Metrics and Measurement Work Sampling Project

Divyang Choudhary 1001391003
Work Sampling Assignment
(Key Assignment 4)
IE-5342-005 Metrics and Measurement
Submitted by: Divyang Choudhary (1001391003)
Submitted to: Dr. Shernette Kydd

Table of Contents
Introduction..................................................................................................................................................1
Observations .............................................................................................................................................1
Description of Activity Categories ..............................................................................................................2
Work Sampling Form (Blank).....................................................................................................................3
Populated Work Sampling Form................................................................................................................5
Data Summary ..........................................................................................................................................6
Calculations...............................................................................................................................................7
Discussion.................................................................................................................................................9
Conclusion ..............................................................................................................................................11
References..............................................................................................................................................11

Introduction
Working sampling is the statistical technique that identifies the percentage of occurrences of
each previously defined category of activity by statistical sampling and random observations.
Traditionally this technique is used for efficiently controlling the organization. For this technique to
work, the complete picture of production and non-production time of machine and workers in work
area is required and can be achieved by direct and continuous observation of shop floor. However,
that would mean, employing a large workforce which is unrealistic and so, it is better to assume that
at a glance at any moment of time, where 80% of the machines and workforce are idle 20% of the
time. If this approach is repeated, it can be said with certain confidence that at any time 80%
machines would work while the other 20% be idle. When the sampling is large enough and taken at
random, it becomes a pretty nice representation of the real situation with some certain percentage of
error. Thus, we can define work sampling as a technique of getting an idea of utilization machines
or human beings through a large number of observations at random time intervals.
Here in this study, my goal is to observe and record the timings of my activities of interest
for a period of 20 weekdays and perform the necessary calculations and analysis to find out how
and where my time is distributed amongst the activities. From the analysis, it will be possible to find
out where time can be redistributed to increase my efficiency and productivity.
Observations
The theoretical exercise allowed me to understand the nature of the parameters involved in
work sampling studies. How each value interacts and behaves if one or some of them are
manipulated. For the exercise, we were given that the margin of error was between 3%-6% while
the confidence interval was to be within the range of 80%-95%. For the first five scenarios, I kept
the confidence interval constant at 90% and manipulated the margin of error (c) value by keeping c,
at 3%, 3.5%, 4%, 5% and 6%. The next set of five scenarios had the c value at a constant of 3%
while the confidence interval varied between the given range as 80%, 83%, 85%, 90% and 95%.
From both the first and the second sets of scenarios, the respective values of the number of
observations (n) were determined and are as follows,
C Confidence Interval ⍺ ⍺/2 Z⍺/2 Phat (1-Phat) N
3% 90% 10% 5% 1.645 35% 65% 684
3.5% 90% 10% 5% 1.645 35% 65% 503
4% 90% 10% 5% 1.645 35% 65% 385
5% 90% 10% 5% 1.645 35% 65% 246
6% 90% 10% 5% 1.645 35% 65% 171
3% 80% 20% 10% 1.285 35% 65% 417
3% 83% 17% 9% 1.345 35% 65% 457
3% 85% 15% 8% 1.405 35% 65% 499
3% 90% 10% 5% 1.645 35% 65% 684
3% 95% 5% 3% 1.885 35% 65% 898

(Key Assignment 4)
2
The above is conclusive of the fact that as the number of observations increases the margin of error
decreases.
Description of Activity Categories
In accordance to my daily routine, I have highlighted about nine activities, including "Others," for
this study. Each activity is significant and is indicative of my goals towards my academic and career
success. Depending on the schedule for the day my day starts off with my alarm going off around
0800hrs to 0830hrs. The thirty minutes leeway is given in consideration of my heavy sleeper nature.
After waking up my first activity is to freshen up which involves me relieving myself,
brushing my teeth and then bathing to cleanse my body. Good hygiene is necessary for a good and
healthy life. Afterward, I dress and get ready to start my day. The activity runs for about an hour or
hour an half.
The activity that follows depends on the schedule for the day. As per the Mondays and
Wednesdays, schedule, the next activity would be cooking. Cooking as the name suggests is the act
of preparing meals for the nourishment of the body. In my case, I prepare a large meal for the entire
day and allows me to save time throughout the day.
Afterward, per my goal of starting off my career, I spend more than an hour job searching
and applying for the jobs that catch my eye. Around 1330hrs to 1430hrs I have my lunch and enjoy
some entertainment or chatting with my family back home.
Being the afternoon, the body circulates more blood in the processing of the ingested food
than to the brain, and the sun at its apex does not help either this is why I choose to give in and take
a Siesta. Siesta refers to an afternoon nap, and I wake up roughly around 1600hrs. Fully rejuvenated
I start studying and preparing for the upcoming lecture in the evening.
Studying involves going through the what was taught in the previous lecture and a little
further to make sure I do not lose myself in class. The activity also helps to highlight any queries
that may have hindered my progress in the subject to ask in class.
At around 1700hrs I leave my apartment and commute towards the 1730hrs lecture. I return
home from the lecture at around 1910hrs. Upon arrival, I am mentally exhausted and hungry. To
0%
10000%
20000%
30000%
40000%
50000%
60000%
70000%
80000%
1 2 3 4 5
Increasing c vs n; with
Confidence Interval constant
at 90%
C n
0%
10000%
20000%
30000%
40000%
50000%
60000%
70000%
80000%
90000%
100000%
1 2 3 4 5
Varying Confidence Interval
vs n; with constant c at 3%
Confidence Interval n

(Key Assignment 4)
3
relive my hunger I have supper and enjoy some entertainment or call home and later to wash the
dishes.
After this activity, all that is left is to catch up on some light reading or research article of
interest and hit the sack at the end. The activity "Others," involves commuting, cleaning dishes,
housework, etc. For the remaining days, only slight changes occur in the order of the activities.
Work Sampling Form (Blank)
Date: Work Sampling Data Page. No - 1
Period of Study: Activity Category (AC)
Observer:
Department:
Notes:
Dates
mm/dd/YYYY mm/dd/YYYY mm/dd/YYYY mm/dd/YYYY mm/dd/YYYY
Times AC Times AC Times AC Times AC Times AC
Dates

(Key Assignment 4)
4
Dates
Dates

(Key Assignment 4)
5
Populated Work Sampling Form
Date: 04/20/18 Work Sampling Data Page. No - 1
Period of Study: 03/26/2018 to 04/20/2018 Activity Category (AC)
Observer: Divyang Choudhary 1-Freshing up 7 - Studying
Department: NA 2 - Eating 8- Reading
Notes: Work sampling on myself for 20 weekdays. 3 - Cooking 9- Others
4 - Siesta
5 - Online Job Application
6 - Attending Class
Dates
3/26/18 3/27/18 3/29/18 3/30/18 3/31/18
8:31 AM 1 8:30 AM 1 8:40 AM 1 9:00 AM 1 8:00 AM 1
9:43 AM 3 9:40 AM 2 9:52 AM 3 9:15 AM 2 8:15 AM 2
10:12 AM 5 10:10 AM 5 10:32 AM 5 10:05 AM 5 8:57 AM 5
1:40 PM 2 1:50 PM 2 1:39 PM 2 1:53 PM 2 12:03 PM 2
2:30 PM 4 2:40 PM 5 2:33 PM 4 2:55 PM 5 2:37 PM 4
4:05 PM 7 4:20 PM 8 4:00 PM 7 4:23 PM 8 4:31 PM 5
5:00 PM 9 6:39 PM 2 5:00 PM 9 5:45 PM 2 5:57 PM 2
5:35 PM 6 7:15 PM 9 5:31 PM 6 6:59 PM 9 6:23 PM 9
7:15 PM 2 7:51 PM 3 7:22 PM 2 7:24 PM 3 6:40 PM 3
7:50 PM 8 8:59 PM 7 8:08 PM 8 8:13 PM 7 7:27 PM 7
Dates
4/2/18 4/3/18 4/4/18 4/5/18 4/6/18
8:39 AM 1 8:35 AM 1 8:35 AM 1 9:16 AM 1 8:08 AM 1
9:48 AM 3 9:51 AM 2 9:43 AM 3 9:20 AM 2 8:36 AM 2
10:20 AM 5 10:22 AM 5 10:24 AM 5 10:21 AM 5 9:08 AM 5
1:43 PM 2 2:05 PM 2 1:33 PM 2 2:02 PM 2 12:15 PM 2
2:39 PM 4 2:45 PM 5 2:27 PM 4 3:03 PM 5 3:01 PM 4
4:10 PM 7 4:22 PM 8 3:55 PM 9 4:32 PM 8 4:57 PM 5
5:04 PM 9 6:46 PM 2 4:58 PM 7 5:55 PM 2 6:21 PM 2
5:45 PM 6 7:27 PM 9 5:19 PM 7 7:03 PM 9 6:48 PM 9
7:25 PM 2 7:58 PM 3 7:18 PM 2 7:38 PM 3 6:57 PM 3
7:57 PM 8 9:01 PM 7 8:00 PM 8 8:28 PM 7 7:44 PM 7

(Key Assignment 4)
6
Dates
4/9/18 4/10/18 4/11/18 4/12/18 4/13/18
8:43 AM 1 8:43 AM 1 8:41 AM 1 9:16 AM 1 8:21 AM 1
9:51 AM 3 9:55 AM 2 9:48 AM 3 9:21 AM 2 8:44 AM 2
10:22 AM 5 10:35 AM 5 10:29 AM 5 10:21 AM 5 9:24 AM 5
1:47 PM 2 2:19 PM 2 1:38 PM 2 2:03 PM 2 12:21 PM 2
2:43 PM 4 2:58 PM 5 2:32 PM 4 3:04 PM 5 3:17 PM 4
4:12 PM 7 4:29 PM 8 4:00 PM 7 4:35 PM 8 5:11 PM 5
5:05 PM 9 6:49 PM 2 5:04 PM 9 5:55 PM 2 6:30 PM 2
5:45 PM 6 7:30 PM 9 5:24 PM 6 7:04 PM 9 7:00 PM 9
7:27 PM 2 8:06 PM 3 7:22 PM 2 7:38 PM 3 7:02 PM 3
7:57 PM 8 9:09 PM 7 8:06 PM 8 8:28 PM 7 7:47 PM 7
Dates
4/16/18 4/17/18 4/18/18 4/19/18 4/20/18
8:45 AM 1 9:07 AM 1 8:43 AM 1 9:19 AM 1 8:26 AM 1
9:53 AM 3 9:59 AM 2 9:50 AM 3 9:21 AM 2 8:49 AM 2
10:27 AM 5 10:56 AM 5 10:36 AM 5 10:21 AM 5 9:27 AM 5
1:48 PM 2 2:30 PM 2 1:39 PM 2 2:06 PM 2 12:26 PM 2
2:44 PM 4 3:09 PM 5 2:33 PM 4 3:04 PM 5 3:22 PM 4
4:13 PM 7 4:39 PM 8 4:08 PM 7 4:35 PM 8 5:16 PM 5
5:11 PM 9 7:00 PM 2 5:10 PM 9 5:56 PM 2 6:33 PM 2
5:50 PM 6 7:42 PM 9 5:31 PM 6 7:06 PM 9 7:03 PM 9
7:33 PM 2 8:30 PM 3 7:30 PM 2 7:41 PM 3 7:05 PM 3
8:01 PM 8 9:26 PM 7 8:12 PM 8 8:31 PM 7 7:50 PM 7
Data Summary
The data for the work sampling study was collected with me as the subject of interest and my
activities defined. For this study, the time period of interest started from 0800hrs in the morning and
ended around 2000hrs. Within this twelve hour period, the start times for all the defined activities
were observed and recorded. The study ran for a period of 20 days from March 26th
of the year 2018
to May 20th
. The start time of the following activity is indicative of the end time of the previous
activity. The recordings were made with the assistance of an activity tracker application on my
phone and based on my weekday schedule.

(Key Assignment 4)
7
Calculations
The first step is to calculate the frequency of occurrence of each operation or in this case activity
category.
AC Frequency
1 20
2 52
3 20
4 12
5 32
6 7
7 21
8 16
9 20
200
The frequency is easily calculated by counting the times; each activity has occurred throughout the
data form for the period in question.
The next step is to determine the proportions of each operation that actually occurred.
Proportions (𝑝̂) =
()*+,*-./ 01 *2.3 04*)2560-7
80529 -,:;*) 01 04*)2560-7
For the first operations, the proportion is,
𝑝< =
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠
=
20
200
= 0.1
Similarly,
The proportions for all the operations were calculated and is as shown below.
AC Frequency Occurrence (p-hat)
1 20 0.1
2 52 0.26
3 20 0.1
4 12 0.06
5 32 0.16
6 7 0.035
7 21 0.105
8 16 0.08
9 20 0.1
200

(Key Assignment 4)
8
Next is to calculate the standard deviations for each operation. The standard deviation can be
calculated as follows,
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑒𝑎𝑐ℎ 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛 X𝜎4Z[ =
𝑝̂(1 − 𝑝̂)
𝑛
Now, for the first operation,
𝜎4Z = ^
4_(`a4_)
-
= ^
b.`∗(`ab.`)
dbb
= ^
b.`∗b.e
dbb
=0.021213203
Similarly, the standard deviations for the remaining proportions are as follows,
AC Frequency Occurrence (p-hat) (1-phat) SD
1 20 0.1 0.9 0.021213203
2 52 0.26 0.74 0.031016125
3 20 0.1 0.9 0.021213203
4 12 0.06 0.94 0.016792856
5 32 0.16 0.84 0.025922963
6 7 0.035 0.965 0.012995191
7 21 0.105 0.895 0.0216766
8 16 0.08 0.92 0.019183326
9 20 0.1 0.9 0.021213203
200
Now we determine the confidence intervals in the work sampling. For the determining the control
limits, we assume the confidence level in this study to be 95% with a margin of error of 5%. The
values for 𝑧∝ d⁄ is obtained from the normal distribution table for the respective
∝
d
values.
Therefore the control intervals for the proportions can be calculated as follows,
Upper Control Limit (UCL) = 𝑝̂ + (𝑧∝ d⁄ ∗ 𝜎4Z)
Lower Control Limit (LCL) = 𝑝̂ − (𝑧∝ d⁄ ∗ 𝜎4Z)
Hence, for the first proportion the control limits are as follows,
Upper Control Limit (UCL) = 𝑝̂ + (𝑧∝ d⁄ ∗ 𝜎4Z) = 0.1+(1.96*0.021213203) = 0.14
Lower Control Limit (LCL) = 𝑝̂ − (𝑧∝ d⁄ ∗ 𝜎4Z) = 0.1-(1.96*0.021213203) = 0.06
Similarly, the control limits for the remaining proportions are as follows:
AC Frequency Occurrence (p-hat) (1-phat) SD LCL UCL
1 20 0.1 0.9 0.021213203 0.06 0.14
2 52 0.26 0.74 0.031016125 0.20 0.32
3 20 0.1 0.9 0.021213203 0.06 0.14
4 12 0.06 0.94 0.016792856 0.03 0.09
5 32 0.16 0.84 0.025922963 0.11 0.21
6 7 0.035 0.965 0.012995191 0.01 0.06
7 21 0.105 0.895 0.0216766 0.06 0.15
8 16 0.08 0.92 0.019183326 0.04 0.12
9 20 0.1 0.9 0.021213203 0.06 0.14
200

(Key Assignment 4)
9
It is within these ranges that the values of the proportions of the activities recorded stand true.
Now, we need to calculate the total number of observation ideally required for the work sampling
study. The ideal "n," is calculated to reduce the statistical error since the number of observations
has an inverse relationship with the number of statistical errors. Also, with the increased number
of observations, the confidence interval becomes narrower, accuracy and precision of our
estimates increases.
Now, based on the above-determined values we can calculate the number of observations by the
following set of equations,
Standard deviation X𝜎4Z[ =
.
•∝ €⁄
Number of observations ( 𝑛) =
4_∗(`a4_)
•‚
€ƒ
Substituting the equation of 𝜎4Z in the equation for n we get,
𝑛 =
(𝑧∝ d⁄ )d
∗ 𝑝̂ ∗ (1 − 𝑝̂)
𝑐d
Now, for the first activity,
𝑛 =
X𝑧∝ d⁄ [
d
∗ 𝑝̂ ∗ (1 − 𝑝̂)
𝑐d
=
(1.96)d
∗ 0.1 ∗ (1 − 0.1)
5d
= 138
Similarly, the for the remaining activities the number of observations required are stated as
follows,
AC Frequency
Occurrence
(p-hat) (1-phat) SD LCL UCL C
Confidence
Interval ⍺ ⍺/2 Z⍺/2 n
1 20 0.1 0.9 0.021213203 0.06 0.14 5% 95% 5% 2.5% 1.96 138
2 52 0.26 0.74 0.031016125 0.20 0.32 5% 95% 5% 2.5% 1.96 296
3 20 0.1 0.9 0.021213203 0.06 0.14 5% 95% 5% 2.5% 1.96 138
4 12 0.06 0.94 0.016792856 0.03 0.09 5% 95% 5% 2.5% 1.96 87
5 32 0.16 0.84 0.025922963 0.11 0.21 5% 95% 5% 2.5% 1.96 207
6 7 0.035 0.965 0.012995191 0.01 0.06 5% 95% 5% 2.5% 1.96 52
7 21 0.105 0.895 0.0216766 0.06 0.15 5% 95% 5% 2.5% 1.96 144
8 16 0.08 0.92 0.019183326 0.04 0.12 5% 95% 5% 2.5% 1.96 113
9 20 0.1 0.9 0.021213203 0.06 0.14 5% 95% 5% 2.5% 1.96 138
200 1313
Discussion
Through this study, I was able to get a bird's eye view on the proportions of the time spent on each
of my activities of interest. Before the recording began, I had a feeling that most of my time was
being spent on job searches and applications and so, I was pretty certain that it would be the highest
ranked with eating as the second. However, from the analysis performed in the study, it can be said
that the three major activities that take up most of my time are the activities of eating, online job

(Key Assignment 4)
10
application and studying. These activities occurred throughout the time period in question with
26%, 16% and 11% margin of the total pie respectively. Also, from observing the time spent on
each activity, it can be stated that amongst the above mentioned significant activities, online job
application utilizes the most time out of the three with the activity of studying as the second most
time consuming and the last being eating. However, it should be noted that during the activity of
eating, I also, indulged myself in leisure activities such as watching a movie or a tv show or even
calling back home. However, that is precisely what I need to decrease and redistribute the time
saved towards other essential activities. The suggested step would increase both my productivity
and efficiency for my future.
Apart from the above observations, there is a matter of the Hawthorne effect. Hawthorne
effect is apparent when the subject under observation knows that they are being observed and try to
either consciously or subconsciously manipulate their performance to impress the observers,
thereby creating a biased data set. For this study, I was both the subject and the observer.
Throughout the study, I have stayed true to my schedule and lifestyle. However, one cannot ignore
the slight possibility that subconsciously I made the data biased since I was aware that I had to track
my activity and was in charge of the application recording the activities. I hope that the data I
collected is true.
If someone else would have been the subject of interest for the work sampling study with me
as the observer, then I would have performed the study without letting him/her know that they are
under observations. The data would be easily obtained since all I have to do is observe and note the
timings of all the activities that govern my subjects day. Data so obtained from that approach would
have been 100% unbiased and true. It would definitely be a bit harder to continuously observe their
day during their working hours without getting detected for 20 days, and chances of our schedule
matching are also, slim if the subject has different courses. However, that would be the only part
which I have to overcome by first researching my subject, his/her schedule and first by choosing
someone who has the courses as I do.
10%
26%
10%
6%
16%
3%
11%
8%
10%
Frequency of operations/activities, throughout the 20
days period
1
2
3
4
5
6
7
8
9

(Key Assignment 4)
11
Conclusion
Work sampling is a great tool and technique that helps one to get a bird's eye view of the
time spent on each work activities and allows us to focus our efforts to areas that consume the most
time and remedy them if they are a negative influence to the overall process.
The study brought to my notice the how efficiently my time was being utilized and where it
could be redistributed. For the most part, I am glad to know that my hunch was right and that my
priorities are still intact. I will be graduating this semester as such my top priority is to search for a
job. The study clearly highlighted the same.
References
1. Groover, M. P. (2007). Work systems and the methods, measurement, and management of
work. Upper Saddle River, NJ: Pearson Prentice Hall.
2. Cherry, K., & Gans, S. (n.d.). What Is the Hawthorne Effect and How Does It Influence
Productivity? Retrieved from https://www.verywellmind.com/what-is-the-hawthorne-effect-
2795234

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