Name
Title | ||
|---|---|---|
Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables. |
Abstract | ||
|---|---|---|
Statistical Process Control monitoring of the ratio Z of two normal variables X and Y has received too little attention in quality control literature. Several applications dealing with monitoring the ratio Z can be found in the industrial sector, when quality control of products consisting of several raw materials calls for monitoring their proportions (ratios) within a product. Tables about the statistical performance of these charts are still not available. This paper investigates the statistical performance of a Phase II Shewhart control chart monitoring the ratio of two normal variables in the case of individual observations. The obtained results show that the performance of the proposed chart is a function of the distribution parameters of the two normal variables. In particular, the Shewhart chart monitoring the ratio Z outperforms the (p=2) multivariate T-2 control chart when a process shift affects the in-control mean of X or, alternatively, of Y and the correlation among X and Y is high and when the in-control means of X and Y shift contemporarily to opposite directions. The sensitivity of the proposed chart to a shift of the in-control dispersion has been investigated, too. We also show that the standardization of the two variables before computing their ratio is not a good practice due to a significant loss in the chart's statistical performance. An illustrative example from the food industry details the implementation of the ratio control chart. Copyright (c) 2013 John Wiley & Sons, Ltd. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1002/qre.1558 | QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL |
Keywords | Field | DocType |
Statistical Process Control,Shewhart control chart,ratio,standardization,average run length | Econometrics,Control limits,X-bar chart,EWMA chart,ar x and R chart,u-chart,Control chart,Chart,Engineering,Statistics,Shewhart individuals control chart | Journal |
Volume | Issue | ISSN |
30 | 8 | 0748-8017 |
Citations | PageRank | References |
2 | 0.48 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Giovanni Celano | 1 | 92 | 12.38 |
| Philippe Castagliola | 2 | 529 | 61.65 |
| Alireza Faraz | 3 | 2 | 0.48 |
| Sergio Fichera | 4 | 102 | 11.40 |