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Analyzing machine efficiency.

Manufacturing companies must provide quality products at low prices if they hope to survive in today's global economy. The production of competitive products requires continuous progress toward the objectives of total quality control and maximum productivity.

Unfortunately, traditional accounting techniques have limited relevance to both objectives. Recognizing this fact, many accountants have directed their attention toward innovative approaches to confront the rising tide of international competition. Just in time (JIT) inventory, activity based costing (ABC) and total quality management (TQM) are three widely recognized examples.

While these developments have made significant contributions, there is still room for innovative applications. The competitive markets demand their development and deployment. Toward this end, we offer the following suggestions for analyzing productivity at the factory level.

Accountants in the past seldom analyzed productivity in a manner that facilitated the management of automated factories. They tended to focus their attention on human performance. For example, accountants often used labor cost or labor hours as the base to measure productivity or to allocate overhead cost.

As the manufacturing process has become increasingly automated, machine intensive operations have gradually replaced the human labor force. With these changes, the relative importance of traditional accounting approaches have declined proportionately. What is needed are analytical techniques that focused on machine efficiency.

It is important to distinguish analytical techniques that are designed to measure machine efficiency from those applied to capital budgeting. Accountants have developed sophisticated techniques to facilitate capital investment decisions. Return on investment, internal rate of return and present value are powerful tools for financial analysis that help managers decide whether or not to invest in particular types of machinery. However, once the decision to invest has been made, these financial techniques offer no insight regarding the effectiveness of operating the machinery.

To improve productivity in the age of factory automation, accountants must provide factory executives with analytical information on machine performance. Readers should also note that machine performance affects product quality. Therefore, factory executives can enhance productivity and product quality by monitoring machine performance with improved accounting information.

The following section of this paper proposes an analytical methodology to measure machine productivity. Some of the ideas suggested originate from Taiwanese practices in managerial accounting. While observing Asian practices, we found many accounting reports consisting of non-financial data. These nontraditional data reports were used by the Taiwanese accountants to support operating controls. We have identified the techniques used to prepare these reports and present them in a form that should be familiar to Western accountants.

Measures of Machine Capacity

It is important to note that the objective function shifts from minimization to maximization when machines rather than humans are being evaluated. For example, a manager using traditional forms of variance analysis establishes rate and efficiency standards for the labor that is required to produce a given product. Favorable variances occur when actual rates or quantities are less than the standards. In other words, employees are encouraged to minimize the cost and quantity of labor used in production.

In contrast, when production is greater, favorable conditions exist when machine usage is greater than expected. Ideally, machines should operate at full capacity. The number of machines required to satisfy a certain level of demand is minimized when the machines run at full capacity. For example, suppose a particular type of machine can produce 1,000 units of product per hour. If production requirements are 5,000 units per hour, five machines operating at full capacity would be required to meet demand. However, if the machines are operated at 62.5% of capacity, eight machines would be required (i.e., 1,000 x .625 x 8 = 5,000); ten machines would be required if they were operated at 50% of capacity (i.e., 1,000 x .50 x 10 = 5,000); and so on. Accordingly, the number of machines and the resultant cost of machinery is minimized when the machines are operated at full capacity. The following analytical techniques are designed to measure machine efficiency in terms of utilized capacity with 100% considered ideal.

Analysis of machine efficiency begins with the definitions of differing levels of capacity. Three capacity measures are commonly used:

* Theory Capacity represents the maximum attainable output assuming that the machine is operated at the fastest possible running speed on a continuous basis (i.e., 24 hours per day). Since theory capacity assumes ideal operating conditions, it may also be referred to as ideal capacity.

* Full Capacity is the level of output attained when the machine is operated at the standard running speed on a continuous basis (i.e., 24 hours per day). This level of production recognizes the fact that machinery is not normally operated at the maximum attainable speed. Even though most automobiles will run in excess of 100 miles per hour, few people actually operate their vehicles at such speeds. Similarly, few manufacturers operate their machinery at maximum speed. Full capacity recognizes practical limitations by setting running speed at the expected level of operations which is referred to as the standard running speed.

* Standard Capacity recognizes the fact that machinery may not be operated on a continuous basis. It represents the level of output that can be attained during the standard running time when equipment is operated at the standard running speed.

It is important to recognize that all three of these measures represent potential capacity. Actual production based on actual running speed at actual running time will differ from any of the capacity measures.

To illustrate computations for the three capacity measures and a hypothetical level of actual production, assume that a machine has a maximum operating speed of 100 pieces per hour, a standard operating speed of 95 pieces of product per hour and an actual operating speed of 90 pieces of product per hour. Further, assume that the standard running time is sixteen hours per day and that actual running time is fourteen hours per day. Using these figures, the three capacity measures and actual production would be computed as follows:

Theory Capacity: 100 pcs/hr x 24 hr/day = 2,400 pcs/day

Full Capacity: 95 pcs/hr x 24 hr/day = 2,280 pcs/day

Standard Capacity: 95 pcs/hr x 16 hr/day = 1,520 pcs/day

Actual Production: 90 pcs/hr x 14 hr/day = 1,260 pcs/day

Utilization Of Machine Capacity

The key managerial issue centers on the amount of capacity that is actually being used. Ideally, actual production would constitute 100% of theory capacity. However, this scenario is highly unlikely. Normally, actual production will fall short of any of the three capacity measures. The relationship between actual production and each of the three capacity measures can provide useful insights to management.

The first measure analyzed is the level of actual production as a percent of theory capacity. In this illustration, actual production constitutes 52.5% of theory capacity (i.e., 1,260/2,400). This means that actual production constituted only slightly more than half the ideal level of productivity. This result is tempered by the fact that no one truly expects to attain the ideal standard. Theory capacity provides a picture of a perfect world that can be used as a managerial vision. An analogy would be having a vision of the perfect spouse, job, home, etc. Managers need visions of perfection to act as directional guideposts. However, more realistic expectations are needed to effectively assess the utilization of resources.

Viewing actual production as a percentage of full capacity provides a better measure of attainable productivity. Using the data outlined above, actual production constitutes 55.3% of full capacity (i.e., 1,260/2,280). The most significant factor associated with the relatively low level of utilization appears to be the continuous operating assumption. Operating 24 hours per day requires three regular eight-hour shifts. Management may choose for a variety of reasons not to operate the factory on a continuous basis. When the factory is not operated continuously, the capacity base should reflect the expected time of operation rather than the 24-hour-per-day ideal.

Standard capacity provides the most realistic base for the evaluation of actual production. By using a standard running speed and operating time period, standard capacity provides a measure of productivity that management believes to be attainable. In this illustration, actual production amounts to 82.9% of standard capacity (i.e., 1260/1520). Clearly, utilization in this illustration has fallen short of attainable expectations. While the ratio highlights this fact, it does not provide insight as to how to improve utilization. In other words, the analysis signals a problem but does not provide for its solution. The next section of the paper addresses analytical techniques that can be used to improve utilization short falls that are highlighted by the capacity ratio analysis.

Analytical Techniques To Assess Capacity Shortfall

Long-Range Analysis

Actual capacity falls short of potential capacity for a variety of reasons. Shortfalls from theory or full capacity are affected by ideal expectations that are unlikely to be accomplished in real world conditions. However, an analysis of these shortfalls may be meaningful for long-range planning. For example, the difference between theory capacity and full capacity (i.e., 2,400 pcs/day - 2,280 pcs/day = 120 pcs/day) is solely attributable to the difference between the ideal running speed of the machine and the standard running speed.

While practical constraints may preclude the immediate accomplishment of ideal running speed, long-term plans may help managers move factories in this direction. For example, the running speed of one machine may be restricted if it receives input from another machine that operates at a slower speed. Accordingly, the speed of the faster machine is uncontrollable in the short run but could be controlled in the long run by replacing the feeder machine.

Similarly, the difference between the full capacity and standard capacity (i.e. 2,280 pcs/day - 1,520 pcs/day = 760 pcs/day) is attributable to the fact that management ran the factory for two shifts rather than three. This level of operation may be due to limited demand, personnel shortages, materials shortages or a variety of other circumstances. Once again, while these factors may be uncontrollable in the short run, long-term solutions may be feasible.

Accordingly, an analysis of shortfalls from ideal capacity measures may be useful for strategic planning. In contrast, differences between standard capacity and actual production offer opportunities to more effectively manage machine efficiency on an immediate basis.

Short-Range Analysis

Accountants can use two different approaches for short-term analyses. Ratio analysis can provide an in-depth review of machine performance. Variance analysis can be used to summarize the results of ratio analysis.

Ratio Analysis

Ratio analysis can be used to examine both the running speed (i.e., number of units produced per hour) and running time (i.e., number of hours of operation) associated with machine performance.

Analysis of Running Speed

First, it is useful to distinguish between standard running speed and scheduled running speed. The difference between these two measures is attributable to planned deviations from expected levels of performance. Perhaps the general skill level of the machine operators is known to be above or below the level that is normally present in factory workers.

Alternatively, the materials used in production could affect the running speed of machinery. Suppose a company takes advantage of a one-time special price on a materials acquisition. The materials were known to be of a lower quality than would be accepted under normal circumstances, but the company felt that the price reduction was worth the tradeoff in lower quality. While the lower quality materials may require processing at lower speeds, management may be willing to accept a reduction in machine running speed to obtain the benefit of lower materials cost. Accordingly, management may plan to run machinery at speeds that are above or below the standard running speed. The planned differences in machine performance can be analyzed by comparing the scheduled running speed with the standard running speed. The result of the comparison will be called the scheduled speed efficiency quotient.

To illustrate the computation of the scheduled speed efficiency quotient, recall that the standard running speed of the machine used in our hypothetical example was 95 units per hour. Now assume that management intends to operate the machines at only 92 units per hour due to a known deficiency in materials quality. The scheduled speed efficiency quotient would be .9684 (i.e., 92 units/95 units). While the machinery ran at 96.84% of standard performance, the difference was expected due to the processing of lower quality materials. Accordingly, differences between scheduled and standard running speeds do not merit elaborate investigations into causal factors. Instead, they serve to remind management that their current practices have deviated from the norm and to establish a target base for planning when operating conditions return to normal.

While management may expect certain deviations from standard performance, other unexpected deviations are also likely to occur. Accordingly, differences between actual running speed and scheduled running speed are common in factory operations. Machines may be set wrong or they may malfunction. Operators may be highly motivated or they may be lazy. Raw materials may have unexpected qualities that cause superior or inferior processing capacities. These and many other conditions can affect the actual operating outtut of machinery. The level of unexpected deviations from normal activity can be measured by dividing the actual running speed by the scheduled running speed. The result is called the actual speed efficiency quotient.

In the hypothetical case presented in this article, the scheduled running speed was 92 pieces of product per hour and the actual running speed was 90 pieces of product per hour. The actual speed efficiency quotient is .9783 (i.e., 90/92). This figure means that actual production amounted to 97.83% of the scheduled running speed. The 2.17% deficiency was unexpected. Management should investigate the cause of this differential and take appropriate action. As with traditional forms of analysis, non-financial ratios merely highlight the existence of deviations from expected norms. Managerial accountants are still responsible for interpreting the numbers and for taking appropriate action to resolve discrepancies.

The overall speed efficiency quotient is computed by multiplying the scheduled quotient times the actual quotient (i.e., .9684 x .9783 = .9474). This efficiency quotient is an aggregate measure of running speed. It includes both expected and unexpected deviations from the standard running speed. This fact can be verified by recomputing the overall speed efficiency quotient as the result of the actual running speed divided by the standard running speed (i.e., 90 pieces per hour/95 pieces per hour = .9474).

Analysis of Running Time

Running time can be analyzed in a manner similar to that used to analyze running speed. Here, also, it is necessary to distinguish between scheduled and standard running times. The difference between these two measures is attributable to planned non-productive time.

Non-productive time includes set-up time, scheduled maintenance and operator disengagement including time off for meals and breaks. Assume that non-productive time amounts to .75 hours per each eight-hour work shift. Accordingly, non-productive time would be 1.5 hours for the standard 16 hours associated with the two eight-hour work shifts. These figures produce a scheduled running time of 14.5 hours (i.e., 16 standard hours -1.5 hours of non-productive time).

The scheduled time efficiency quotient can be expressed as the amount of scheduled running time divided by the standard running time (i.e., 14.5 hours/16 hours = .9063). This computation suggests that the machine's operating capacity is not being fully utilized.

Several courses of action may be considered for improving efficiency. For example, to improve maintenance scheduled time, plant managers may decide to replace the out-of date machines, implement an incentive plan to motivate maintenance personnel to reduce maintenance time, step up preventive maintenance or keep the operation of machines within their design specifications to prevent overload. Further, personnel that float from one machine to another during meal times and breaks could be used to reduce the level of non-productive time associated with employee disengagement's. Finally, an emphasis can be placed on quality to prevent rework time.

The scheduled running time efficiency quotient is based on scheduled running time and measures management's efficiency of scheduled time. But scheduled running time is not always actual running time because of unexpected down time. It is important to understand the extent that such down time affects machine efficiency.

To understand this factor, the actual time efficiency quotient can be computed. The actual time efficiency quotient is equal to the actual running time divided by the scheduled running time. To illustrate, assume that unexpected down time amounts to .5 hours for the 16 hours of scheduled running time. Accordingly, the actual time efficiency quotient would be .9655 (i.e., 14 hours/14.5 hours). Down time in this example resulted in a 3.45% waste of planned running time.

Understanding the nature and extent of down time may help management reduce this factor to the minimum. Based on down-time data, managers may be able to rearrange maintenance schedules to coincide with down time for particular machines.

The overall time efficiency quotient is equal to the scheduled efficiency quotient times the actual efficiency quotient (i.e., .9063 x .9655 = .875). The overall time efficiency quotient is an aggregate measure of machine utilization. Note that it can also be computed as the actual running time divided by the standard running time (i.e., 14 hours/16 hours = .875). Based on these computations, there would be a 87.5% utilization of equipment.
Table 1

Running Speed Variance

Standard Actual Actual Running
{Running - Running} x Running = Speed
Speed Speed Time Variance
(95 - 90) x 14 = 70

Running Time Variance

Standard Actual Standard Running
{Running - Running} x Running = Time
Time Time Speed Variance
(16 - 14) x 95 = 190

Total Variance

Running Speed Variance 70 pcs/day Unfavorable
Running Time Variance 190 pcs/day Unfavorable
Total Variance 260 pcs/day Unfavorable

Variance Analysis

The primary results of the ratio analysis used by the Taiwanese can also be developed through slight variations of traditional forms of variance analysis that are more familiar to Western accountants. While some of the richness of the analysis is lost, it may be insightful to compare the results of the two forms of analysis. Accordingly, the following section presents variance computations and compares the results to the ratio analysis that was presented earlier.

Differences between standard capacity and actual production is 260 pieces of product per day (i.e., 1,520 pcs/day -- 1,260 pcs/day = 260 pcs/day). First, note that the 260 pcs/day represents an unfavorable variance. Recall that the objective function is to maximize machine utilization. Since the actual production is below the standard, the variance is unfavorable.

Two factors contribute to the total variance. First, the actual running speed was below the standard running speed; that is, actual production amounted to 90 pcs/hr instead of the standard 95 pcs/hr. Second, actual running time fell below standard running time; that is, actual time amounted to 14 hours per day rather than the standard running time of 16 hours per day. Accordingly, the total variance can be subdivided as shown in Table 1.

Notice that these figures are consistent with the results provided by the ratio analysis. First, the total variance can be computed by determining the aggregate efficiency quotient. This quotient is computed by multiplying the overall speed efficiency quotient times the overall time efficiency quotient (i.e., .9474 x .8750 = .8289). This quotient verifies that actual production is 82.89% of standard capacity. As a result, the total variance is 17.11% (i.e., 100% - 82.89%) of standard capacity (i.e., 1,520 x .1711 = 260 pieces).

Similarly, the running time variance is computed as 12.5% (i.e., 100% - 87.50)% of standard capacity (i.e., 1520 x .125 = 190 pieces). Since the shared variance is assigned to running speed, the running speed variance is computed as 5.26% (i.e., 100% - 94.74%) of the standard production computed at actual capacity (i.e., 95 pieces x 14 hours = 1,330 pieces). Accordingly, the running speed variance is verified at 70 pieces (i.e., .0526 x 1,330 = 70).

As indicated earlier, the richness of the analysis is reduced when traditional variance techniques are used because they do not distinguish between scheduled activity and standard activity. Accordingly, planned deviations are mixed with unexpected deviations when variance analysis is used. However, it should be noted that the variance computations could be refined to reflect the additional detail.

Just as flexible budgeting is used to adapt traditional variance formulas to changes in the volume of activity, a similar approach could be used to adjust for planned deviations in the variance formulas for machine performance. The method of analysis (i.e., ratio or variance) is much less important than the recognition of the need for analysis. As factories become increasingly automated, the efficiency of the operations must come under scrutiny if progress in productivity and quality is to proceed.


The importance of analyzing machine performance is substantiated by the trend toward machine-intensive operations in the manufacturing industry. Setting up measures of machine capacity is the first step to analyzing the capacity utilization rates of equipment.

Accountants can further analyze the capacity utilization of equipment based on long-term and short-term aspects. The long-term analysis helps management improve productivity by enhancing capacity utilization rate through strategic planning. Accountants must accept the constraints of time, existing facility and work force when conducting the short-term analysis and look for ways to improve the overall machine efficiency.

The non-financial measures proposed in this article highlight needed improvements from physical operations, and unlike financial measures they isolate these measurement figures from price and input variations. Utilization and efficiency measures will assist managers in their decision making and control activities in order to improve productivity, flexibility and innovation in the future.

Cindy D. Edmonds is assistant professor and Bor-YI Tsay is associate professor at the University of Alabama at Birmingham. Wen-Wei Lin is a quality control engineer at Formosa Plastics Group.
COPYRIGHT 1994 National Society of Public Accountants
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 1994 Gale, Cengage Learning. All rights reserved.

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Author:Edmonds, Cindy D.; Tsay, Bor Yl; Lin, Wen-Wei
Publication:The National Public Accountant
Date:Dec 1, 1994
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