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Albright, T. L. and H. Roth. 1993. Controlling quality on a multidimensional level. Journal of Cost Management (Spring): 29-37.

Summary by Lorrie Ramirez
Master of Accountancy Program
University of South Florida, Summer 2002

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The purpose of this article is to show that multivariate control charts are more helpful and produce more complete information than univariate charts when multiple variables are being measured simultaneously. In addition, this article presents the various types of processes and activities that SPC charts can be applied to.

Statistical Process Control Charts

Statistical process control charts are a widely used quality management tool because they can be applied in many different situations. When maintained in real time, these charts provide an early warning about quality problems. Most cost management and accounting literature focuses on control charts with only a single variable, even though many variables can be measured for the same process.

Univariate (one-variable) charts measure only one characteristic, while multivariate (many-variable) charts monitor more than one characteristic simultaneously. A single variable control chart can, under certain conditions, give misleading information when multiple variables are being measured concurrently. This article shows how a multivariate control chart can be used to acquire more useful information about a process or activity when more than one characteristic is monitored at once.

Control Chart Elements

An SPC chart is a graph that shows the measurements of some characteristic of interest. This characteristic can be a qualitative or a quantitative attribute. In general, SPC charts possess the following elements:

Center line, or process average, surrounded by individual observations.

Upper and lower control limits (three standard deviations from the short-term process average).

Horizontal axis that identifies observations and preserves the time order of their collection.

Vertical axis scaled to the values of the observations.

SPC charts are used to identify points that differ from the process average as well as to reveal shifts in the process. If the points (observations) in a chart fall within the upper and lower limits then the process is considered to be in statistical control. If an observation falls outside of the control limits or a run is detected in the data then the process is considered to be out of control. (A run is a series of consecutive points above or below the center line). An investigator tries to discover the source of variation and determine a remedy by evaluating the existing conditions when a process is considered out-of-control.

Uses of SPC Analysis

Though SPC isn’t the only quality management tool, it is important that managers and employees understand its possible applications.

Generally, SPC can be used in three ways:

1. Helping to control the quality of repetitive manufacturing processes.

2. Evaluating the performance of processes and activities.

3. Measuring the quality of accounting and other administrative processes.

As mentioned earlier, SPC charts can be used to monitor quality in repetitive manufacturing processes. Production employees and machine operators are often responsible for maintaining control charts for these processes; thus, they need to understand the statistical basis for the chart’s validity. In addition, managers and others in the organization need to have a basic understanding of the charts to have a greater appreciation of the quality control efforts of the production function.

A control chart can also be used to evaluate the non-financial aspects of various processes and activities (i.e. cycle time, schedule attainment, machine availability, defect rate, etc.). Performance measurement is a recurring part of the accounting function. Employees in this area should have an understanding of the control chart and how they can help in evaluating performance.

Administrative processes, especially repetitive ones, are also candidates for SPC (i.e. payroll, accounts payable, accounts receivable). If SPC is used, personnel would gain a greater understanding of the natural variability in the processes and of how reducing variation could result in better services.

The Multivariate Control Chart

A multivariate control chart should be used to obtain more complete information about the state of control when more than one variable is being measured simultaneously. The purpose of this chart is to determine if the variation present in a process is attributable to unusual influences. This chart measures several variables at once and sends out a signal when the relationship among the variables changes unexpectedly.

Differences Between Multivariate and Univariate Charts

Three main differences occur between multi- and univariate control charts:

1. Calculating the data point to be plotted on the chart - points plotted on a univariate control chart for averages are the sample means. In a multivariate control chart based on samples, the points plotted are a quadratic form of the means of the measurements in each sample.

2. Calculating the control limits - there is only an upper control limit in a multivariate control chart due to the way the observations are calculated.

3. Investigating out-of-control points - in a multivariate control chart, the investigator must first determine which characteristic caused the process to be out-of-control. This is not necessary in a univariate control chart because only one characteristic is measured.

Multivariate Charts Complement Univariate Charts

Both multivariate and univariate charts should be used together because they complement each other. The univariate chart signals when an observation falls outside of the upper and lower control limits. The multivariate chart sends out a signal when an imbalance exists among the variables. This shows that when multiple variables are concurrently monitored for the same process or activity, the best and most complete information is generated when using the two charts in conjunction with one another.

Advantages of Multivariate Charts

Provides an out-of-control signal when the variables move in a direction that is unexpected.

Indicates whether this variation is statistically significant.

Easier to examine than multiple univariate charts simultaneously.

Detects differences in the degree of movement away from a process average.

May detect subtle changes in the relationships among the variables that would not be noticeable from separate univariate charts.

Allows users to evaluate the system as a whole rather than the sum of many individual parts.

Requires no additional data if the data currently are accumulated for univariate control charts.


Related summaries:

Albright, T. L. and H. P. Roth. 1994. Managing quality through the quality loss function. Journal of Cost Management (Winter): 20-37. (Summary).

Deming, W. E. 1993. The New Economics for Industry For Industry, Government & Education. Cambridge: Massachusetts Institute of Technology Center for Advanced Engineering Study. Chapter 10. (Summary).

Francis, A. E. and J. M. Gerwels. 1989. Building a better budget. Quality Progress (October): 70-75. (Summary).

Holmes, D. S. and R. E. Hurley. 2003. How SPC enhances budgeting and standard costing - Another look. Management Accounting Quarterly (Fall): 57-62. (Summary).

Kim, M. W. and W. M. Liao. 1994. Estimating hidden quality costs with quality loss functions. Accounting Horizons (March): 8-18. (Summary).

Lucier, G. T. and S. Seshadri. 2001. GE takes six sigma beyond the bottom line. Strategic Finance (May): 40-46. (Summary).

Martin, J. R. Not dated. Summary of the 1992 PBS Program Quality or Else. Management And Accounting Web.

Martin, J. R. Not dated. What is Six Sigma? Management And Accounting Web.

Nolan, T. W. and L.P. Provost. 1990. Understanding Variation. Quality Progress (May): 70-78. (Summary).

Reeve, J. M. 1989. The impact of variation on operating system performance.Proceedings of the Third Annual Management Accounting Symposium. Sarasota: American Accounting Association: 75-89. (Summary).

Roehm, H. A., L. Weinstein, and J. F. Castellano. 2000. Management control systems: How SPC enhances budgeting and standard costing. Management Accounting Quarterly (Fall): 34-40. (Summary).

Roth, H. P. and T. L. Albright. 1994. What are the costs of variability? Management Accounting (June): 51- 55. (Summary).

Taguchi, G. and D. Clausing. 1990. Robust quality. Harvard Business Review (January-February): 67-75. (Summary).

Walter, R., M. Higgins and H. Roth. 1990. Applications of control charts. The CPA Journal (April): 90-93, 95. (Summary).