Abstract
The cases where a functional relationship between a response variable and one or more explanatory variables is used to monitor the quality of a product or process appear to be common in practice. This relationship usually is referred to as profile with parameters that are rarely known and have to be estimated prior to starting online monitoring. Phase II initiates after a statistically in-control condition is established, and parameters of the underlying distribution are estimated. It is obvious that phase II analysis of control charting is affected by errors in the estimated parameters. In this paper, the effect of estimation error on phase II analysis of simple linear profiles is studied. The in-control and out-of-control performance of the exponentially weighted moving average (EWMA)-3 method are evaluated using average run length (ARL) criterion. Overall, the in-control ARL in average decreases about 96.7 % when we have m = 100 samples in phase I to estimate the parameters. This value reduces to 2.4 % for m = 900 for a fixed sample size of n = 4. The behavior of the EWMA-3 chart in the out-of-control situation totally depends on the direction of the occurring shifts and whether the ill-estimated parameter is overestimated or underestimated.
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Noorossana, R., Aminmadani, M. & Saghaei, A. Effect of phase I estimation error on the monitoring of simple linear profiles in phase II. Int J Adv Manuf Technol 84, 873–884 (2016). https://doi.org/10.1007/s00170-015-7078-2
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DOI: https://doi.org/10.1007/s00170-015-7078-2