Statistical Thinking and Applications

8/3/2019 Statistical Thinking and Applications

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Page 1Prof. Rushen Chahal

Prof. Rushen ChahalProf. Rushen Chahal

Statistical Thinking

and Applications

1




Statistical Thinking

All work occurs in a system of

interconnected processes

Variation exists in all processes Understanding and reducing variation

are the keys to success

2




Sources of Variation

in Production Processes

3

Materials

Tools

Operators MethodsMeasurement

Instruments

HumanInspection

Performance

EnvironmentMachines

INPUTS PROCESS OUTPUTS




Variation

Many sources of uncontrollable

variation exist (common causes)

Special (assignable) causes of variation can be recognized and

controlled

Failure to understand thesedifferences can increase variation in

a system

4




Importance of Understanding

Variation

5

time

PREDICTABLE

? UNPREDECTIBLE




Two Fundamental

Management Mistakes1. Treating as a special cause any fault,

complaint, mistake, breakdown, accident

or shortage when it actually is due tocommon causes

2. Attributing to common causes any fault,

complaint, mistake, breakdown, accident

or shortage when it actually is due to aspecial cause

6




Note to Instructors

The following slides can be used to guide

a class demonstration and discussion of

the Deming Red Bead experiment usingsmall bags of M&M¶s® Chocolate Candies,

from a suggestion I found on a TQ

newsgroup several years ago. The good

output (³red beads´) are the blue M&Ms,with the instructor playing the role of Dr.

Deming.

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Page 8Prof. Rushen Chahal 8

We¶re Going into Business!!!

We have a new global customer and have to start

up several factories. So I need teams of 5 to do

the work:

1 production worker

2 inspectors

1 Chief Inspector 1 Recorder




Production Setup

9

1. Take the bag in your left hand.

2. Tear a 3/4´ opening in the right corner.(only large enough for one piece at a

time)




Production Process

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1. Production worker produces 10 pieces

and places them on the napkin.

2. Each inspector, independently, countsthe blue ones, and passes to the Chief

Inspector to verify.

3. If Chief Inspector agrees, s/he tellsthe recorder, who reports it to me.




Do it right

the first

time!

Be a Quality Worker!

Take Pride in

Your Work!




Lessons Learned

Quality is made at the top.

Rigid procedures are not enough.

People are not always the main source

of variability.

Numerical goals are often meaningless.

Inspection is expensive and does not

improve quality.

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Statistical Methods

Descriptive statistics

Statistical inference

Predictive statistics

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Review of Key Concepts

Random variables

Probability distributions

Populations and samples

Point estimates

Sampling distributions Standard error of the mean

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Important Probability

Distributions Discrete

±Binomial

±Poisson

Continuous

±Normal

±Exponential

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Central Limit Theorem

If simple random samples of size n are

taken from any population, the

probability distribution of sample meanswill be approximately normal as n

becomes large.

16




Sampling Methods

Simple random sampling

Stratified sampling

Systematic sampling

Cluster sampling

Judgment sampling

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Sampling Error

Sampling error (statistical error)

Nonsampling error (systematic error)

Factors to consider:

±Sample size

±Appropriate sample design

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Design of Experiments

A test or series of tests to compare twoor more methods to determine which isbetter, or to determine levels of controllable factors to optimize the yieldof a process or minimize the variabilityof a response variable.

Factorial experiment ± Analysis of all combinations of factor levels

to understand main effects and interactions

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Excel Descriptive Statistics

Tool Tools«Data Analysis« Descriptive Statistics

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Excel Histogram Tool

Tools«Data Analysis«Histogram

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Process Capability

The range over which the natural variation

of a process occurs as determined by the

system of common causes

Measured by the proportion of output that

can be produced within design

specifications

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Types of Capability Studies

Peak performance study - how a process

performs under ideal conditions

Process characterization study - how a

process performs under actual operatingconditions

Component variability study - relative

contribution of different sources of variation(e.g., process factors, measurement system)




Process Capability Study

1. Choose a representative machine or process

2. Define the process conditions

3. Select a representative operator

4. Provide the right materials

5. Specify the gauging or measurement method

6. Record the measurements

7. Construct a histogram and compute descriptivestatistics: mean and standard deviation

8. Compare results with specified tolerances




Process Capability

27

specification specification

specification specification

natural variation natural variation

(a) (b)

natural variation natural variation

(c) (d)




Process Capability Index

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Cp = UTL - LTL

6W

Cpl, Cpu }

UTL - Q3W

Cpl = Q - LTL

3W

Cpk = min{

Cpu =




PROCESS_CAPABILITY.XLS

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Statistical Thinking and Applications