1. Running Head: Walter Shewhart and the Theory of Varibility McNabb 1
Walter Shewhart and the Theory of Varability
Thomas McNabb
Amberton University
Paper presented in Partial Fulfillment
Of the Requirements of
MGT5203.E1 Operations Management
Dr. Kimyana Ards
Summer 2014
June 15th, 2014

2. Walter Shewhart and the Theory of Varibility McNabb 2
Abstract
It has been almost 90 years since Walter Shewhart developed a statistical analysis method for
sampling, which allows variations to be identified. His methods for quality improvement of a
product are far from the norm of his time. This is why neither his name, nor his methods have
been forgotten because SPC, statistical process control, charts are still synonymous with Shewart
charts (Shah, 2010). Over the years, statistical analysis has been made easier with computers and
calculators, thus many improvements have been made to Shewhart’s concepts. However, his
statistical analysis methods, along with their improvements, have carried over into many of the
techniques still being used today. Some of the more common techniques are Project Evaluation
and Review Technique (PERT), qualitative, and quanitative analysis, and Shewharts statiscal
analysis methods, which are still the root of six sigma.
Key words: Project Evaluation and Review Technique (PERT), Statistical Process Control
(SPC), Work Breakdown Schedule (WBS), Duration, Beta Distribution, Standard Deviation,
Sigma, Six Sigma, Critical Path Method CPM,

3. Walter Shewhart and the Theory of Varibility McNabb 3
Contributor Introduction
Walter Shewhart, holding a doctorate in Physics, starts working for the Western Electric
Company in 1918; this company provides telephone equipment to the Bell Telephone company
(Giants of quality - Walter Shewhart, 2011). Most of the telephone lines are being buried, so if
an issue arises, of course the repairs become very difficult. Shewhart observes the failures, and
becomes concerned with the variation of the process in the production of the telephone
equipment. With this concern in mind, “[i]n 1924, Shewhart propose[s] his theory of variability
in which he attribute[s] the sources of variability as either assignable-cause or chance-cause
variation. On 16 May 1924 he prepare[s] a technical memorandum of less than one page in
which he introduce[s] the control chart as a tool for distinguishing between these two sources of
variability. By using the control chart to bring the process into a state of statistical control, where
only chance causes are present, and maintaining this in-control state, it is possible to predict how
the future process output will behave and from this the process can be managed economically”
(Giants of quality - Walter Shewhart, 2011). The contributor is one of this author’s favorite
because of the importance of SPC charts in Operations Management, and PERT analysis in
Project Management.
Operations Management and its Importance
This author has been using SPC, Statistical Process Control, charts for most of his
operational career to ensure the plant process stays within a specified range predetermined by a
process engineer. Although all the operators realized the concept, and thus followed the
instructions, the SPC charts were not thoroughly explained. For example, there is a 68% chance
the sample will fall directly on the mean, but a 99.7% chance the sample will stay within 3

4. Walter Shewhart and the Theory of Varibility McNabb 4
sigmas of the mean, which is considered normal. (These calculation percentages will be
explained under PERT analysis.) If the samples fall outside of the range, there is a .03 chance
that the sample is normal, so the odds are that an issue needs to be resolved. The below SPC
chart is an example of tracking variations by enacting operations management, which “…is the
management of systems or processes that create goods and/or provide services” (Stevenson,
2012, p. 4). By using SPC charts, the company that employed this author is able to receive an
ISO 9001 accreditation for meeting quality standards. The ISO standard allows for
unencumbered international trade.
(SkyMark, 2014)
Program Evaluation and Review Technique (PERT) Analysis
The ability to pinpoint durations of various activities in the Work Breakdown Schedule,
WBS, that is being developed has a lot of subjectivity. In the article, Uncertainty in Project
Scheduling- Its use in PERT/CPM Conventional Techniques, Omar writes that “the duration of
each activity is assumed to have one value… yet, the time required for completing an
activity…[includes variations such as]…resources, methods, technology, site condition, weather,

5. Walter Shewhart and the Theory of Varibility McNabb 5
and regulations” (Omar, 2009, p. 30). The PERT method uses a Beta distribution of time
estimated duration, which are called optimistic, most likely, and pessimistic to determine a mean.
According to the book, project management, the managerial process, the original formula for
PERT is “(a+(4*M)+b/6)… standard deviation= (b-a)/6…[which means that] PERT is almost
identical to the Critical Path Method (CPM) technique except it assumes each activity duration
has a range that follows a statistical distribution” (Larson & Gray, 2011, pp. 242-245).
Based on the article, Probabilistic Forecasting of Project Duration Using Bayesian
Inference and the Beta Distribution, if one chooses to use Bayesian Inference and Beta
distribution, a forecast of an upcoming project can become much more accurate. A common
practice in which to predict performance forecasting is “...to use the earned value method (EVM)
for cost and schedule forecasting, and … to use the (EVM) for cost forecasting and the critical
path method for schedule forecasting” (Kim & Reinschmidt, 2009, p. 178), but in reality, they
are just linear extrapolations. They suggest that by adding S-curve models and Bayesian
Inferences to the scheduling methodologies, one may improve the accuracy of the schedule based
on statistical measurements. The main concern the authors express when using CPM is that
although mathematically it is simplistic compared to some of the statistical methods, detailed
technical knowledge is required for all activities.
By using Program Evaluation and Review Technique (PERT) Analysis, one may
calculate the probability of meeting scheduled durations by using the formula found in Project
Management The Managerial Process as Z= (Scheduled project duration - Critical Path
Duration)/square root of standard deviation ^2. What does all this mean one may ask, well PERT
wants to give a 1/6 value to Optimistic, a 2/3 value to Most Likely, and a 1/3 value to

6. Walter Shewhart and the Theory of Varibility McNabb 6
Pesimistic, so if Optimistic =5 days, Pessimistic =10 days, and Most Likely =7 days, then
(5+(4*7)+10)/6 = 7.17 days, which is the mean, and has a confidence level of approximately
68% according to the Z table. If one were to add one sigma, which according to the Z table is
1.645* Standard Deviation, and add, and subtact it to the mean, it will gain a confidence of 90%.
To get a confidence of 95% requires 2 * standard deviation plus or minus the Mean. Three
sigmas, which is 3* standard deviation plus and minus the Mean will gain a confidence level of
99.7%. In this case 7.17 +/- (3*(10-5/6)) = 4.68 to 9.66, which basically states that 99.7% of the
time, the amount of days to complete the project will take between 4.68 and 9.66 days according
to Shewhart’s original calculation, and the new improved Z-table. Since each of the three
additions to either side of the mean is referred to as a sigma, then 99.7% confidence = six sigma.
Qualitative and Quantitative Analysis
Currently at this author’s place of enployment, a BORA, bypass override application,
form is filled out whenever it becomes necessary to temporary change normal operations
management. By using statistical analysis, the qualitative analysis will allow one to calculate the
possibility of an unscheduled variation occuring. By using statistical analysis for quantitative
analysis, one will be able to see the cost associated with the unscheduled variation. By
overlapping the qualitative and quantitative analysis, one may accurately predict the possibility
and the cost associated with the variation to see if the bypass is safety or cost viable.

7. Walter Shewhart and the Theory of Varibility McNabb 7
In order to determine the severity of the risks identified by the team, the above qualitative
and quantitative matrix is used to identify the cause and the effect each risk has on the project.
By identifying and prioritizing the risks, the operations manager or designee gets an opportunity
to mitigate the risks before the project begins. Once the risks are assigned a probability and
impact, they are assigned an appropriate position on the chart. Since this document captures all
the risk activities, it allows the operations manager or designee to move to the process of risk
mitigation/avoidance planning.
Conclusion, Improving the Contribution
Because of the complexity of statistical analysis, this author’s suggestion does not delve
on improving the contribution of Shewhart. Instead, he encourages a company to train all of its
operational staff on Shewhart’s statistical analysis by sending them all to Six Sigma training.
This training will allow one to fully understand SPC charts, Pert Analysis, and it will open the
door to many of the qualitative, and quantitative analysis’ being used in the current market. The
H M L
Fatality/Multiple
Injuries
Major Injury/
LTI
Recordable/First
Aid
Cost: > $75MM Cost: $10-$75MM Cost: < $10MM
Prod.: 4 Train Days
Prod.: 2 - 4 Train
Days
Prod.: < 2 Train
Days
Major
Environmental/
Regulatory
non-compliance
Localized
Environmental/
Regulatory
(reportable)
Localized
Environmental/
Regulatory (non-
reportable)
H > 50% U C S
M 10-50% C S M
L < 10% S M I
Probability/
Likelihood
Risk Rank:
I: Insignificant;
M: Minor
S: Significant
C: Critical;
U: Unacceptable
Impact/Severity

8. Walter Shewhart and the Theory of Varibility McNabb 8
contributor, Walter Shewhart, only opens the door to improving Operations Management. There
have been many other contributors, such as W. Edwards Deming, who have taken Shewhart’s
original concept, and have expanded on it, improving his contribution. The text book reads that,
“ [p]rocess analysis and improvement includes cost and time reduction, productivity
improvement, process yield improvement, and quality improvement and increasing customer
satisfaction. This is sometimes referred to as the six sigma process” (Stevenson, 2012, p. 26).
From the above statement, if one is trained in six sigma, it will help provide an understanding of
the actions of Shewhart. The training will also bring to light the concepts of many engineers and
statisticians who have used Shewhart’s concepts, and expanded on them to improve project
management, qualitative and quantitative analysis, and operations management.

9. Walter Shewhart and the Theory of Varibility McNabb 9
References
Giants of quality - Walter Shewhart. (2011, 12). Quality & Reliability Engineering International,
979.
Kim, B., & Reinschmidt, K. (2009). Probablistic Forecasting of Project Duration Using Bayesian
Inference and the Beta Distribution. Journal of Construction Engineering and
Management, 178-186.
Larson, E., & Gray, C. (2011). Project Management the Managerial Process. New York:
McGraw- Hill Irwin.
Omar, A. (2009). Uncertainty in project Scheduling - Its Use in PERT/CPM. Cost Engineering,
51(7), 30-34.
Shah, S. S. (2010). Control chart: A Statistical Process Control Tool in Pharmacy. Asian Journal
of Pharmaceutics, 4(3), 184-192.
SkyMark. (2014). Retrieved from Control Charts:
http://www.skymark.com/resources/tools/control_charts.asp
Stevenson, W. J. (2012). Operations Management. New York: McGraw-Hill Irwin.