7-1 An analyst has timed a metal-cutting operation for 50 cycles. The average time per cycle was 11.0 minutes, and the standard deviation was 1.20 minutes for a worker with a performance rating of 121 percent. Assume an allowance of 12 percent of job time. Find the standard time for this operation. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Standard time minutes Problem 7-2 A job was timed for 60 cycles and had an average of 1.9 minutes per piece. The performance rating was 96 percent, and workday allowances are 16 percent. Determine each of the following: a. Observed time. (Round your answer to 1 decimal place.) Observed time minutes b. Normal time. (Round your answer to 2 decimal places.) Normal time minutes c. Standard time. (Round your answer to 2 decimal places.) Standard time minutes Problem 7-3 A time study was conducted on a job that contains four elements. The observed times and performance ratings for six cycles are shown in the following table. OBSERVATIONS (minutes per cycle) Performance Element Rating 1 90% 2 85 3 110 4 100 1 0.44 1.50 0.84 1.10 2 0.50 1.53 0.89 1.14 3 0.43 1.47 0.77 1.08 4 0.45 1.51 0.83 1.14 5 0.42 1.49 0.83 1.16 6 0.46 1.52 0.80 1.26 a. Determine the average cycle time for each element. (Round your answers to 3 decimal places.) Element 1 2 3 4 Average cycle b. Find the normal time for each element. (Round your answers to 3 decimal places.) Element 1 2 3 4 Normal time c. Assuming an allowance factor of 11 percent of job time, compute the standard time for this job. (Round your answers to 3 decimal places.) Element 1 2 3 4 Standard time Problem 7-4 Given these observed times (in minutes) for four elements of a job, determine the observed time (OT) for each element. Note: The second element only occurs every other cycle. (Round your answers to 2 decimal places.) Element 1 2 3 4 Element 1 2 3 1 4.1 3.2 2.7 2 4.0 1.5 3.2 3.5 CYCLE 3 4 5.0 4.1 2.0 3.5 3.2 2.7 2.8 Observed Time 5 4.1 3.3 2.8 6 4.1 1.4 3.3 2.8 4 Problem 7-5 Given these observed times (in minutes) for five elements of a job, determine the observed time (OT) for each element. Note: Some of the elements occur only periodically. (Round your answers to 2 decimal places.) CYCLE Element 1 2 3 4 5 1 2.1 3.4 4.0 1.4 Element 1 2 3 4 5 2 2.0 1.6 3.5 1.4 3 2.7 3.3 2.3 4 2.1 1.0 3.8 4.7 1.5 5 2.1 3.4 1.5 6 1.2 3.3 1.4 Observed Time Problem 7-6 Using the following data, develop an allowance percentage for a job element that requires the worker to lift a weight of 15 pounds while (1) standing in a slightly awkward position, (2) in light that is very inadequate standards, and (3) with intermittent very loud noises occurring. The monotony for this element is low. Include a personal allowance of 5 percent and a basic fatigue allowance of 4 percent of job time. (Leave no cells blank - be certain to enter "0" wherever required. Omit the "%" sign in your response.) Percent A. Constant allowances: 1. Personal allowance B. 2. Basic fatigue allowances Variable allowances: 1. Standing allowance 2. Abnormal position allowance: a. Slightly awkward Percent 4. Bad light: 5 4 2 0 a. Slightly below recommended b. Well below c. Very inadequate 5. Atmospheric conditions (heat and humidity) variable 6. Close attention: 0 2 5 0-10 b. Awkward (bending) c. Very awkward (lying, stretching) 3. Use of force or muscular energy (lifting, pulling, or pushing): Weight lifted (in pounds): 2 a. Fairly fine work 0 7 b. Fine or exacting 2 c. Very fine or very exacting 5 7. Noise level: a. Continuous 5 0 10 1 15 2 20 3 25 30 35 40 45 50 60 70 Factor Personal Fatigue Standing Lifting Bad Light Noise Level Monotony Total % b. Intermittent loud c. Intermittent very loud d. Highpitchedloud 8. Mental strain: 4 a. Fairly complex process 5 b. Complex or wide span of attention 7 c. Very complex 9 9. Monotony: 11 a. Low 13 b. Medium 17 c. High 22 10. Tediousness: a. Rather tedious b. Tedious c. Very tedious 0 2 5 5 1 4 8 0 1 4 0 2 5 Problem 7-7 A worker-machine operation was found to involve 4.5 minutes of machine time per cycle in the course of 40 cycles of stopwatch study. The worker's time averaged 3.1 minutes per cycle, and the worker was given a rating of 120 percent (machine rating is 100 percent). Midway through the study, the worker took a 10-minute rest break. Assuming an allowance factor of 15 percent of work time which is appliedonly to the worker element (not the machine element), determine the standard time for this job. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Standard time minutes Problem 7-11 How many observations should a time study analyst plan for in an operation that has a standard deviation of 1.7 minutes per piece if the goal is to estimate the mean time per piece to within .5 minute with a confidence of 95.5 percent? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of observations Problem 7-12 How many work cycles should be timed to estimate the average cycle time to within 2 percent of the sample mean with a confidence of 99 percent if a pilot study yielded these times (minutes): 5.2, 5.5, 6.2, 5.3, 5.5, and 5.1? The standard deviation is .393 minutes per cycle. (Use the "mean time" value to 2 decimal places and other values to 3 decimal places for intermediate calculations. Round up your final answer to the next whole number.) Number of work cycles Problem 7-13 In an initial survey designed to estimate the percentage of time air-express cargo loaders are idle, an analyst found that loaders were idle in 10 of the 50 observations. a. What is the estimated percentage of idle time? (Omit the "%" sign in your response.) Estimated percentage of idle time % b. Based on the initial results, approximately how many observations would you require to estimate the actual percentage of idle time to within 7 percent with a confidence of 95 percent? (Do not round intermediate calculations. Round up your final answer to the next whole number.) Number of observations Problem 7-15 A job in an insurance office involves telephone conversations with policyholders. The office manager estimates that about half of the employee's time is spent on the telephone. How many observations are needed in a work sampling study to estimate that time percentage to within 5 percent and have a confidence of 98 percent? (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Number of observations Problem 7-17 Design a schedule of work sampling observations in which eight observations are made during one eight-hour day. Using the following table, read the last digit going down column 4 for hours (e.g., 1 7 4 4 6 . . . ), and read across row 4 from left to right in sets of two for minutes (e.g., 16 32 15 46 . . . ). Arrange the times chronologically. Note: It is only possible to sample observations between 00:00and 07:59. Therefore, discard any sampled hour or minute values that do not conform to this time range. (Leave no cells blank - be certain to enter "0" wherever required.) 1 2 3 4 5 6 7 8 9 10 11 12 1 6912 3491 4715 1632 8510 3950 7871 2716 2935 8533 0508 2951 2 7264 1192 2486 1546 7209 1328 7752 1396 8259 9957 1640 0131 3 2801 0575 2776 1950 0938 7343 0521 7354 9912 9585 2768 4359 Chronological order: Observation Time 1 2 3 4 5 6 7 8 4 8901 7547 2664 1844 2376 6083 8511 0249 3761 1039 4666 3095 5 4627 2093 3856 1123 0120 2108 3956 7728 4028 2159 9530 4421 6 8387 4617 0064 1908 4237 2044 3957 8818 9207 2438 3352 3018 1: 1: 1: 3: 4: 4: 6: 7: Problem 7-19 A work sampling study is to be conducted on rush-hour traffic (4:00 p.m. to 6:59 p.m.) five days per week. The study will encompass 40 days. Determine the day, hour, and minute for 10 observations using the following procedure and table. 1 2 3 4 5 6 7 8 9 10 11 12 1 6912 3491 4715 1632 8510 3950 7871 2716 2935 8533 0508 2951 2 7264 1192 2486 1546 7209 1328 7752 1396 8259 9957 1640 0131 3 2801 0575 2776 1950 0938 7343 0521 7354 9912 9585 2768 4359 4 8901 7547 2664 1844 2376 6083 8511 0249 3761 1039 4666 3095 5 4627 2093 3856 1123 0120 2108 3956 7728 4028 2159 9530 4421 6 8387 4617 0064 1908 4237 2044 3957 8818 9207 2438 3352 3018 a. Read two-digit numbers going down the first two digits of column 2 (e.g., 72 11 24 . . .), and then down the second two digits of that column (e.g., 64 92 86 . . .) for days. b. For hours, read one-digit numbers going from left to right across row 9 and then across row 10. (Read only 4s, 5s, and 6s.) c. For minutes, read two-digit numbers going down column 2, first using the last two digits (e.g., 64 92 86 . . .), and, after exhausting those numbers, repeat using the first two digits of that column (e.g., 72 11 24 15 . . .). Arrange your times chronologically by day, then hour, and then minute. Observation 1 2 3 4 5 6 7 8 9 10 Day Time :40 :31 :46 :52 :59 :28 :57 :09 :11 :24 Problem 6-1 An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate for 450 minutes per day. a. What are the minimum and maximum cycle times? (Round your answers to 1 decimal place.) Minimum cycle time Maximum cycle time minutes minutes b. What range of daily output is theoretically possible for the line? (Round your answers to 1 decimal place. Enter the smaller value in the first box and the larger value in the second box.) Range of output to units/day c. What is the minimum number of workstations needed if the maximum output rate is to be sought? (Round up your answer to the next whole number.) Minimum number of workstations d. What cycle time will provide an output rate of 125 units per day? (Round your answer to 1 decimal place.) Cycle time min/cycle e. What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes? Cycle Time (1) (2) 2. Problem 6-2 Potential Output units units A manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 331/3 units. Assume the shop works a 60-minute hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. In order of most following tasks. Tiebreaker: greatest positional weight. Work Station I II III IV Tasks b. In order of greatest positional weight. Work Station I II III IV Tasks c. What is the efficiency? (Round your answer to 2 decimal places. Omit the "%" sign in your response. ) Efficiency % Problem 6-3 A manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 4 units. The department uses a working time of 56 minutes per hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. In order of most following tasks. Tiebreaker: greatest positional weight. Work Station I II III IV Tasks b. In order of greatest positional weight. Work Station I II III IV Tasks c. What is the efficiency? (Round your answer to 2 decimal places. Omit the "%" sign in your response. ) Efficiency % Problem 6-4 A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible. Task a b Length (minutes) 0.2 0.4 Immediate Predecessor a c d e f g h 0.3 1.3 0.1 0.8 0.3 1.2 b, c e d, f g a. Do each of the following: (2) Assign tasks to stations in order of greatest number of following tasks. Work Station I II III IV Task a b c d e f g h Task Assigned Following Tasks (3) Determine the percentage of idle time. (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Percentage of idle time % (4) Compute the rate of output in printers per day that could be expected for this line assuming a 420-minute working day. (Round your answer to the nearest whole number.) Rate of output units per day b. Answer these questions: (1) What is the shortest cycle time that will permit use of only two workstations? (Round your answer to 1 decimal place.) Shortest cycle time minutes (2) Determine the percentage of idle time that would result if two stations were used and each station was loaded with the worktime shown in Part b(1). (Leave no cells blank - be certain to enter "0" wherever required. Omit the "%" sign in your response.) Percentage of idle time % (3) What is the daily output under this arrangement using the operating time from Part a(4)? (Round your answer to 1 decimal place.) Daily output units per day (4) Determine the output rate that would be associated with the maximum cycle time using the operating time from Part a(4). (Round your answer to 2 decimal places.) Rate of output units per day Problem 6-5 As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of 240 units per eight-hour day. Task times and precedence relationships are as follows: Task a b c d e f g Duration (minutes) 0.2 0.4 0.2 0.4 1.2 1.2 1.0 Immediate Predecessor a b d c e, f Do each of the following: b. Determine the minimum cycle time, the maximum cycle time, and the calculated cycle time. (Round your answers to 1 decimal place.) The minimum cycle time The maximum cycle time Calculated cycle time minutes minutes minutes c. Determine the minimum number of stations needed. (Round your answer to the next whole number.) Minimum number of stations d. Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice. Work stations I II III IV Following Tasks e. Compute the percentage of idle time for the assignment in part d. Use the actual bottleneck cycle time in your calculation. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) Percentage of idle time % Problem 6-6 Twelve tasks, with times and precedence requirements as shown in the following table, are to be assigned to workstations that have a fixed machine cycle time of 1.5 minutes. Two heuristic rules will be tried: (1) greatest positional weight, and (2) greatest number of following tasks. In each case, the tiebreaker will be shortest task time. Task a b c d e f g h i j k l Length (minutes) 0.1 0.2 0.9 0.6 0.1 0.2 0.4 0.1 0.2 0.7 0.3 0.2 Immediate Predecessor a b c d, e f g h i j k b. Assign tasks to stations under each of the two rules. (1) greatest positional weight Work Station I II III Tasks (2) greatest number of following tasks Work Station I II III Tasks c. Compute the percentage of idle time for each rule. (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Percentage of idle time Problem 6-7 % For the set of tasks given below, do the following: Task A B C D E F G H I J Task Time(seconds) 45 11 9 50 26 11 12 10 9 10 Immediate Predecessor A B D E C C F, G, H I 193 b. Determine the minimum and maximum cycle times in seconds for a desired output of 500 units in a seven-hour day. (Round your answers to 1 decimal place.) The minimum cycle time The maximum cycle time seconds seconds c. Determine the minimum number of workstations for output of 500 units per day. (Round your answer to the next whole number.) Minimum number of workstations d. Balance the line using the largest positional weight heuristic. Break ties with the most following tasksheuristic. Use a cycle time of 50 seconds. Work stations I II III IV V Following Tasks e. Calculate the percentage idle time for the line. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) Percentage of idle time %