ISEN 220 Introduction to Production and Manufacturing Systems Dr. Gary Gaukler

ISEN 220Introduction to Production

and Manufacturing Systems

Dr. Gary Gaukler

6 – 2

Quality and Profit Profit = Revenue – Cost Quality impacts on the revenue

side:

Quality impacts on the cost side:

6 – 33

Defining Quality

The totality of features and characteristics of a product or

service that bears on its ability to satisfy stated or implied needs

American Society for Quality

6 – 44

Costs of Quality Prevention costs - reducing the

potential for defects Appraisal costs - evaluating

products, parts, and services

Internal failure - producing defective parts or service before delivery

External costs - defects discovered after delivery

6 – 55

Costs of Quality There is a tradeoff between the

costs of improving quality, and the costs of poor quality

Philip Crosby (1979): “Quality is free”

6 – 66

Inspection Involves examining items to see if

an item is good or defective Detect a defective product

Does not correct deficiencies in process or product

It is expensive Issues

When to inspectWhere in process to inspect

6 – 77

Inspection Many problems

Worker fatigueMeasurement errorProcess variability

Cannot inspect quality into a product

Robust design, empowered employees, and sound processes are better solutions

6 – 88

Statistical Process Control (SPC) Uses statistics and control charts to

tell when to take corrective action Drives process improvement Four key steps

Measure the process When a change is indicated, find the

assignable cause Eliminate or incorporate the cause Restart the revised process

6 – 99

An SPC Chart

Upper control limit

Coach’s target value

Lower control limit

Game number

| | | | | | | | |1 2 3 4 5 6 7 8 9

20%

10%

0%

Plots the percent of free throws missed

Figure 6.7

6 – 1010

Control Charts

Constructed from historical data, the purpose of control charts is to help distinguish between natural variations and variations due to assignable causes

6 – 1111

Variability is inherent in every processNatural or common causesSpecial or assignable causes

Provides a statistical signal when assignable causes are present

Detect and eliminate assignable causes of variation

Statistical Process Control (SPC)

6 – 1212

Natural Variations Also called common causes Affect virtually all production processes Expected amount of variation Output measures follow a probability

distribution For any distribution there is a measure

of central tendency and dispersion If the distribution of outputs falls within

acceptable limits, the process is said to be “in control”

6 – 1313

Assignable Variations

Also called special causes of variation Generally this is some change in the process

Variations that can be traced to a specific reason

The objective is to discover when assignable causes are present Eliminate the bad causes Incorporate the good causes

6 – 1414

SamplesTo measure the process, we take samples and analyze the sample statistics following these steps

(a) Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight

Freq

uenc

y

Weight

#

## #

##

##

#

# # ## # ##

# # ## # ## # ##

Each of these represents one sample of five

boxes of cereal

Figure S6.1

6 – 1515

SamplesTo measure the process, we take samples and analyze the sample statistics following these steps

(b) After enough samples are taken from a stable process, they form a pattern called a distribution

The solid line represents the

distribution

Freq

uenc

y

WeightFigure S6.1

6 – 1616

SamplesTo measure the process, we take samples and analyze the sample statistics following these steps

(c) There are many types of distributions, including the normal (bell-shaped) distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shape

Weight

Central tendency

Weight

Variation

Weight

Shape

Freq

uenc

y

Figure S6.1

6 – 1717

SamplesTo measure the process, we take samples and analyze the sample statistics following these steps

(d) If only natural causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable

WeightTimeFr

eque

ncy Prediction

Figure S6.1

6 – 1818

SamplesTo measure the process, we take samples and analyze the sample statistics following these steps

(e) If assignable causes are present, the process output is not stable over time and is not predicable

WeightTimeFr

eque

ncy Prediction

????

???

???

??????

???

Figure S6.1

6 – 1919

Central Limit Theorem

Regardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curve

1. The mean of the sampling distribution (x) will be the same as the population mean m

x = m

s nsx =

2. The standard deviation of the sampling distribution (sx) will equal the population standard deviation (s) divided by the square root of the sample size, n

6 – 2020

Population and Sampling Distributions

Three population distributions

Beta

Normal

Uniform

Distribution of sample means

Standard deviation of the sample means

= sx =s

n

Mean of sample means = x

| | | | | | |

-3sx -2sx -1sx x +1sx +2sx +3sx

99.73% of all xfall within ± 3sx

95.45% fall within ± 2sx

Figure S6.3

6 – 2121

Control Charts for Variables

For variables that have continuous dimensions Weight, speed, length, strength, etc.

x-charts are to control the central tendency of the process

R-charts are to control the dispersion of the process

These two charts must be used together

6 – 2222

Setting Chart LimitsFor x-Charts when we know s

Upper control limit (UCL) = x + zsx

Lower control limit (LCL) = x - zsx

where x = mean of the sample means or a target value set for the processz = number of normal standard deviationssx = standard deviation of the sample means

= s/ ns = population standard deviationn = sample size

6 – 2323

Setting Control LimitsHour 1

Box Weight ofNumber Oat Flakes

1 172 133 164 185 176 167 158 179 16

Mean 16.1s = 1

Hour Mean Hour Mean1 16.1 7 15.22 16.8 8 16.43 15.5 9 16.34 16.5 10 14.85 16.5 11 14.26 16.4 12 17.3

n = 9

LCLx = x - zsx = 16 - 3(1/3) = 15 ozs

For 99.73% control limits, z = 3

UCLx = x + zsx = 16 + 3(1/3) = 17 ozs

6 – 2424

17 = UCL

15 = LCL

16 = Mean

Setting Control LimitsControl Chart for sample of 9 boxes

Sample number

| | | | | | | | | | | |1 2 3 4 5 6 7 8 9 10 11 12

Variation due to assignable

causes

Variation due to assignable

causes

Variation due to natural causes

Out of control

Out of control

6 – 2525

Setting Chart LimitsFor x-Charts when we don’t know s

Lower control limit (LCL) = x - A2R

Upper control limit (UCL) = x + A2R

where R = average range of the samplesA2 = control chart factor found in Table S6.1 x = mean of the sample means

6 – 2626

Control Chart Factors

Table S6.1

Sample Size Mean Factor Upper Range Lower Range

n A2 D4 D32 1.880 3.268 03 1.023 2.574 04 .729 2.282 05 .577 2.115 06 .483 2.004 07 .419 1.924 0.0768 .373 1.864 0.1369 .337 1.816 0.184

10 .308 1.777 0.22312 .266 1.716 0.284

6 – 2727

Setting Control LimitsProcess average x = 16.01 ouncesAverage range R = .25Sample size n = 5

6 – 2828

Setting Control Limits

UCLx = x + A2R= 16.01 + (.577)(.25)= 16.01 + .144= 16.154 ounces

LCLx = x - A2R= 16.01 - .144= 15.866 ounces

Process average x = 16.01 ouncesAverage range R = .25Sample size n = 5

UCL = 16.154

Mean = 16.01

LCL = 15.866