Lesson 4 - Work Sampling PDF

Quezon City Polytechnic University Work Measurement LESSON 4: Work Sampling Work sampling is the method of finding the percentage occurrence of a certain acti...

Quezon City Polytechnic University Work Measurement LESSON 4: Work Sampling Work sampling is the method of finding the percentage occurrence of a certain activity by statistical sampling and random observations in which a large number of instantaneous observations are made at random time intervals over a period of time. It is a method in which a large number of instantaneous observations are made at random time interval over a period of time or group of machines or workers. Each observations records what is happening at that instant and the percentage of observation recorded for a particular activity or ideness. Scope of the study Before making our actual observations, it is important that we decide on the objective of our work sampling. The simplest objective is that of determining whether a given machine is idle or working. In such a case, our observations aim at detecting one of two possibilities only: Observations Machine /man working Machine/man Idle Cutting Boring Filling Waiting Waiting Personal Idle for for needs of repairs Supplies workers Work sampling has a long and impressive list of applications but all of them fall into one of the following three categories: (i) Work sampling can be used as ratio study of working and idle times. (ii) It can be utilized as performance sampling study in which working and idleness on working times are measured and a performance index is prepared. (iii) It can be used as a work measurement technique. Theory of Work Sampling: It states that the percentage of observations recorded on an operation/ process in any state is a reliable estimate of the percentage time the operation/ process is in that state, provided, “sufficient number of observations are taken at random”. It may be noted that here, particular stress should be paid on the words “random” and “sufficient number of observations”. In this technique, some error may occur but the magnitude of error tends to decrease as the number of samples increases. Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Work sampling is a sampling method and depends upon the laws of probability. A sample taken at random from a large population provides a good estimate of the distribution of the population. To make it clearer, let us consider the following example. A worker while working during his shift either does the job assigned to him or remains idle for one or the other reason. The following table shows that out of total 50 observations, there were 45 working observations and five idle observations. Status of worker No of observations Percentage Working 45 q= Idle 5 p= Example1. Simple work sampling record sheet of a machine Date: Observer: Study No. No. of observations: 75 Total Percentage Machine 62 q= Running Machine 13 p= Idle In order to obtain a complete and accurate picture of the productive time and idle time of the machines in a specific production area, it would be necessary to observe continuously all the machines in that area and to record when and why any of the machines were stopped. It would of course be quite impossible to do this unless a large number of workers spent the whole of their time on this task alone — an unrealistic proposition. As it is not generally possible to do this either, the next best method has to be adopted; that of making tours of the factory at random intervals, noting which machines are working and which are stopped, and noting the cause of each stoppage. This is the basis of the work sampling technique. When the sample size is large enough and the observations made are indeed at random, there is quite a high probability that these observations will reflect the real situation, plus or minus a certain margin of error. ✓ Sampling – process or technique in obtaining a sample ✓ Sample –is a group in research study in which information is achieved. ✓ Probability – extent of which an event is likely to occur. Example: Tossing a coin, Probability : 50% head 50% tail Concept of work sampling L. Tippet develop work sampling in England in 1927 for studying activities in cotton industry, to proportion the time that the worker and machines spends on various activities and its idle time. Utilization of machines Observe performance of man and machine Assign how many machines a man can operate Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Establishing confidence levels The normal distribution curve / confidence level – is the typical of the kind of frequency distribution which is important in work sampling because it represents graphically the probability of occurrence of certain change in phenomena. Properties of normal distribution: The area under the part of the normal curve that lies within o 1 standard deviation of the mean is = 68% o 2 standard deviation of the mean is = 95% o 3 standard deviation of the mean is = 99.7% Note: in work sampling, the most commonly used levels are 90%, 95%, 99%, 99.9% confidence level it is the area under the curve of two sigma or two standard deviation this means that the probability is 95% of the time in random observation will represent the facts (based on actual observation) Probability Confidence Level Value 90% 1.645 95% 1.960 99% 2.326 99.9% 3.250 Margin of Error The margin of error is a statistic expressing the amount of random sampling error in a survey's results. The larger the margin of error, the less confidence one should have that the poll's reported results are close to the "true" figures; that is, the figures for the whole population. Margin of error occurs whenever a population is incompletely sampled. The term "margin of error" is often used in non-survey contexts to indicate observational error in reporting measured quantities. Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Sample size We can apply a statistical method or a conventional method for the statistical method, we have first to take a number of preliminary readings (n'). We then apply the following equation 2 √𝑛′ ∑ 𝑥 2 − (∑ 𝑥)2 𝑛 = (40 ) ∑𝑥 Where: n = sample size we wish to determine n’= number of reading taken in the preliminary study ∑ = sum of values x = value of the readings An example will make the point clear. Let us suppose that we take five readings for a given element, and find that the value of the elapsed time in 1/lOOths of a minute is 7, 6, 7, 7, 6. We can then calculate the squares and the X X2 7 6 7 7 6 Ex = Ex2 = n' = 5 readings. By substituting these values in the above formula, we obtain the value n=8.81 or 9 reading 2 √𝑛′ ∑ 𝑥 2 − (∑ 𝑥)2 𝑛 = (40 ) ∑𝑥 𝑛= 𝑛= Therefore the number of preliminary readings is less than the required sample size of 9. Then we must increase the sample size from 5 readings to 9 readings Example The following data was obtained by time study analyst during the preliminary observation in making a bracelet. Determine how many readings or observations the analyst should perform for accurate study? Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Time in minutes Cycle (X) X2 1 8.75 76.5625 2 7.67 58.8289 3 6.34 40.1956 4 8.24 67.8976 5 7.45 55.5025 6 9.12 83.1744 7 8.75 76.5625 8 7.45 55.5025 9 6.34 40.1956 10 7.28 52.9984 77.39 607.4205 2 √𝑛′ ∑ 𝑥 2 − (∑ 𝑥)2 𝑛 = (40 ) ∑𝑥 2 √10(607.4205)−77.392 𝑛 = (40 77.39 ) 𝑛 = 4.7650 𝑜𝑟 5 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 Therefore, there is an excess reading of 5 Determination of sample size As well as defining the confidence level for our observations we have to decide on the margin of error that we can allow for these observations. We must be able to say that: "We are confident that for 95 per cent of the time this particular observation is correct within ±5 per cent, or 10 per cent", or whatever other range of accuracy we may decide on. Statistical Method: the formula used in this method is: Formula: 𝒛𝟐 𝒑 (𝒒) n = 𝒆𝟐 n = number of observation z = confidence level value p = percent idle time q = percent working time e = limit error Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Sample Problems 1. Let us assume that some 100 observations were carried out as a preliminary study and at random, and that these showed the machine to be idle in 25 times of the cases and to be working 75 times of the time. Let us choose a confidence level of 95 per cent with a ±10 per cent margin of error. How many observations should be made? If we reduce the margin of error to ±5 how many observations are needed? 2. Let us assume that some observations were carried out in the working area. In the preliminary study at ramdom observations, it shows that the machine was idle for 30% of the case and to be working 70% of the time. Let us choose a confidence level of 95% 3. A work sampling study requires 95% confidence level with 5% limit error. How many observations are required if the machine down time is 8% 3. At 99% confidence level, the analyst estimate the activity having 20%. How many observations should be made if it is expected to have a 5% margin of error? 5. Suppose that a total of 95 observations were made, and in preliminary study, 20% showed that machine was idle. What is the probability at 9.55% limit error? Ref. www.yourarticelibrary.com Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement WORK SAMPLING IN BRACELET ASSEMBLY Objectives: 1. To facilitate student’s teamwork skills. 2. Appreciate the application of Statistical work sampling techniques to study work activities. 3. Apply statistical sampling techniques by taking number of observations at random times. Problem: PROBLEM: A Bead String Company makes a bracelet consisting of beads on a nylon string. The time study analyst was assigned by the owner of the company to take a work sampling on how to make a bracelet. During the observation which last up to 10 observations or trials, the operator was idle for 2 minutes of the time. The time study analyst would like to determine the limit error of the study. Below is the table to be filled up by the analyst. BRACELET ASSEMBLY TIME IN (MINUTES) TRIAL 1 TRIAL 2 TRIAL 3 TRIAL 4 TRIAL 5 TRIAL 6 TRIAL 7 TRIAL 8 TRIAL 9 TRIAL 10. Materials needed 10 pieces Nylon string 20 inches long Beads Scissors Ruler Steps in making a Bracelet 1. Cut a nylon string 10 inches long 2. Put the beads on the string. Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement 3. Count the desired number of beads on the string and if okay, close the bracelet by knotting the ends. 4. Inspect the bracelet, check the number of beads and if the beads are okay. GIVEN: REQUIRED: FORMULA: SOLUTION: Laboratory Activity No.4 Work Sampling – Flash Light Assembly Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Objective: to conduct a work sampling activity using both the conventional method and statistical sampling in Flash Light Assembly. Discussion: Assume a two previous observations of flash light assembly and compute the number of observations needed by applying the formula for conventional method: 2 √𝑛′(∑ 𝑥 2 )−(∑ 𝑥 2 ) N=40( ∑𝑥 In work sampling, z=95% confidence level and limit error of 5% Problem: Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Sample Problems A cutting machine is idle for 25% of the time. The sample should be accurate with the limit of 3%. How many observations should be made to have a 95% confidence level? Solution: 𝑝(𝑞) N = z2 𝑒2 = (1.960)2(0.25)(1-0.25) 0.032 N = 800 observations Let us assume that some observations was carry out in the working area. In the preliminary study at ramdom observations, it shows that the machine was idle for 30% of the case and to be working 75% of the time. Let us choose a confidence level of 95% 6. Find the no of observations at limit error of 10% 7. Find the no of observations at limit error of 3% Solution: 𝑝(1−𝑝) 1. N = z2 𝑒2 N = 1.9602 (0.30)(1-0.30) 0.102 N = 80.67 observations N = 81 observation 𝑝(1−𝑝) 2. N = z2 𝑒2 N = 1.9602 (0.30)(1-0.30) 0.052 N = 322.69 observations N = 323 observations A work sampling study requires 95% confidence level with 5% limit error. How many observations are required if the machine down time is 8% Solution: 𝑝(1−𝑝) N = z2 𝑒2 N = 1.9602 (0.80)(1-0.80) 0.052 N = 246 observations Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement At 99% confidence level, the analyst estimate the activity having 20%. How many observations should be made if it is expected to have a 5% margin of error? Solution: 𝑝(1−𝑝) N = z2 𝑒2 N = 2.3262 (0.20)(1-020) 0.052 N = 346.25 observations N = 347 observations 4. Suppose that a total of 95 observations were made, and in preliminary study, 20% showed that machine was idle. What is the probability at 9.55% limit error? Solution: N = z2 p (1-p) E2 Z2 = ne2 P(1-p) √𝑛 Z = e √𝑝(1−𝑝) √𝟗𝟓 z = 9.55% x √𝟎.𝟐𝟎(𝟏−𝟎.𝟐𝟎) Z = 2.327 Z = 99% probability Seat Work: 1. In a work sampling study requires 95% confidence level. How many observations are required if the machine is running 80% of the total time at 5% limit error? If brownout had occurred 30% of the 5% limit error, how many observations the analysts should take? Given: z = 95% confidence level= 1.960 working = 80% idle = 100% -20% = 80% e = 5% Required: 1. What is n at 80% running time at 30% downtime n = Z2 p ( w) e2 n = (1.960)2(0.2)(0.8)= 245.86 observations = 246 observations (0.05)2 Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement n = (1.960)2(0.3)(0.7)= 322.6944 observations = 323 observations (0.05)2 Quiz in Work Sampling: 1. The branch manager of office estimates that her employee is idle for a certain percentage of time and wishes to conduct a work sampling from one of its employee. Below are the details of work sampling study. Number of Observations Details 465 Meeting with welfare client 130 Idle 76 Personal time 27 Discussion with supervisor 130 Filing and computer data entry In the course of his study, the analyst would like to find out the following: 1. What is the %idle time? 2. What is the confidence level value at +- 3.5% limit error? Given: n=828 P= 130 + 77 = 207 E=+-3.5% Required: 1. What is Idle Time? 2. What is the confidence level value? Formula: N = Z2P (1-P) X2 Solution: 1. Idle time = 130 + 77 825 = 0.25 = 25% 𝒁𝟐 𝒑 (𝟏−𝒑) 2. N = 𝒆𝟐 ne2 = 𝒛𝟐 𝒑( 𝟏 − 𝒑) 𝑛 Z = e √ 𝑝(1−𝑝) Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement 828 Z = 3.5 % √ 0.25(1−0.25) z = 2.326 2. In a certain activity in ABC company, it is observed by the analyst under 40 observations that the operator is idle 36 times. Find the following: 1. What is the %idle time of the operator? 2. If the operator perform the task for 8 hrs per day, how many minutes the operator is idle? 3. How many minutes the operator is working in a 8hr/day operation? 4. What will be the confidence level value if the analyst will have an 8.67% limit error? Solution: 1. % idle time = 4 minutes 40 min. =0.1 = 10% 2. Operator idle time in 8 hr/day operation = 8hr x 60 minutes x 4 minutes Day 1 hr 40 = 48 minutes 3. Operator working time in 8 hr/day operation = 8hr x 60 minutes x 36 minutes Day 1 hr 40 = 432 minutes 𝑝(1−𝑝) 4. N = z2 𝑒2 ne2 = 𝒛𝟐 𝒑( 𝟏 − 𝒑) 𝑛 Z = e √ 𝑝(1−𝑝) 40 Z = 8.67 % √ 0.1(1−0.1) Z = 1.645 3. Upon observing a certain activity, the time study analyst gathered a 125 samples with an estimate a 95% probability. The person doing the activity was observed to be 20% idle. Find what is the limit error? Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement Solution: 1. N = z2 p (1-p) E2 Ne2 = z2 p ( 1-p) E2 = z2 p( 1-p) N 𝑝(1−𝑝) E = Z2 √ 𝑛 0.2(1−0.2) E = 1.9602 √ 125 (0.2)(0.8) E = 1.9602 √ 125 E = 13.74% E = 14% 4.A motorcycle company uses a conveyor belt in assembly of a scooter. During 100 observations, The analyst observed that the machine was working for 75% of the time. If at 95% probability and margin of error of +-10%, 1. Determine the exact number of observation the analyst should perform? 2. How many excess observations were made? 3. If the margin of error was reduced to +-5%, determine the number of observations? Solution: Z = 95% E = 10% W = 75% 2. N = z2 p (1-p) E2 = (1.960)2 (0.25)(1-0.25) (0.10)2 = 72.03 = 73 observations 3. 27 excess observations 4. N = z2 p (1-p) E2 = (1.960)2 (0.25)(1-0.25) Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement (0.05)2 = 288.12 n = 283 observations Sample size We can apply a statistical method or a conventional method for the statistical method, we have first to take a number of preliminary readings (n'). We then apply the following equation4 for the 95.45 confidence level and a margin of error of ± 5 per cent: 2 √𝑛′ ∑ 𝑥 2 − (∑ 𝑥)2 𝑛 = (40 ) ∑𝑥 Where: 𝑛 = 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒 𝑤𝑒 𝑤𝑖𝑠ℎ 𝑡𝑜 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒 n’= number of reading taken in the preliminary study ∑ = 𝑠𝑢𝑚 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠 x = value of the readings Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement An example will make the point clear. Let us suppose that we take five readings for a given element, and find that the value of the elapsed time in 1/lOOths of a minute is 7, 6, 7, 7, 6. We can then calculate the squares and the X X2 7 49 6 36 7 49 7 49 6 36 Ex = 33 Ex2 = 219 n' = 5 readings. By substituting these values in the above formula, we obtain the value n=8.81 or 9 reading 2 √𝑛′ ∑ 𝑥 2 − (∑ 𝑥)2 𝑛 = (40 ) ∑𝑥 2 √5(219)−332 𝑛 = (40 33 ) 𝑛 = 8.81 𝑜𝑟 9 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 Therefore the number of preliminary readings is less than the required sample size of 9. Then we must increase the sample size from 5 readings to 9 readings Example The following data was obtained by time study analyst during the preliminary observation in making a bracelet. Determine how many readings or observations the analyst should perform for accurate study? Time in minutes Cycle (X) X2 1 8.75 76.5625 2 7.67 58.8289 3 6.34 40.1956 4 8.24 67.8976 5 7.45 55.5025 6 9.12 83.1744 7 8.75 76.5625 8 7.45 55.5025 9 6.34 40.1956 10 7.28 52.9984 77.39 607.4205 2 √𝑛′ ∑ 𝑥 2 − (∑ 𝑥)2 𝑛 = (40 ) ∑𝑥 Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM  Quezon City Polytechnic University Work Measurement 2 √10(607.4205)−77.392 𝑛 = (40 ) 77.39 𝑛 = 4.7650 𝑜𝑟 5 𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠 Therefore, there is an excess reading of 5 Quezon City Polytechnic University, Quezon City Philippines Department of Industrial Engineering Engr. Aura Marie B. Novesteras, MAED-EM