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ISEN 220 Introduction to Production and Manufacturing Systems Dr. Gary Gaukler. Quality and Profit. Profit = Revenue – Cost Quality impacts on the revenue side: Quality impacts on the cost side:. Defining Quality. - PowerPoint PPT Presentation
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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