# Statistical Process Control for a Limited Amount of Data

### José Gomes Requeijo, António Abreu, Ana Sofia Matos

#### Abstract

Some production systems control many quality characteristics with a restricted amount of data, not allowing a convenient estimation of the process parameters (mean and variance), thereby creating a difficulty in implementing the traditional Statistical Process Control (SPC). In order to address this question, the approach suggested is to adopt the developments proposed by by Charles Quesenberry, which consists in the statistics sample transformation at time i. This transformation is based on a parameter estimation at time (i – 1). This paper addresses two situations, the univariate and multivariate SPC, with the use of Q dimensionless statistics. Both univariate (Q) and multivariate (MQ) statistics are distributed according to standard Normal distribution. It is also suggested the application of new capability indices QL and QU to study the univariate process capability, which are represented in the mean Q control chart to evaluate in real time the performance of the various processes and predict the possibility of production of nonconforming product, which will increase customer satisfaction. The methodology is applicable to different production systems, both for industry and services. Based on a methodology developed, a case study is presented and discussed.

#### References

- Bothe, D. R., 1988. SPC for Short Production Runs, Quality, Vol. 27, pp. 58-59, 1988.
- Montgomery, D. C., 2012. Introduction to Statistical Quality Control, 7th Edition, John Wiley & Sons, Inc., New York.
- Pereira, Z. L. e Requeijo, J. G., 2012, Quality: Statistical Process Control and Planning, 2th Edition, Fundation of FCT/UNL, Lisbon (in portuguese).
- Pyzdek, T., 1993. Process Control for Short and Small Runs, Quality Progress, Vol. 26(4), pp. 51-60, 1993.
- Quesenberry, C. P., 1997. SPC Methods for Quality Improvement, John Wiley & Sons, Inc., New York.
- Shewhart, W. A., 1931. Economic Control of Quality of Manufactured Product, D. Van Nostrand Company, Inc., New York.
- Wheeler, D. J., 1991. Short Run SPC, SPC Press, Knoxville, Tennessee.

#### Paper Citation

#### in Harvard Style

Gomes Requeijo J., Abreu A. and Matos A. (2014). **Statistical Process Control for a Limited Amount of Data** . In *Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-017-8, pages 190-195. DOI: 10.5220/0004812101900195

#### in Bibtex Style

@conference{icores14,

author={José Gomes Requeijo and António Abreu and Ana Sofia Matos},

title={Statistical Process Control for a Limited Amount of Data},

booktitle={Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2014},

pages={190-195},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004812101900195},

isbn={978-989-758-017-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Statistical Process Control for a Limited Amount of Data

SN - 978-989-758-017-8

AU - Gomes Requeijo J.

AU - Abreu A.

AU - Matos A.

PY - 2014

SP - 190

EP - 195

DO - 10.5220/0004812101900195