Statistical techniques in business ecohomics chap017

Seventeen Statistical Quality ControlDefine and understand the terms chance causes, assignable cause, in control and out of control, and variable... Statistical Process ControlA collect

Seventeen Statistical Quality Control

Define and understand the terms chance causes, assignable

cause, in control and out of control, and variable.

17- 3

Statistical Quality Control

Statistical Process Control

A collection of strategies,

techniques, and actions taken by

an organization to ensure they

are producing a quality product

or providing a quality service

Statistical Process Control

17- 5

Causes of Variation

Assignable Variation is not random in nature and can be reduced or eliminated by

investigating the problem and finding the cause.

be entirely eliminated.

A technique for tallying the number and type of defects that happen within a product or service

Produce a vertical bar chart

to display data

Diagnostic Charts: Pareto Chart

Pareto Analysis

Steps in pareto analysis

Tally the type

17- 7

The accounting department of a

large organization is spending

significant time correcting travel

vouchers submitted by

employees from its numerous

locations Accounting staff

noted that typical errors

included wrong travel codes,

incorrect employee

identification numbers,

inaccurate math, placing

expenses on the wrong lines of

the form, and failure to include

proper documentation of

Department staff pulled

a sample of 100 vouchers and tallied errors in the various

categories

Error Type Number found

Pareto Chart for Voucher Errors

0 10 20 30 40 50 60 70 80 90

Inaccurate form placement

Wrong codes Incomplete

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Major causes listed on left-hand side of diagram

Diagnostic Fishbone Chart

Also called cause-and-effect diagram

personnel

Problem or effect

is head of fish

Fishbone chart

those found along an interstate highway,

has recently been experiencing

complaints from customers that the food

being served is cold

Example 2

In the following

fishbone diagram,

notice each of the

subcauses are listed as

assumptions Each of

these subcauses must

be investigated to find

the real problem

regarding the cold food

Food placed under heating lights

Food heated to correct tem perature Food at correct

starting tem perature Packaging insulates enough

Therm ostat working properly

Heating lights at correct height

Em ployees operating equipm ent correctly

Servers deliver food quickly

Example 2

Purpose of Quality Control Charts

selecting a random sample from the current production

Purpose of Quality-Control Charts

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Types of Quality Control Charts-Variables

X

where is the mean of the sample means

Mean ( x -bar) Chart

Designed to control

variables such as

weight or length

Limits How much variation can be expected for a given sample size

UCL: upper control limitLCL: lower control limit

U C L = X + 3 s

n L C L = X - 3 s

n

UCL X A R and LCL X A R   2   2

is the mean of the sample rangesR

X

where is the mean of the sample means

Shortcut method for UCL and LCL

A2 is a constant used in computing the upper and lower control limits, factors found in Appendix B.

Shortcut method

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Types of Quality Control Charts-Variables

UCL  D R and LCL4  D R3

Designed to show whether the overall range

of measurements is in or out of control

Range Chart

range diameter UCL=2.282(5.8) = 13.24

LCL=2.282(0) = 0

Example 3 continued

No points outside limits:

Process in control

Example 3 continued

No points outside limits:

Process in control

Types of Quality Control Charts-Attributes

samples of

Number

defectives percent

the of

The UCL and UCL LCL LCL

computed as the

mean percent

defective plus or

minus 3 times the

standard error of the

percents

n

p

p p

LCL and

UCL  3 (1 )

defective Ten samples of 400 shoes revealed the mean

percent defective was 8.0% Where should the manufacturer set the control limits?

Types of Quality Control Charts-Attributes

UCL and LCL c  3 c

C -chart ( c -bar chart)

UCL and LCL found by

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Example 5

84.46

.2

6.236

.2

6.210

/26

UCL c

c-bar chart for Number of Defects per Circuit Board

Example 5

17- 27

Acceptance Sampling

c is the maximum number

of defective units that may

be found in the sample for

the lot to still be considered acceptable

Acceptance sampling

A method of determining

whether an incoming lot of

a product meets specified

standards

Based on random

sampling techniques

A random sample of n

units is obtained from the

entire lot

387

349

)10.,

10/

1(

914

315

599

)05.,

10/

P

n X

P

Suppose a manufacturer and a supplier agree on a sampling plan with n=10 and acceptance number

of 1 What is the probability of accepting a lot with 5% defective? A lot with 10% defective?

is 677

Example 6