Statistics

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APPLIED
STATISTICS
Submitted by
Arathy K M
Athul Raj
Gouri Vinod
Muhammad Fayis

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INDRODUCTION TO
STATISTICAL CONTROL
Statistical control, also known as statistical process control
(SPC), is a method used in quality control to monitor
processes and ensure they remain stable and predictable
over time.
It involves collecting and analyzing data to detect any
variations or deviations from the expected performance.

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The goal is to identify and address
any factors that may cause the
process to produce defective
products or services.
Statistical control typically relies on
techniques like control charts, which
visually display process data over
time, helping to distinguish between
common cause variation (inherent to
the process) and special cause
variation (due to external factors).

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CONTROL CHARTS FOR
PROCESS CONTROL
 Control charts are a fundamental tool in statistical process control (SPC)
for monitoring and managing processes. They help distinguish between
natural process variation and significant deviations that may indicate an
out-of-control situation.

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Important uses of the control chart.
 Most processes do not operate in a state of statistical control.
Consequently, the routine and attentive use of control charts
will identify assignable causes.
 If these causes can be eliminated from the process, variability
will be reduced and the process will be improved.
 The control chart only detects assignable causes.Management,
operator, and engineering action will benecessary to eliminate
the assignable causes.

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X Bar Chart
 The X-Bar chart, also known as the Xchart, is a widely used
control chart for monitoring the central tendency or average of a
process over time. It’s particularly suitable for situations where
the quality characteristic being measured is continuous and
normally distributed.
 Control Limits: X-bar Chart:
 Upper Control Limit (UCL) = CL + (A2 x R- bar)
 Lower Control Limit (LCL) = CL (A2 x R-bar)

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Sigma Chart
 Sigma chart, also known as a Sigma control chart or Sigma
capability chart, is a statistical tool used in quality control to
monitor the stability and performance of a process over time.
 It displays the process capability in terms of sigma levels, which
indicate how well the process is meeting its specifications.
 The higher the sigma level, the fewer defects per million
opportunities (DPMO) the process produces.
 Sigma charts help organizations identify areas for improvement
and maintain consistent quality standards.

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R Chart
 An R chart, also known as a range chart, is a statistical tool used
in quality control to monitor the process variability by plotting the
range (the difference between the maximum and minimum
values) of a subgroup of samples taken from a process over
time. It helps in identifying any shifts or changes in process
variability, which can indicate potential issues or improvements
needed in the manufacturing process.
 R=Maximum(data)−Minimum(data)

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