Comprehensive Analysis: Statistics and Its Applications in Engineering

This report provides a comprehensive overview of the crucial role of statistics in various engineering fields. It highlights the application of statistical methods in data collection, analysis, and presentation, emphasizing their importance in designing products, solving technological issues, and optimizing processes. The report explores the use of statistical concepts such as probability, regression analysis, and sampling techniques in different engineering disciplines, including construction, manufacturing, and transport. It discusses how engineers utilize statistical models for predicting outcomes, assessing risks, and improving the efficiency and reliability of systems. Furthermore, the report emphasizes the significance of statistics in areas such as reliability theory, model simulation, and the development of transport systems. Overall, the document showcases how statistics are integral to engineering practices, enabling informed decision-making and driving innovation across diverse technological applications. The report also mentions the relevance of statistical data in market analysis and academic institutions.

Running Head: STATISTICS 1
Statistics
Name of Student
Name of Supervisor
Course Affiliated
Date

STATISTICS 2
Executive summary
Technology advancement mainly focuses on incorporating various science fields to
enhance quality production in varies firms. The statistic is fundamental for testing and analyzing
data, system error and assessing risks. Most consumable products such as electronics and
automobiles use reliability theory in statistics to determine product failure. The engineers mostly
apply statistics to construct, operate and to manage construction systems. To achieve the best
architecture model, engineers incorporate model simulation and another statistical model to have
the best presentation.

STATISTICS 3
There are many roles played by statistics in engineering and technology fields. Engineers
need statistician help in designing a product. Statistics deals with data collection, data analysis,
and presentation (Huber, P. 2011). The data is used to create an operational model used in
deciding the progress for the Company. Statistic engineers help in solving critical technological
issues in society by applying scientific principles and analyze an existing product or design a
new product that satisfies the customer. Manufacturing activities in industries mostly take place
in closed-loop control with the automation aiming to ensure processes variables are okay. In
paper or chemical industries, the engineers often have to apply closed-loop concepts to control
the system to minimize the impact of activities disturbance.
As per Rees (2018), elements of statistics used in conducting research include linear
regression and correlation, chi-square, statistical inferences, descriptive analysis, and probability
sample design among others. According to Anderberg (2014), probability sample design is
applied in carrying out field studies. Simple random sampling is a statistical procedure which
gives all elements in the sample population equal chance of being selected. For example, in
conductions poll, all votes are given a fair opportunity of elected a preferred leader. Another
critical element in statistics field is study design where the specific protocol followed while
conducting the study. The investigator can translate the conceptual hypothesis obtain from the
research to an operation or real world event. One fundamental principle of statistical data it must
have a decent meaning level of consistency two or more measures, and it should upload validity
or trustfulness concept.

STATISTICS 4
Building and construction engineers apply probability model in establishing and
predicting corrosion process and load capability degradation for an existing concrete structure
over time (Devore, J. 2011). The engineers have to take into account the stochastic and duration
dependent characteristics of the existing concrete structure at the service environment. The time-
dependent probability distribution for corrosion ratio reinforcement, load capacity loss, cracks
width, chloride penetration is simulated using numerical calculation. Therefore computer
simulation is applicable for the deterioration process for corrosion initiation of reinforcement and
load capability reduction process. The parameters needed are steel corrosion ratio, load capacity
reduction action, the percentage for the cracked concrete and the crack width. The statistics data
from field information of concrete structure proves prediction results.
The safety level for any construction process is crucial for planning of maintenance and
repair process. Effectiveness for any construction interventions depends on analytical models the
engineers will adapt to predicting time-dependent of corrosion reinforcement (Frangopol, D.
2011). The engineers have to develop models that describe on-set of corrosion, time of the
structural effects for corrosion and transport mechanism of chlorides to concrete cover. The
impact of structural corrosion calculates in probabilistic condition. As per (Sclavounos, P. 2012),
Karhunen-Loeve expansion series and finite element method are applicable for the numerical
discretization procedure purpose. A 2D mathematical model is used to ingress chloride into
concrete structure taking into account point to point environmental condition and variability of
material.
According to Kline (2013), Bayesian statistics approach combine prior data for a variable
used in assessing existing reinforced concrete structure with experimental findings. The phased
procedure defines predictive distributions and updated parameter figures of the resistance and

STATISTICS 5
actions variables. Data is updated about variables through the collection of site-specific
information to reduce uncertainties for characteristics values of a considered variable and
particular partial aspect. The statistical method helps to reduce the effect of changed data in the
specific amount and experimental figure found. The partial factor is in form coefficients of
variation for the variable associated in estimating the impact of changed data on variables. For
reliability purpose variables are classified either as dominant or non-dominant and the sensible
factor assigned. Two curves are drawn for the partial factors when the respective variable is
dominant or not
The resistance of the structure to destruction can be predicted using models consisting of
three variables which include the dimension of members and derived quantities, constituent
materials relevant and uncertainties of the resistance model used. Effect of corrosion of steel bar
structure may be quantified and is known. Probabilistic constraints for the model uncertainty
variables inferred for simplified models applied in finding bending ability to reinforce concrete
beams with reinforced corroded bars. The probabilistic model applied in analyzing the reliability
of the model constructed. The optimization procedure for assessing reliability is applied for the
generic member of the construction with the expected working life while assuming moderate
costs for the safety measure and failure significances. The reliability level of a structure to be
repaired or not depends on resistance ability before repair over resistance by Eurocodes obtained.
E[Ctot 1 (d0lim , tr)] = E[Ctot 2 (dopt ,tr)] Ctot1 = total cost for cases where there is no repair, Ctot 2 total
cost in instance where there is repair, dop is the optimum value for decision parameters. If dopt is
greater than d0lim repair is needed as the reliability level for existing structure is too low
(Cervenka, V. 2013).

STATISTICS 6
Another field that statistics is applicable in the engineering field is in the transport field to
identify the capacity of local highways. The statistical data will be more critical in developing a
reliable road connection affect considering all aspect with knowledge of a statistician. In this
scenario, the typical problem involves information on home-based trips and the number of
vehicles per household to provide a trip generation model that associate trips to the number of
individual and cars in each home. Mathematical modeling is used to construct a reliable model to
be implemented by engineers while making decisions and creating models for construction
purposes (Hinton, P. 2014). Trip-generation model is an essential tool in the planning of the
transport system for any country. Another applicable statistical method implemented in the
engineering field is the regression analysis used to enhance the proper allocation of resources.
Manufacturing industries use stratified sampling in tracing the defectives items. The
bottling company, for example, has to inspect the manufactured item in the production process.
Engineers have to employ sampling method in identifying the number of defective products by
using random sampling then apply probability tool to find the approximate number of faulty
items in each production set. Using such an idea help most manufacturing industries identifying
the minor issues which could affect the outcome of production; thus it helps to uphold the
company image. Statistics and engineering go hand in hand, to present numerical facts and
symbol for new products that will be inclusive of public demand. The probability theory is
applicable in almost all sector of production to predict the outcome of an investment (Robinson,
O. 2014). Having a clue about the issue is essential for a person to be prepared psychologically
in real life.
In conclusion, referring to malaria vaccine test and other research and application, it’s
clear that statistical elements help the scientist in optimizing the available resources to obtain

STATISTICS 7
results. Every process begins with researching the viability of the organization. Statistical data is
critical for engineers to know the market demand from the information conduct in the survey
carried out before the company set up. Incorporating statistics and engineering in academic
institutions will also help learns to focus on generating bold ideas that will focus on maximizing
on resources to achieve the best products while minimizing wastage.

STATISTICS 8
References
Anderberg, M. R. (2014). Cluster analysis for applications: probability and mathematical
statistics: a series of monographs and textbooks (Vol. 19). Academic press.
Cervenka, V. (2013). Reliability‐based non‐linear analysis according to fib Model Code
2010. Structural Concrete, 14(1), 19-28.
Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences. Cengage
learning.
Frangopol, D. M. (2011). Life-cycle performance, management, and optimisation of structural
systems under uncertainty: accomplishments and challenges 1. Structure and
Infrastructure Engineering, 7(6), 389-413.
Hinton, P. R. (2014). Statistics explained. Routledge.
Huber, P. J. (2011). Robust statistics (pp. 1248-1251). Springer Berlin Heidelberg.
Kline, R. B. (2013). Beyond significance testing: Statistics reform in the behavioral sciences.
American Psychological Association.
Rees, D. G. (2018). Essential statistics. Chapman and Hall/CRC.
Robinson, O. C. (2014). Sampling in interview-based qualitative research: A theoretical and
practical guide. Qualitative research in psychology, 11(1), 25-41.
Sclavounos, P. D. (2012). Karhunen–Loeve representation of stochastic ocean
waves. Proceedings of the Royal Society A: Mathematical, Physical and Engineering
Sciences, 468(2145), 2574-2594.