Statistical Methods | Course Paper

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1/14/2019

Statistical

Methods in

Quality

Management

Part 1

Statistics

The science concerned with “the collection,

organization, analysis, interpretation, and

presentation of data.”

The use of statistical methods in quality dates back

to 1903 at the Bell Telephone system. In the 1920s,

Bell Labs thought that statistical tools would have

applications in the factory, and began to experiment

with statistical sampling, eventually leading to the

development of control charts.

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Quality Profile: Graniterock Co.

Graniterock produces construction materials.

Charts for each product line help executives assess

performance on key product and service attributes.

Many employees are trained in statistical process

control, root-cause analysis, and other quality-

assurance and problem-solving methods.

Applying statistical process control to all product lines

has helped the company reduce variable costs and

produce materials that exceed customer specifications

and industry- and government-set standards.

Quality Profile: Branch-Smith

Printing Division

Fourth-generation family-owned business.

Data-driven approaches geared toward providing the

best possible customer service at the lowest possible

cost. Databases and software tools are used

extensively to gather information about, and to

improve, processes throughout the company.

The Quality Information Database places key data

dealing with suppliers, opportunities for

improvement, customer complaints, and internal

nonconformance in a central location.

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Basic Probability Concepts

An experiment is a process that results in some

outcome.

The outcome of an experiment is a result that we

observe

E.g.: the number of defective parts in the sample or the

length of time until the bulb fails.

The collection of all possible outcomes of an

experiment is called the sample space.

Probability is the likelihood that an outcome occurs.

Probability Properties

Label the n outcomes in a sample space as O1, O2, …

On, where Oirepresents the ith outcome in the sample

space.

The probability associated with any outcome must be

between 0 and 1

0 ≤ P(Oi) ≤ 1 for each outcome Oi

The sum of the probabilities over all possible outcomes

must be 1.0

P(O1) + P(O2) + … + P(On) = 1

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Events

An event is a collection of one or more outcomes from

a sample space

E.g.: finding 2 or fewer defectives in the sample of 10, or

having a bulb burn for more than 1000 hours.

If A is any event, the complement of A, denoted as Ac,

consists of all outcomes in the sample space not in A.

Two events are mutually exclusive if they have no

outcomes in common.

Calculating Probabilities

Rule 1: The probability of any event is the sum of the

probabilities of the outcomes that compose that event.

Rule 2: The probability of the complement of any event

A is P(Ac) = 1 – P(A).

Rule 3: If events A and B are mutually exclusive, then

P(A or B) = P(A) + P(B)

Rule 4: If two events A and B are not mutually

exclusive, then P(A or B) = P(A) + P(B) – P(A and B)

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Example 6.1

Conditional Probability

Conditional probability is the probability of