Applications of control charts. (charts used for analyzing repetitive processes)by Roth, Harold P.
Editor's Note: We were at a bit of a loss to decide in which department the following article on control charts should appear. As you will see, the use of control charts crosses disciplinary lines. So somewhat arbitrarily the material is presented here.
U.S. companies have recently become more quality conscious as they try to compete in the current economic environment. To remain competitive, many companies have implemented statistical methods to improve quality and maintain control over manufacturing processes. Although the term "quality control" is often referred to in the context of a manufacturing environment, accounting processes can also benefit from the application of statistical quality control techniques. Thus, if accountants understand the statistical methods used in quality control, they may be able to use them to improve accounting procedures as well as their company's or client's manufacturing processes.
Specifically, this article examines the use of "control charts" for analyzing and controlling accounting processes. Control charts are graphic illustrations of data collected from a process over time, thereby providing running records of performance. Examples of accounting processes where control charts are useful include the issuance of invoices and other accounting documents, the preparation of tax returns, and various auditing processes. Benefits of using control charts to monitor accounting processes include higher quality services, reduced costs, and higher profitability.
How Control Charts Work
Control charts are useful for analyzing and controlling repetitive processes because they help to determine when corrective actions are needed. Because they display running records of performance, control charts provide numerous types of information to management. For example, control charts are useful for:
1. Pinpointing errati or unpredictable processes;
2. Obtaining warning of impending trouble, such as an unexpected change in a process;
3. Evaluating product (service) consistency over time;
4. Decreasing performance variability in a process, thereby decreasing the level of post-process inspection of the output generated by the process;
5. Determining the cause of trouble when a process is generating output which has errors and mistakes; and
6. Knowing when a process is doing the best that can be expected from it.(1)
A control chart is a graph that contains a centerline, and upper and lower control limits. The centerline represents the process average. The control limits represent the upper and lower boundaries of acceptability around the centerline. The horizontal axis represents sample numbers or points in time, and the vertical axis represents measurements from samples.
Control charts are usually based on data collected from samples of a process. After a sufficient number of samples are drawn and the data is plotted on a control chart, the stability of the process is evaluated. A process which is stable is deemed to be "in control" whereas an "out of control" process is unstable, and therefore, unpredictable. Figure 1 illustrates the difference between a process that is in control and processes that are out of control.
In Figure 1, Part A, the process is in statistical control. The sample measurements are within the control limits and appear to be randomly distributed around the centerline. The off-centerline (off-average) points are caused by common, unavoidable variation which is always present and part of the process. The area between the upper control limit (UCL) and the lower control limit (LCL) represents the band of normal variability for the process.
The process illustrated in Figure 1, Part B, is out of control because numerous points lie outside the control limits. These out of control points represent "special" or "assignable" causes of variation that should be investigated. An investigation of these points may show that process conditions changed around the time the sample was taken and may lead to the discovery of the problem causing the process to be unstable.
Figure 1, Part C, also illustrates an out of control process. Although all measurements are inside the control limits, long runs of points on either side of the centerline indicate that a process shift has occurred. Thus, one or more assignable causes of variation exist, and an investigation is needed to determine the cause of the process shift. After the cause is determined, appropriate action can be taken to bring the process back into statistical control.
Types of Control Charts
Before control charts can be used to help control an accounting process, the type of chart to use must be determined and then samples for measurement collected. Selection of the proper control chart depends upon the nature of the process and the type of data to be collected from the samples. If the wrong type of chart is used for a particular measurement, the results will be either meaningless or misleading.(2)
The following section contains four different applications of control charts to accounting processes. Table 1 provides an overview of each case, including: (1) the accounting process being evaluated; and (2) the measurements taken from the process, which are graphed on a control chart.
Control charts provide the greatest benefits in large-scale, repetitive processes. The following examples illustrate the application of control charts to some typical accounting, auditing, and tax processes. Of course, a cost/benefit analysis should be made before deciding whether to implement control charts for a given accounting process.
Case 1--Internal Auditing. A function of internal auditing is to determine the extent to which company policies and procedures are being followed. Since many of the procedures are repetitive, internal auditors can use control charts to monitor various accounting processes throughout the year. Processes that can be monitored via control charts include payroll accounting, invoice payments, and revenue collection. Payroll accounting is illustrated here.
The repetitive procedures involved in payroll accounting include the proper authorization of overtime, approval of time records, and checks on the calculation of gross pay and payroll deductions. To ensure that the internal controls over these procedures are in effect throughout the year, internal auditors might sample individual employee pay records during each pay period. For each employee pay record in a sample, the internal auditors would verify documentation of the required authorizations and approvals. A missing authorization or approval constitutes an audit exception or nonconformity.
To construct a control chart for this process, the number of audit exceptions for each sample is counted and graphed, as illustrated in Figure 2.
This control chart provides a visual picture of the internal control over the payroll process for 20 successive pay periods. By examining the control chart, an internal auditor can evaluate whether the internal controls are in effect. Out of control points, such as samples (6) and (15), represent unexpected changes in the payroll process and warrant immediate investigation. Possible assignable causes for these out of control points may be the hiring of a new employee or the rotation of job responsibilities. If the problem is due to one of these causes, additional training or education for the employee should prevent such errors from occurring in the future.
Although Figure 2 illustrates an out of control situation, a control chart which is in control may also provide information that can be used to improve internal controls. For example, the average number of exceptions per sample (the centerline) in Figure 2 is two. Since the number of exceptions per sample should be low, the internal auditor can evaluate whether two exceptions per sample is excessive. If so, the auditor should recognize that the payroll authorization process must be changed since the current process is centered around an average of two exceptions. Changing the process is management's responsibility, but the internal auditor should be able to use the control chart to illustrate that a problem exists.
Case 2--Customer Billing. Control charts may also be useful in helping a firm improve its financial position. For example, one method of improving cash position is to speed up collections from customers. Reducing the amount of time between the point that goods (services) are provided and the point that customers are billed is a key step in speeding up collections.
In using control charts to evaluate the customer billing process, a company may periodically draw random samples of invoices. For each invoice, the amount of time between the delivery date and billing date is measured. As illustrated in Figure 3, Part A, the amount of variation in billing time within samples of invoices is graphed on a control chart. The average billing time for the sample as a whole is graphed on a second control chart, as shown in Figure 3, Part B.
To evaluate the customer billing process, both control charts must be considered. The first control chart is used to evaluate changes in variation in the billing process from sample to sample. The centerline represents the standard amount of variation in billing time for a sample of invoices. This chart is inspected first, since a change in variation may be the cause of a change in the average billing time. In Figure 3(a), the chart is in control, and therefore, the process variation is stable. If the chart had been out of control, an investigation would be needed to determine what caused the excessive variation in the out of control samples.
If the process variation is stable, the process average should then be evaluated. The second control chart shows shifts in the average billing time from sample to sample. The centerline on this chart represents the standard amount of time between delivery and billing. As shown in Figure 3(b), the standard billing time for this company is five days. Samples (9) and (18) represent out of control points. Perhaps employee illness or vacations caused the billing delays during these time periods.
Case 3--Tax Return Preparation. Although the preceding illustrations have focused on accounting procedures within a company, public accountants can also use control chart techniques for evaluating internal controls of audit clients or for evaluating their firm's internal billing process. In addition, public accounting firms may also find unique uses for control charts, such as in tax return preparation. For example, if computers are used for preparing tax returns, the accountant takes information provided by the taxpayer and transfers it to computer input sheets. The input sheets may be sent to a tax service which generates the tax return, or the return may be generated in-house. Improper completion of an input form results in an incorrect tax return, and the process must be repeated. The end result is lower profits for the firm.
The preparation of computer input forms is a process that can be graphed on control charts. The main issue is whether or not the input forms are correct; the number of errors on the forms is not as important since even a single error results in an unusable tax return. An appropriate control chart for this type of process displays the fraction defective for each sample of tax returns, as illustrated in Figure 4.
To evaluate the performance of the firm's personnel, each preparer's output can be graphed on a separate control chart. The centerline on each chart represents the percentage of defective tax returns expected of a competent person. If this is used as the standard, the firm will assess the accuracy of each preparer against it. If an out of control point occurs, the reason should be investigated. For example, suppose that the first point and every sixth point thereafter (as in Figure 4) falls above the upper control limit on the control chart of a particular preparer. Investigation may lead to the discovery that these out of control points occur every Monday (assuming a six-day work week during tax season). The firm should counsel the employee concerning this finding and try to learn why there are more errors on Mondays than on other days of the week. Once the cause is known, the employee may be able to avoid these out of control points in the future.
Case 4--Travel and Entertainment Expenses. Organizations can use control charts to manage costs and expenses. Effective monitoring of expenses includes controls that ensure that expenses are properly authorized and documented, and controls that monitor the level of expenses.
Travel and entertainment is an expense that should be monitored for both cost control and tax reasons. Selection of the appropriate control chart depends upon whether the primary focus is on monitoring the level of expenses, or on monitoring whether travel and entertainment expenses have been properly authorized and documented.
To monitor authorization and documentation, a company can take samples of travel and entertainment expense vouchers on a monthly basis. Each voucher would be examined to verify that the expenses were properly authorized and that proper documentation is attached. If a voucher has incomplete documentation or a missing authorization, it represents a nonconformity.
For example, suppose that the sample size is 50 vouchers. The number of nonconforming vouchers per sample is graphed on a control chart, as shown in Figure 5. This figure illustrates an out of control process where the control limits are centered around an average of three per sample. The one out of control point may be due to the hiring of several new salespeople who were misinformed as to the proper procedures for submitting travel vouchers. As soon as the out of control point appears and the cause is determined, the salespeople should be advised of the proper procedures.
The examples presented here illustrate only four possible applications of control charts to accounting processes. Many other accounting and financial processes which are repetitive in nature can also be evaluated using similar charts.(3) These processes might include:
1. Number of invoices processed per period;
2. Time required to prepare a monthly statement;
3. Average age of accounts receivable;
4. Number of purchase discounts lost; and
5. Sales returns per salesperson, when commissions are based on the amount of gross sales.
Once accountants learn the basics of statistical quality control and how easy control charts are to prepare, they can readily identify other repetitive processes involved in the accounting function in which control charts will be useful as a control technique.
Benefits of Understanding Control Charts
Because many manufacturers are now using control charts to evaluate their processes, accountants have to understand statistical process control if they are going to continue to provide maximum services to their employers or clients. In addition, accountants will undoubtedly find many uses for control charts within their departments or firms. If the quality of accounting processes is improved by using statistical methods, firms should experience higher profitability. This increase in profitability will occur because of an increase in the quality of accounting services and a reduction in the costs incurred to provide the services. To remain competitive in today's environment, all departments, including accounting, must try to provide high quality services and products at the lowest possible cost. Figures 1 to 5 Omitted Tabular Data 1 Omitted
(1)For a detailed list of typical control chart applications, see Irving W. Burr, Statistical Quality Control Methods (New York: Marcel Dekker, Inc., 1976). (2)For additional information on specific control charts, see Irving W. Burr, Statistical Quality Control Methods (New York: Marcel Dekker, Inc., 1976), and Eugene L. Grant and Richard S. Leavenworth, Statistical Quality Control, 5th ed. (New York: McGraw-Hill Book Company, 1980). (3)For some examples of applications of control charts in financial management see James M. Reeve and John W. Philpot, "Applications of Statistical Process Control for Financial Management," Journal of Cost Management for the Manufacturing Industry (Fall 1988), pp. 33-40.
Richard M. Walter, Assistant Professor of Accounting Texas Tech University, Lubbock, TX; Mark M. Higgins, Assistant Professor of Accounting, University of Rhode Island, Kingston, RI; and Harold P. Roth, Associate Professor of Accounting, The University of Tennessee, Knoxville, TN
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