (2000) · Zbl 0941.62129 |
| [12] | Basseville M., Detection of Abrupt Changes: Theory and Applications (1993) · Zbl 0825.94107 |
| [13] | DOI: 10.1002/(SICI)1099-095X(200003/04)11:2<125::AID-ENV392>3.0.CO;2-8 · doi:10.1002/(SICI)1099-095X(200003/04)11:2<125::AID-ENV392>3.0.CO;2-8 |
| [14] | Harvey A.C., Forecasting Structural Time Series Models and the Kalman Filter (1989) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
