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Assignment
DRIVE FALL 2015
PROGRAM MBA
SEMESTER 3
SUBJECT CODE & NAME QM0021: Statistical ProcessControl
BK ID B1928
CREDIT & MARKS 4 CREDITS & 60 MARKS
Note:Answer all questions.Each questionisfollowedby evaluationscheme.
1(a) What are the two main causes of variation?Explain.
Answer: Twocausesof variation:
There are two forms of variation: continuous and discontinuous variation. Characteristics showing
continuous variation vary in a general way, with a broad range, and many intermediate values between
the extremes. As a matter of fact, if you consider a large enough sample from a population, perhaps
plottingfrequencyasa histogramor as a
(b) Define the term ‘processes.Give an example ofprocess.
Answer: Sequence of interdependent and linked procedures which, at every stage, consume one or
more resources (employee time,energy, machines, money) to convert inputs (data, material, parts, etc.)
into outputs. These outputs then serve as inputs for the next stage until a known goal or end result is
reached.
2(a) What is meant by Standard Deviation?
Answer: In statistics and probability theory, the standard deviation (SD) (represented by the Greek letter
sigma, σ) measures the amount of variation or dispersion from the average. A low standard deviation
indicatesthatthe data pointstend

2. (b) Calculate the standard deviation of the following data, which represents the number of defective
products by a machine:4, 2, 5, 8 and 6
Answer:
Total Numbers:5
Mean (Average):5
Standarddeviation: 2.
3a) Give the meaningof the followingbasicterminologiesin Probability:
(i) Sample Space
Answer: The sample space of an experiment or random trial is the set of all possible outcomes or results
of that experiment.A sample space is usually denoted using set notation, and the possible outcomes are
listed as elements in the set. It is common to refer to a sample space by the labels S, Ω, or U (for
"universal set").
ii) MutuallyExclusive events
Answer: Two events are mutually exclusive if they cannot occur at the same time. An example is tossing
a coin once,which can resultineitherheadsortails,butnotboth.
In the coin-tossingexample,
b) Mentionthe propertiesof probability
Answer:
Property 1:
If A is an outcome ina sample space S,then
P(A) > 0
Property 2:
c) Define the term ‘random variable’
Answer: A random variable, aleatory variable or stochastic variable is a variable whose value is subject
to variations due to chance .A random variable can take on a set of possible different values (similarly to
other mathematical variables), each with an associated probability, in contrast to other mathematical
variables.

3. 4(a) Differentiate betweenaccuracyand precision.
Answer: Accuracy and precision are defined in terms of systematic and random errors. The more
common definition associates accuracy with systematic errors and precision with random errors.
Another definition, advanced by ISO, associates trueness with systematic errors and precision with
randomerrors,and definesaccuracyas the combinationof bothtruenessandprecision.
A measurementsystemcanbe
(b) Write a briefnote on ‘Funnel Experiment’
Answer: The Funnel Experiment was devised by Dr. Deming to describe the adverse effects of tampering
with a process by making changes to it without first making a careful study of the possible causes of the
variationinthatprocess.
In the experiment, a marble is dropped through a funnel onto a sheet of paper, which contains a target.
The objective of the process is to get the marble to come to a stop as close to the target as possible. The
experiment uses several methods to attempt to manipulate the funnel’s location to achieve the
objective.
5 Define the terms: ‘processcapability’and ‘processstability’.ExplainCp indexand Cpk index.
Answer: A process is a unique combination of tools, materials, methods, and people engaged in
producing a measurable output; for example a manufacturing line for machine parts. All processes have
inherentstatistical variabilitywhichcanbe evaluatedbystatisticalmethods.
The Process Capability is a measurable property of a process to the specification, expressed as a process
capability index (e.g., Cpk or Cpm) or as a process performance index (e.g., Ppk or Ppm). The output of
thismeasurementisusuallyillustratedby
6. Give the meaningof the following:
i) Hypothesistesting
Answer: A statistical hypothesis is a scientific hypothesis that is testable on the basis of observing a
process that is modeled via a set of random variables. A statistical hypothesis test is a method of
statistical inference usedfortestingastatistical hypothesis.
A test result is called statistically significant if it has been predicted as unlikely to have occurred by
chance alone,accordingto a
ii) Control chart

4. Answer: Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior
charts, instatistical
iii) Experimental design
Answer: In an experiment, we deliberately change one or more process variables (or factors) in order to
observe the effectthe changes
iv) Acceptance Sampling
Answer: Acceptance sampling uses statistical sampling to determine whether to accept or reject a
production lot of material. It has been a common quality control technique used in industry. It is usually
done as products leave the factory, or in some cases even within the factory. Most often a producer
suppliesaconsumer
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