Estimating missing values from negligible interactions in factorial designs

Xampeny, Rafel; Cintas, Pere Grima; Tort‐Martorell, Xavier

doi:10.1002/qre.2172

Cited by 6 publications

(8 citation statements)

References 14 publications

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“…For example, if the values of the randomly generated effects in scenario S8 3 then, by assessing their significance by means of their representation in a Normal Probability Plot (NPP) (Figure 1, left), the effects that are truly different from 0 (A, B, and C) appear as significant, and therefore, in this case, no error would be made.…”

Section: Simulation Scenariosmentioning

confidence: 99%

“…Another problem with this procedure is that the estimation of missing values is not always possible. For example, if in a 2 3 design there were two missing values and the interactions BC and ABC could be considered negligible, we would have 28 possible pairs of missing values, and only the values of 16 of them could be estimated. Table 2 shows the contrasts associated with interactions BC and ABC.…”

Section: Introductionmentioning

confidence: 99%

“…Additionally, as said above, when some response values have been estimated, the effects are not independent. Following with the previous example we have TABLE 1 Contrasts and responses for a 2 3 design…”

Section: Introductionmentioning

confidence: 99%

“…In addition, when there is more than one missing response, the variances of the estimated values depend on which those responses are and also on the interactions used for their estimation. In Xampeny et al, it is shown that if in a 2 4 design, the five interactions of three or more factors can be considered negligible, there will be 4368 possible quintets of missing responses, of which it is impossible to estimate the values of 1360 of them due to their systems of equations being inconsistent. For the combinations that can be estimated, there are notable differences in the variances of the estimated values, depending on the missing responses.…”

Section: Introductionmentioning

confidence: 99%

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Consequences of using estimated response values from negligible interactions in factorial designs

Xampeny

Cintas

Tort‐Martorell

2018

Quality & Reliability Eng

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This article analyzes the increase in the probability of committing type I and type II errors in assessing the significance of the effects when some properly selected runs have not been carried out, and their responses have been estimated from the interactions considered null from scratch. This is done by simulating the responses from known models that represent a wide variety of practical situations that the experimenter will encounter; the responses considered to be missing are then estimated, and the significance of the effects is assessed. Through comparison with the parameters of the model, the errors are then identified. To assess the significance of the effects when there are missing values, the Box‐Meyer method has been used. The conclusions are that one missing value in eight run designs, and up to three missing values in 16 run designs experiments can be estimated without hardly any notable increase in the probability of error when assessing the significance of the effects.

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Section: Simulation Scenariosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Consequences of using estimated response values from negligible interactions in factorial designs

Xampeny

Cintas

Tort‐Martorell

2018

Quality & Reliability Eng

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“…Factorial designs with missing values are examined by Xampeny, Grima, and Tort-Martorell, 4 where a solution when interactions are negligible is proposed to deduce missing values.…”

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confidence: 99%

The ENBIS‐16 quality and reliability engineering international special issue

Bergquist

Colosimo

2017

Quality & Reliability Eng

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Grazia Vicario (Politecnico di Torino) chaired the Programme Committee, and Eleanor Stillman (University of Sheffield) chaired the Organizing Committee. The abstracts of all oral and poster presentations, in most instances accompanied by full papers and presentation slides, are available on the ENBIS website (www.enbis.org).The 2017 special issue of Quality and Reliability Engineering International is a result of the call for papers announced during the ENBIS-16 conference. All the submitted papers were peer-reviewed by 2 anonymous referees before being accepted for publication in this special issue. This special issue covers advances in statistical methods from an industrial and business perspective, as is the purpose of ENBIS. Most of the papers focus on manufacturing, starting from product design, moving to process optimization and control, and eventually arriving to end-of-life performance, as briefly summarized in the following.Product design and development is considered in the first 2 papers. In particular, Halabi, Kenett, and Sacerdote, 1 propose dynamic Bayesian networks as a tool to integrate information from multiple sources to calculate risks at different product development stages. Hejazi and Esfahani 2 consider challenge of multistagemultiresponse problems in gear manufacturing with special attention to the design stage, where stresses affecting the mechanical component have to be taken into account. It is specifically shown that robust estimation of surfaces perform better than ordinary least squares regression.Acceptance testing is faced by Santos-Fernández, Govindaraju, and Jones, 3 where consumer risks of imperfect testing is considered in different scenarios of a presence-absence sampling plans used in the food industry to determine whether a batch of food is contaminated.Factorial designs with missing values are examined by Xampeny, Grima, and Tort-Martorell, 4 where a solution when interactions are negligible is proposed to deduce missing values.Motivated by a real semiconductor problem, Zappa and Borgoni 5 propose a method to extract a subgrid from an initial monitored network to effectively maintain the spatial representativeness.Multistage reliability and multistage-multiresponse problems are faced in 2 papers. In the first paper, Moslemi and Esfahani 6 consider the manufacturing challenge of multistage processes in gear production. Multistage processes require special considerations for experimenters, and here, a robust estimation of surfaces is found to perform better than ordinary least squares regression in these cases. In the second paper, Hejazi 7 presents an approach to optimize multiple quality metrics of a multistage system that considers the stochastic behaviour of input, intermediate, and output variables via stochastic programming.Problems affecting traditional control charts design when the data sampling sequence is relevant (ie, data are not random) are examined and commented by Shper and Adler. 8 They review the possible drawbacks and suggest a new test for data randomness....

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