QM0021: Statistical Process Control

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Assignment

DRIVE	FALL 2015
PROGRAM	MBA
SEMESTER	3
SUBJECT CODE & NAME	QM0021: Statistical Process Control
BK ID	B1928
CREDIT & MARKS	4 CREDITS & 60 MARKS

Note: Answer all questions. Each question is followed by evaluation scheme.

1(a) What are the two main causes of variation? Explain.

Answer: Two causes of 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 plotting frequency as a histogram or as a

(b) Define the term ‘processes. Give an example of process.

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 indicates that the data points tend

(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

Standard deviation: 2.

3a) Give the meaning of the following basic terminologies in 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) Mutually Exclusive events

Answer: Two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.

In the coin-tossing example,

b) Mention the properties of probability

Answer:

 Property 1:

If A is an outcome in a 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.

4(a) Differentiate between accuracy and 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 random errors, and defines accuracy as the combination of both trueness and precision.

A measurement system can be

(b) Write a brief note 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 variation in that process.

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: ‘process capability’ and ‘process stability’. Explain Cp index and 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 inherent statistical variability which can be evaluated by statistical methods.

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 this measurement is usually illustrated by

6. Give the meaning of the following:

i) Hypothesis testing

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 used for testing a statistical hypothesis.

A test result is called statistically significant if it has been predicted as unlikely to have occurred by chance alone, according to a

ii) Control chart

Answer: Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, in statistical

iii) Experimental design

Answer: In an experiment, we deliberately change one or more process variables (or factors) in order to observe the effect the 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 supplies a consumer

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