SLN (Straight-Line Depreciation)
● SLN (cost, salvage, life).
● Calculates the straight-line depreciation of an asset for a given year:
cost: First cost or basis of the asset.
salvage: Salvage value.
life: Recovery period.
SYD (Sum-Of-Year-Digits Depreciation)
● SYD (cost, salvage, life, period).
● Calculates the SOYD depreciation of an asset for a given year:
cost: First cost or basis of the asset.
salvage: Salvage value.
life: Recovery period.
period: The year for which the depreciation is to be calculated.
VDB (Variable Declining Balance)
● VDB (cost, salvage, life, start-period, end-period, factor, no-switch).
● Calculates the depreciation schedule using the DB method with a switch to SLN in the year in which straight line has a larger depreciation amount. This function can be used for MACRS depre- ciation schedule computations.
cost: First cost or basis of the asset.
salvage: Salvage value.
life: Recovery period.
start-period: First period for depreciation to be calculated.
end-period: Last period for depreciation to be calculated.
factor: (optional) Enter 1.5 for 150% DB and so on. The function will use 2.0 for 200% DB if omitted.
no-switch: (optional) If omitted or entered as FALSE, the function will switch from DB or DDB to SLN depreciation when the latter is greater than DB depreciation. If entered as TRUE, the function will not switch to SLN depreciation at any time during the depreciation life.
References
Alloway, J.A., Jr., Spreadsheets: enhancing learning and application of engineering economy techniques, Eng. Econ., 3, 263–274, 1994.
Badiru, A.B., Project Management in Manufacturing and High Technology Operations, 2nd ed., Wiley, New York, 1996.
Badiru, A.B. and Omitaomu, H.O., Design and analysis of tent cash flow models for engineering econ- omy lectures, Eng. Econ., 48, 363–374, 2003.
Blank, L.T. and Tarquin, A., Engineering Economy, 5th ed., McGraw-Hill, New York, 2002.
Canada, J.R., Sullivan, W.G., and White, J.A., Capital Investment Analysis for Engineering and Management, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1996.
Eschenbach, T.G., Engineering Economy: Applying Theory to Practice, 2nd ed., Oxford University Press, New York, 2003.
Lavelle, J.P., Reader’s forum: enhancing engineering economy concepts with computer spreadsheets, Eng.
Econ., 4, 381–386, 1996.
Newnan, D.G., Eschebach, T.G., and Lavelle, J.P., Engineering Economic Analysis, 9th ed., Oxford University Press, New York, 2004.
Omitaomu, O.A., Smith, L.D., and Badiru, A.B., The ENGINeering Economic Analysis (ENGINEA) soft- ware: enhancing teaching and application of economic analysis techniques. Comput. Educ. J., in press.
Park, C.S., Contemporary Engineering Economics, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ, 2001.
Sullivan, W.G., Wicks, M.E., and Luxhoj, T.J., Engineering Economy, 12th ed., Prentice-Hall, New Jersey, 2003.
7
Work Sampling
7.1 Introduction...7-1 7.2 Basic Concepts of Work Sampling ...7-1 7.3 Accuracy ...7-2 7.4 Confidence Interval ...7-2 7.5 Sample Size...7-2 7.6 Random Observation Times...7-3 7.7 Control Charts ...7-3 7.8 Plan of a Typical Work Sampling Study...7-3 7.9 Applications of Work Sampling ...7-4
Machine Utilization • Allowances for Personal and Unavoidable Delays • Summarizing the Sampling Data • Determining Work Standards
7.10 Computerized Work Sampling ...7-6 7.11 Conclusion ...7-6
7.1 Introduction
One very useful technique of work measurement is work sampling, which can be applied in a wide vari- ety of work situations. In its simplest form, it is used by the shop supervisor or foreman to estimate idle times of machines, e.g., if he notices a machine idle for two out of his ten trips, he estimates that the machine is idle for 20% of the time.
The technique was first applied in the British textile industry by L.H.C. Tippett (Tippett, 1953) under the name of “ratio delay.” R.L. Morrow (Morrow, 1941) introduced the technique in the United States in 1941. The name “work sampling” was introduced by C.L. Brisley (Brisley, 1952) and H.L. Waddell (Waddell, 1952) in 1952, Ralph M. Barnes reproduced the name work sampling with permission of Tippett in his book on work sampling (Barnes, 1980). Several other names, e.g., “activity sampling,”“ratio delay,” “snap readings,” or “occurrence sampling,” (Konz and Johnson, 2000) are occasionally used syn- onymously for “work sampling.” The technique is particularly useful in measuring indirect work, in serv- ice activities, and in cases where a stopwatch method is not acceptable. Since the 1950s, the technique has become a standard tool used by industrial engineers for measuring indirect and service jobs. Performance sampling may be applied to fine tune the ratios more accurately in work sampling (Meyers, 1999).
7.2 Basic Concepts of Work Sampling
Work sampling is based on the laws of probability and is used to determine the proportions of the total time devoted to the various components of a task. The probability of an event occurring or not occur- ring is obtained from the statistical binomial distribution. When the number of observations is large, the 7-1 Paul S. Ray
The University of Alabama
binomial distribution can be approximated to normal distribution. The binomial probability of x occur- rences is calculated as follows:
b(x) ⫽nCx pxq(n⫺x) (7.1)
where p ⫽ probability of x occurrences
q ⫽ 1⫺p ⫽ probability of no x occurrence n ⫽ number of observations
Normal distribution is used instead of binomial distribution in work sampling for convenience. The normal distribution of a proportion p has an average value of ratio ⫽ p and standard deviation
σp ⫽兹p(苶1苶⫺p)苶/n苶 (7.2)
where p ⫽ proportion of occurrence of an event n ⫽ number of observations
A ⫽ sp ⫽ zσp where A ⫽ desired absolute accuracy
s ⫽ relative accuracy for a propfortion p
7.3 Accuracy
Absolute accuracy indicates the range within which the value of p is expected to lie. It is the closeness of the ratio p to the true ratio p. If p ⫽ 30% and relative accuracy ⫽ 10%, then A ⫽ (0.3)(0.1) ⫽ 0.03 or 3%.
Example 1 For a study where the true p value ⫽ 30%, a ⫾3% absolute accuracy level indicates that the calculated value of p will be between (30 ⫾ (30⫻ 0.03)) ⫽ 30 ⫾0.75 or between 29.25 and 30.75.
7.4 Confidence Interval
“Confidence interval” denotes the long-term probability that the ratio p will be within the accuracy lim- its. The concept relies on the relative frequency interpretation of probability. Thus, 95% confidence means that if a large number of samples is taken, 95 out of 100 of these will contain the true value of p.
The probability value is given by the proportion of the area under the normal curve included for a spec- ified value of standard deviation (z). The usual confidence levels and the corresponding “z” values are given in Table 7.1.
7.5 Sample Size
The number of observations or sample size can be determined using Equation (7.1) as follows:
A ⫽ zσp ⫽ z兹p(苶1苶⫺p)苶/n苶or n⫽(z2/A2)(p(1⫺p)) (7.3)
TABLE 7.1 Confidence Levels and Corresponding “z” Values Confidence Level (%) Standard Deviations (z)
68 ⫾1.00
90 ⫾1.64
95 ⫾1.96
99.73 ⫾3.00
where A is usually 0.05 or 5% for industrial work
p ⫽ percentage of total work time a component occurs
z ⫽ number of standard deviations depending on the confidence level desired Example 2 Determine the idle percentage of a milling machine.
Relative accuracy desired ⫽ 0.05%.
Confidence level desired ⫽ 95%.
Preliminary study indicated p ⫽ 30%.
For this, accuracy A ⫽ (0.05)(0.3) ⫽ 0.015, and z ⫽ 1.96 n ⫽ (z2/A2) (p(1⫺p)) ⫽ (1.962/0.0152) (0.30 ⫻ 0.70) n ⫽ 3585.49 ⬵ 3586
7.6 Random Observation Times
To be statistically acceptable, it is essential that the work sampling procedure give each individual moment during observation an equal chance of being observed. The observations have to be random, unbiased, and independent so that the assumption of the binomial theory of constant probability of event occurrence is attained. Hence, it is essential that observations be taken at random times when conduct- ing a work sampling study. To ensure the randomness of observations, a convenient manual way is to use the random number table published in many handbooks. Random numbers can also be obtained by ran- dom number generators programmed in many handheld engineering calculators. Another way of obtain- ing random numbers is to write and place a large number of valid times mixed up in a hat, and pick up slips of paper at random. The required number of times of observations may be determined from a ran- dom number table as follows: for a picked number 859, the time may be taken as 8.59 A.M. if the start time of shift is 8.00 A.M. Another way of getting trip times is to multiply two-digit random numbers by ten (Niebel and Freivalds, 2003) to get time values in minutes after the start of shift. Only the time values falling within the work time are accepted for planning trips.
Example 3 For two-digit random numbers 04, 31, and 17, the observation times will be 4⫻10 ⫽ 40 min, 31⫻10 ⫽ 310 min, and 17⫻10 ⫽ 170 min after start of the shift, typically 8:00 A.M. The observa- tion times are then 8.40 A.M., 1.10 P.M., and 10.50 A.M., respectively. The process is repeated until the required numbers of valid observation times within the shift work time are obtained.
7.7 Control Charts
Control charts are extensively used in quality-control work to identify when the system has gone out of control. The same principle is used to control the quality of the work sampling study. The 3σ limit is nor- mally used in work sampling to set the upper and lower limits of control. First, the value of p is plotted in the chart as the centerline of the p-chart. The variability of p is then found for the control limits.
Example 4 For p ⫽ 0.3 and sample n ⫽ 500, σ⫽兹p(苶1苶⫺p)苶/n苶⫽0.0205 and 3σ⫽0.0615. The limits are then 0.3 ⫾ 0.0615 or 0.2385 and 0.3615 as shown in Figure 7.1.
On the second Friday, the calculated value of p, which was based on observations, fell beyond limits, indicating the need for investigation and initiation of corrective action.
7.8 Plan of a Typical Work Sampling Study
A typical work sampling plan has the following steps:
● Determine the objective.
● Identify the elements of the study.
● Conduct a preliminary study to estimate the ratio percentages.
● Determine the desired accuracy and confidence levels.
● Determine the required number of observations.
● Schedule the random trip times and routes.
● Design the observation form.
● Collect sampling data.
● Summarize the study.
7.9 Applications of Work Sampling
Work sampling is most suitable for determining (1) machine utilization, (2) allowances for unavoidable delays, and (3) work standards for direct and indirect work. The technique is particularly suitable for deter- mining standards for indirect and service work. Each type of application is illustrated below with an example.
7.9.1 Machine Utilization
Example 5 ABC Company was concerned about the utilization of forklift trucks and wanted to deter- mine the average idle time of the forklift trucks in their plant. A work sampling study was conducted for 5 weeks. The data collected for 5 weeks are given in Table 7.2. The desired confidence level and relative accuracy were 95 and 5.0%, respectively.
Forklift truck utilization ⫽ (1500/2000) ⫻ 100% ⫽ 75%.
Idle percentage ⫽ (500/2000) ⫻ 100% ⫽ 25%.
Assuming that the desired confidence level is 95%, the accuracy of idle percentage is determined as follows:
A ⫽ s∗ 0.25 ⫽ 1.96兹p(苶1苶⫺p)苶/n苶⫽ 1.96兹0.苶25苶⫻苶0.苶75苶/2苶00苶0苶⫽ 0.0190 relative accuracy (s) ⫽ (0.0190/0.25) ⫻ 100% ⫽ 7.60%.
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40
M T W R F M T W T F
p -Value
Day p -Value
Day FIGURE 7.1 Control chart on daily basis.
TABLE 7.2 Work Sampling Summary Sheet
Elements Number of Observations Total Numbers
Working 11111 11111 11111 11111 ……….… 1500
Idle 11111 11111 11111 ……… 500
2000
The desired accuracy required was 5%. The number of observations required to achieve the accuracy was found as follows:
0.05∗ 0.25 ⫽ 1.96兹0.苶25苶苶⫻ 0苶.7苶5/苶n苶 or n ⫽ 1.96/(0.05⫻0.25)2 (0.05⫻0.25) ⫽ 3074 The number of observations per day during the preliminary study was 2000/25 ⫽ 80.
The same sampling group was assigned to collect additional sampling data at 80 observations per day.
Hence, the additional number of days required for study to achieve the desired accuracy was (3074⫺
2000)/80 ⫽ 13.4 d ⬵ 14 d.
7.9.2 Allowances for Personal and Unavoidable Delays
Example 6 presents a method for determining allowances for personal and unavoidable delays.
Objective The industrial engineering department of the ABC Company wanted to determine the allowance for personal reasons and unavoidable delays for their machine shop.
Identify the Elements of the Study The elements were (1) working, (2) personal delay, and (3) unavoidable delay.
Design the Observation Form The observation form is task specific and has to be designed specifi- cally for each job. For the ABC study in Example 5, a sampling form was developed as shown in Table 7.3 for the elements required to be observed: (1) working, (2) personal activities, e.g., drinking water, and (3) unavoidable delay, e.g., stopped for answering to foreman. Each tally mark indicated one observation of the corresponding element. At times, more elements may be included in the work sampling form to meet some future requirements of an organization.
Preliminary Study to Estimate the Ratio Percentages The preliminary work sampling study was con- ducted to estimate the approximate percentage values for the elements as given in Table 7.3.
Confidence Level and Accuracy The desired levels of confidence and accuracy were 95 and 0.05%, respectively.
Sample Size The preliminary estimates were used to determine the sample size required. The small- est value of the percentage occurrence was used for computation to ensure the desired level or higher accuracy for all elements.
A ⫽ 0.05⫻0.05 ⫽ 0.0025, and z ⫽ 1.96
n ⫽ (z/A)2(p)(1⫺p) ⫽ (1.96/0.0025)2(0.05)(0.95)
⫽ 29,197
There were ten workers working on similar machines. Hence the number of observation per trip was ten.
The number of trips required was 29,197/10 ⫽ 2,920. One work sampler could make 5 trips/h or 40 trips/day of 8 h shift. Three persons were available for sampling. Together, they could make 120 trips/day.
Hence, the duration of study required was 2920/120 ⫽ 24.33 d ⬵ 5 weeks.
Schedule of Trips A random number table was determined to schedule 40 random trips per day for each observer. The procedure has been explained in Section 7.6. In addition, the routes of the observers were changed randomly each day.
TABLE 7.3 Pilot Work Sampling Summary (ABC Company)
Work Elements Observations Total Number of Percentage
Observations Occurrence (%)
1. Working 1111 1111……… 102 85
2. Personal activities 1111……….… 6 5
3. Unavoidable delays 1111 1111……… 12 10
Total 120 100
Collecting Sampling Data The observers were trained to be objective and not anticipate any expected observation. Each trip had a randomly selected route in addition to the random times. Video cameras may be used to minimize bias in collecting data, as the camera records any ongoing activity accurately.
7.9.3 Summarizing the Sampling Data The ABC study is summarized in Table 7.4.
Certain unavoidable delay should be based on the work element data alone (24,730), if the unavoid- able delay under study happens to be highly dependent on work time, as in case of fatigue.
7.9.4 Determining Work Standards
For the ABC Company, work standards for the above machine shop were developed as follows:
Given that during the study period, the machine shop produced 100,000 pieces of fan motor shafts, a fatigue allowance of 8% is allowed as per company policy in the machine shop. The section had five work- ers working on similar machines. The performance rating was found to be 110%, determined by esti- mating the pace of work periodically during the sampling study, and thought to be reasonable.
Total work time ⫽ 5 weeks⫻5 days/week⫻40 h/day ⫻ 5 operators ⫽ 5000 m h Observed time per piece ⫽ 5,000 ⫻ 60/100,000 ⫽ 3.0 min/pc
Normal time ⫽ 1.10 ⫻ 3.00 ⫽ 3.30 min Total allowance ⫽ 5 ⫹ 10.3 ⫹ 8.0 ⫽ 23.30%
Standard time per pc ⫽ 3.30 ⫻ (1.233) ⫽ 4.07 min/piece of motor shaft
7.10 Computerized Work Sampling
A number of software packages with a variety of features are available for work sampling. Application of these packages saves the clerical time associated with recording and summarization of sampling data. The well-known ones among them are WorkSamp, by the Royal J. Dossett Corp.; CAWS/E, by C-Four; and PalmCAWS, by C-Four. These software packages reduce time for the clerical routines of work sampling and allow faster processing with greater accuracy. Use of computers may save about 35% of total work sampling study cost (Niebel and Freivalds, 2003) by eliminating the clerical work time, which is compar- atively high relative to actual observation time.
7.11 Conclusion
Work sampling is a valuable technique for determining equipment utilization and the allowances that should be assigned for unavoidable delays in production operations. Determining standards for service and indirect work is another area in which work sampling has been found to be practical and economi- cal. The trend of continued increase in service jobs, e.g., plant maintenance activities, custodial tasks, and nonindustrial jobs, where work sampling is the only practical and economical tool for establishing stan- dards, is enhancing the value of work sampling as an industrial engineering tool in the 21st century.
TABLE 7.4 Study Summary
Work Elements Total Number of Percentage Occurrence
Observations
Working 24,730 24,730/29,200 ⫽0.8469 ⫽84.69%⬵84.7%
Personal delay 1,470 1,470/29,200 ⫽0.503 ⫽5.03% ⬵5.0%
Unavoidable delay 3,000 3,000/29,200 ⫽0.1027 ⫽10.27% ⬵10.3%
Total 29,200
References
Barnes, R.M., Work Sampling, 7th ed., Wiley, New York, 1980.
Brisley, C.L., How you can put work sampling to work, Factory Manage. Maint., 110, 83–89, 1952.
Konz, S. and Johnson, S., Work Design Industrial Ergonomics, 5th ed., Holcomb Hathaway, Arizona, 2000.
Morrow, R.L., Ratio delay study, Mech. Eng., 63, 302–303, 1941.
Meyers, F.E., Motion and Time Study for Lean Manufacturing, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1999.
Niebel, B. and Freivalds A., Methods. Standards, and Work Design, 11th ed., McGraw-Hill, New York, 2003.
Tippett, L.H.C., The ratio delay technique, Time and Motion Study, May 1953, pp. 10–19.
Waddell, H.L., Work sampling — a new tool to help cut costs, boost productivity, make decisions, Factory Manage. Maint., 110, 1952.