Statistical Process Control by the Quotient of Two Correlated Normal Variables

Öksoy, Dolun; Boulos, E. N.; Pye, L. D.

doi:10.1080/08982119308918717

Cited by 21 publications

(14 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Oksoy et al . discuss some useful guidelines to design and implement a control chart monitoring the ratio Z = X/Y of two normal variables when a set of N Phase I samples are available from a stable process.…”

Section: The Rz‐shewhart Control Chart For the Ratiomentioning

confidence: 99%

“…Oksoy et al 19 discuss some useful guidelines to design and implement a control chart monitoring the ratio Z = X/Y of two normal variables when a set of N Phase I samples are available from a stable process. To avoid problems related to the estimation of vector μ W0 and Σ W0 , which is out of the scope of our paper, we compute the statistical properties of the RZ-Shewhart chart only for the Phase II condition, by assuming μ W0 and Σ W0 as perfectly known.…”

Section: The Rz-shewhart Control Chart For the Ratiomentioning

confidence: 99%

See 1 more Smart Citation

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Celano

Castagliola

Faraz

et al. 2013

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

Section: The Rz‐shewhart Control Chart For the Ratiomentioning

confidence: 99%

Section: The Rz-shewhart Control Chart For the Ratiomentioning

confidence: 99%

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Celano

Castagliola

Faraz

et al. 2013

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…Spisak and Davis and Woodall introduced an example coming from an unemployment insurance quality control program. Öksoy et al proposed a set of guidelines for the implementation of Shewhart‐type control charts to perform online monitoring in the glass industry. Recently, Celano et al studied the statistical properties of a Shewhart chart for individual measurements (denoted as Shewhart‐RZ control chart), monitoring the ratio of 2 normal variables.…”

Section: Introductionmentioning

confidence: 99%

Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

Tran

Knoth

2018

Quality & Reliability Eng

View full text Add to dashboard Cite

Very recently, control charts for monitoring the ratio of 2 normal variables have been investigated in statistical process control. In the two‐sided case, however, these control charts tend to be average run length (ARL) biased, in the sense that some out‐of‐control ARL values are larger than the in‐control ARL. This paper proposes an ARL‐unbiased EWMA control chart for monitoring of this kind of ratio with each subgroup consisting of n⩾1 sample units. Also, to study the long‐term properties of ARL‐unbiased EWMA‐RZ control chart, we investigate the steady‐state ARL. Several tables and figures are given to show the statistical properties of the proposed control charts. The comparison results show that the proposed ARL‐unbiased chart outperforms other two‐sided control charts in terms of the zero‐state and steady‐state ARL. An example illustrates the use of this chart on a real quality control problem from the food industry.

show abstract

“…A control chart monitoring the ratio of two random variables has been discussed by Spisak and Davis and Woodall, who investigated an example coming from an unemployment insurance quality control program. This topic has also been discussed by Oksoy, Boulos, and Pye who proposed a set of guidelines for the implementation of Shewhart type control charts to perform on‐line monitoring in the glass industry, where the glass oxide composition versus its density is an important quality characteristic. Very recently, Celano et al .…”

Section: Introductionmentioning

confidence: 99%

Monitoring the Ratio of Two Normal Variables Using EWMA Type Control Charts

Tran

Castagliola

Celano

2015

Qual. Reliab. Engng. Int.

View full text Add to dashboard Cite

In many fields, there is the need to monitor quality characteristics defined as the ratio of two random variables. The design and implementation of control charts directly monitoring the ratio stability is required for the continuous surveillance of these quality characteristics. In this paper, we propose two one‐sided exponentially weighted moving average (EWMA) charts with subgroups having sample size n > 1 to monitor the ratio of two normal random variables. The optimal EWMA smoothing constants, control limits, and ARLs have been computed for different values of the in‐control ratio and correlation between the variables and are shown in several figures and tables to discuss the statistical performance of the proposed one‐sided EWMA charts. Both deterministic and random shift sizes have been considered to test the two one‐sided EWMA charts' sensitivity. The obtained results show that the proposed one‐sided EWMA control charts are more sensitive to process shifts than other charts already proposed in the literature. The practical application of the proposed control schemes is discussed with an illustrative example. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

Statistical Process Control by the Quotient of Two Correlated Normal Variables

Cited by 21 publications

References 5 publications

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Statistical Performance of a Control Chart for Individual Observations Monitoring the Ratio of Two Normal Variables

Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

Monitoring the Ratio of Two Normal Variables Using EWMA Type Control Charts

Contact Info

Product

Resources

About