Basic Quality control with R

2. Introduction to
Quality

3. Quality is a situation when a set of inherent characteristics,
consistently fulfill the continuously changing requirements of
the organization's customers and other stakeholders.
What is Quality …. ???
Quality is based on the presence or absence of particular
attribute(s).
According to ANSI/ASQC Standard A3-1987:
Quality is the totality of features and
characteristics of a product or service that bear
on its ability to satisfy implied or stated needs.

4. Satisfaction of Consumers: Through better quality
Reduction in Production Cost: By effective inspection, Control over operations.
Effective Utilization of Recourses: By minimizing wastage and inefficiency.
Increased Goodwill: By providing quality goods/services to users.
Higher Morale of Employees: By working in effective quality atmosphere.
Improved techniques and methods of production: By supplying technical data for
manufacturing processes improved methods and designs of production.
Increased Sales: Quality control ensures production of quality products which is
immensely helpful in attracting more customers for the product thereby increasing
sales. working in effective quality atmosphere.
How Quality is Beneficial for Society ..?

5. Food: Precise definitions that are used to sort food into quality grades. For
example, apples might be sorted according to size, ripeness, color, symmetry and
condition to offer a premium and non-premium grade.
Manufacturing: A bicycle manufacturer performs automated quality control
testing on all units before shipping based on specifications such as detailed
measurements designed to ensure that a bicycle's tire is properly aligned to its
assembly.
Infrastructure: A solar panel manufacturer guarantees the conversion
efficiency of its modules over time. This is based on a specification of rated
power output and percentage of that output that can be expected as the panels
approach end-of-life, often 25 years.

6. Formulations: The amount of a high quality ingredient in a product e.g. a
beverage that is 30% organic pineapple juice.
Materials: Material quality such as the thread count of a fabric.
Software: Specifications for the performance of a software service such as a
99.99% ability rate.
Services: A hotel chain defines detailed specifications of what it means for a
room to be clean. This is used to define processes for cleaning services and
quality control checks.
More real life applications in process monitoring can be seen in quality
control literature.
Real Life Applications

7. Statistical
Quality Control

8. Statistical quality control (SQC)
The set of statistical tools used by quality professionals
Descriptive Statistics
• Mean, Standard Deviation, and Range.
Statistical Process Control (SPC)
• Involves inspecting the output from a process
• Quality characteristics are measured and charted
• Helpful in identifying in-process variations
Acceptance Sampling
• Used to randomly inspect a batch of goods to determine
acceptance/rejection
Three SQC Categories

9.  Histogram
 Pareto Chart
 Cause and Effect Diagram
 Defect Concentration Diagram
 Control Chart
 Scatter Diagram
 Check Sheet
SPC is collection of fundamental tools which are used to monitor process
behavior. The SPC tools are as follows
Statistical Process Control

10. Control Chart
• Control chart is a graphical display of a quality characteristic that has been
measured or computed from a sample versus the sample number or time.
Introduced by Walter, A. Shewhart in 1924 as a useful tool of SPC
Objective
• To detect abnormal variations in process parameters
Types of Variation
• Natural Variation or Common Causes Variation
(has a consistent pattern over the time)
• Un-Natural Variation or Special Causes Variation
(has unpredictable behavior over the time)
Control Charts
• Help in quick detection of special causes variation

11. Control Charts Types

12. Control Chart Phases
Retrospective Phase (Phase I)
• Analysis of historical data to determine stability of the Process
• Detection and removal of inconsistent observations
• Good at detection of large process shifts, outliers, measurement errors etc.
• Estimation of control limits for Phase II
Monitoring Phase (Phase II)
• Process is assumed to be stable
• Detection of departures of the process parameters from their in-control values
• Corrective actions

13. Control Charts
Shewhart Chart
• Based on current sample information
• Good at detecting large process shifts
Cumulative Sum (CUSUM) Chart
• Based on cumulative sum of the deviations of sample values from a target value
• Good at detecting small process shifts
Exponentially weighted moving average (EWMA) Chart
• Based on varying weight scheme
• Good at detecting small process shifts
• Lower values of λ are better for the detection of small shifts
𝒄𝒊 =
𝒋=𝟏
𝒊
𝒙𝒋 − 𝝁 𝟎
𝒁𝒊 = 𝝀 𝑻𝒊 + 𝟏 − 𝝀 𝒁𝒊−𝟏

14. Control Chart Display
Shewhart Chart

15. Control Chart Display
Cumulative Sum (CUSUM) Chart

16. Control Chart Display
Exponentially Weighted Moving Average (EWMA) Chart

17. as
Computational
Tool of SQC

18. • Essential for Professionals: Be familiar with computational
techniques using software programs.
• Expensive Softwares: The majority of these software are sold at
high prices for freelance professionals, small businesses, and
especially students.
• GNU R Interface: An open source and provides free access as
one of the alternatives.
• Accepted: R has been well accepted in the academic
(researchers, students) and non-academic areas (government
agencies, businesses, multinational corporations, industries)
during the past few years.
• R can deal: Data handling and storage: numeric, textual; matrix
algebra, statistical functions, graphics and especially
programming language: loops, branching, subroutines etc.
R Software

19. R Commander: It is an open source interface of R that is not
available in the default R installation. It is can be downloaded and
installed through a package “Rcmdr”.
RExcel: It is a supplement for Microsoft Excel and enables access to
the R package within Excel. This supplement is already integrated
in the “Rcmdr” interface. However, it runs only in Windows.
RStudio: It is a powerful and productive interface for R, as it is also
a free open source application for various operating systems, such
as Windows, Mac, and Linux. Students can feel more comfortable
using RStudio than the other R interfaces, which makes it become a
good option for teaching in the classroom
Commonly used Interfaces of R Software

20. R Packages: Collections of functions and data sets developed by
community. Contain many libraries for performing data analysis.
QCC Package: The “qcc” is very famous R package for Statistical
Quality Control Charts, which provides:
• Shewhart, CUSUM and EWMA Charts
• Operating Characteristic Curves
• Process Capability Analysis
• Pareto Chart
• Cause & Effect Chart and
• Multivariate Control Charts
Websites: Further details about “qcc” can be seen on…
https://www.rdocumentation.org/packages/qcc/versions/2.6
https://cran.r-project.org/web/packages/qcc/qcc.pdf
https://cran.r-project.org/web/packages/qcc/vignettes/qcc_a_quick_tour.html
R Packages

21. Demonstration
“qcc” Package

22. Dealing with Control Charts: Most of the times, the data is
generated/simulated from a probability distribution by Monte
Carlo simulation method.
Monte Carlo Simulation: A computer based simulation technique
that is used to obtain approximate solution to certain
mathematical, statistical and physical problems involving
the replacement of probability distribution by sample values (c.f.
https://www.collinsdictionary/english/monte-carlo-method).
Further literature: Monte Carlo simulation can be seen in
Mundform, D. J., Schaffer, J., and J., K. M. (2011). Number of Replications Required in Monte Carlo
Simulation Studies: A Synthesis of Four Studies, Journal of Modern Applied Statistical Methods, 10(1), 4.
Robert, C. P., and Casella, G. (2009). Introducing Monte Carlo Methods with R (Use R), Berlin, Heidelberg:
Springer-Verlag.
Robert, C. P., and Casella, G. (2005). Monte Carlo Statistical Methods (Springer Texts in Statistics) (Second
ed.), New York: Springer-Verlag.
Monte Carlo Simulation with R

23. Average Run Length (ARL): The number of samples to be taken before a
false alarm is detected in the process. The ARL evaluates the performance of a
charting structure at a specific shift point.
• ARL0: The expected number of samples before an out-of-control false alarm
is detected when the process is at in-control state.
• ARL1: The former is the expected number of samples before an out-of-control
false alarm occurs when the process is shifted to an out-of-control state.
Extra Quadratic Loss (EQL): The Extra Quadratic Loss (EQL) is an
alternative performance measure which describes the overall effectiveness of a
control chart. It is defined as a weighted average ARL over the whole process shift
domain δmin<δ< δmax using the square of shift (δ2) as a weight. Mathematically:
𝑬𝑸𝑳 = 𝜹 𝒎𝒂𝒙 − 𝜹 𝒎𝒊𝒏
−𝟏
𝜹 𝒎𝒊𝒏
𝜹 𝒎𝒂𝒙
𝜹 𝟐 𝑨𝑹𝑳 𝜹 𝒅𝜹, ∀ 𝜹 ∈ 𝜹 𝒎𝒊𝒏, 𝜹 𝒎𝒂𝒙
Performance Measures

24. Relative Average Run Length (RARL): The overall effectiveness of particular a
chart relative to the benchmark chart. It examines that how close a particular
chart performs to the benchmark chart for each shift Mathematically:
𝑹𝑨𝑹𝑳 = 𝜹 𝒎𝒂𝒙 − 𝜹 𝒎𝒊𝒏
−𝟏
𝜹 𝒎𝒊𝒏
𝜹 𝒎𝒂𝒙
𝑨𝑹𝑳 𝜹 𝑨𝑹𝑳 𝒐𝒑𝒕 𝜹 𝒅𝜹
ARL 𝛿 and ARLopt 𝛿 are the ARLs of a particular and optimum charts,
respectively, at 𝛿. For an optimum chart RARL=1
Performance Comparison Index (PCI): Compares the performance of charts
based on the ranking of EQL values. The ratio of EQL value of a specific chart to
EQL value of optimum chart defines PCI. Similar to RARL, PCI also attains two
values: 1 for optimum chart and greater than 1 for all the other charts.
Mathematically:
𝑷𝑪𝑰 = 𝑬𝑸𝑳 𝑬𝑸𝑳 𝒐𝒑𝒕
Similar Types of Measures: Average Time to Signal (ATS), Average Extra
Quadratic Loss (AEQL), Average Ratio to ATS (ARATS) are available in quality
control literature.

25. Flow Chart
of
Monte Carlo
Simulation

26. Demonstrations
Monte Carlo Simulation