nota bab 1 jf608
TRANSCRIPT
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CHAPTER THREE – CONTROL CHART FOR VARIABLES
Understand control chart for variables
TOPICSCHAPTER ONE – BASIC STATISTIC
Explain basic statistic
CHAPTER TWO – BASIC QUALITY CONCEPT
Explain Quality Concept
CHAPTER FOUR – CONTROL CHART FOR ATTRIBUTE
Understand control chart for attribute
CHAPTER FIVE – Acceptance Sampling
Describe the method of a acceptance sampling in quality
control
CHAPTER SIX – Quality Cost
Describe quality cost in quality control
CHAPTER SEVEN – Quality Improvement Technique
Explain the quality improvement technique in quality control
CHAPTER EIGHT – ISO 9000 SERIES
Describe ISO 9000 Series for quality management
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Course Learning Outcome
CLO1 Express the relation of statistics and quality management system in understanding the principles and concept of quality control and
their application tools.
CLO2 Measure the quality of products and services by using control charts.
Statistical Process Control and Acceptance Sampling Methods.
CLO3 Propose the tools and technique that can be used to improve quality including cost associated in controlling quality of products
and services based on quality system ISO 9000 series.
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BASIC STATISTIC
CHAPTER ONE
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I N T R O D U C T I O N
This note will cover the basic
statistical functions of mean,
median, mode, standard deviation
of the mean, weighted averages
and standard deviations
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ET W H AT I S S TAT I S T I C ?
STATISTIC is the study of how to collect , organize, analyze
and interpret numerical information from data.
STATISTIC is both the science of uncertainty and the
technology of extracting information from data.
STATISTIC is a collection of methods for collecting,
displaying, analyzing, and drawing conclusions from data.
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A Few Examples Of Statistical Information We Can Calculate
Are:
Average Value (Mean)
Most Frequently Occurring Value (Mode)
On Average, How Much Each Measurement Deviates From
The Mean (Standard Deviation Of The Mean)
Span Of Values Over Which Your Data Set Occurs
(Range), And
Midpoint Between The Lowest And Highest Value Of
The Set (Median)
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Example (Examples of Engineering/Scientific Studies)
Comparing the compressive strength of two or more cement
mixtures.
Comparing the effectiveness of three cleaning products in
removing four different types of stains.
Predicting failure time on the basis of stress applied.
Assessing the effectiveness of a new traffic regulatory measure in
reducing the weekly rate of accidents.
Testing a manufacturer’s claim regarding a product’s quality.
Studying the relation between salary increases and employee
productivity in a large corporation.
W H Y S TAT I S T I C ?
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-it is an observations and information that come from
investigations.
It can also be described as sample.
Sample is taken from a population that is to be
analyzed.
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TYPES OF DATA
• those that represent the quantity or amount of something, measured on a numerical scale.
• i.e: the power frequency (measured in megahertz) of semiconductor
QUANTITATIVE DATA
• Those that have no quantitative interpretation
• i.e: they can only br classified into catogaries.The set of n occupations corresponding to a group of engineering graduates.
QUALITATIVE DATA
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Qualitative and quantitative variables may be
further subdivided:
Nominal
Qualitative
Ordinal
Variable
Discrete
Quantitative
Continuous
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STATISTIC DATA
UNGROUPED DATA
o Data has not been summarized
o Data are collected in original
form and also called raw data
GROUPED DATA
o Data that has been organized into groups ( into a
frequency distribution).
o Frequency Distribution : is the organizing of raw
data in table form, using classes and frequencies.
66 78 72
54 83 69
61 85 73
50 60 58
73 59 84
56 48 61
Class Frequency
0-5 4
6-10 5
11-15 4
16-20 3
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Building a Frequency Table
Find the class width, class limits, and class boundaries of the data.
Use Tally marks to count the data in each class.
Record the frequencies (and relative frequencies if desired) on the table.
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Frequency Tables
A frequency table
organizes quantitative data.
partitions data into classes (intervals).
shows how many data values are in each class.
Class Class
Boundaries
Frequency
50-59 49.5-59.5 4
60-69 59.5-69.5 5
70-79 69.5-79.5 4
80-89 79.5-89.5 3
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Data Classes and Class Frequency
Class: an interval of values.
Example: 60 x 69
Frequency: the number of data values that fall within a
class.
“Five data fall within the class 60 x 69”.
Relative Frequency: the proportion of data values that fall
within a class.
“31% of the data fall within the class
60 x 69”.
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Structure of a Data Class
A “data class” is basically an interval on a number line.
It has:
A lower limit a and an upper limit b.
A width.
A lower boundary and
an upper boundary
(integer data).
A midpoint.
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Analysis of Data
176
Descriptive Analysis
Range: difference between maximum value and minimum value Min: the lowest, or minimum value in variable Max: the highest, or maximum value in variable Q1: the first (or 25th) quartile Q2: the third (or 75th) quartile
1 2 3 4 5 6 7 8 9 10 11 12 13
Min MaxMean or Mode25th 50th
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Histograms
Histogram – graphical summary of a frequency table.
Uses bars to plot the data classes versus the class frequencies.
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12-19
MEAN- UNGROUPED DATA
The arithmetic mean is defined as the sum of the observations divided by
the number of observations
where
= the arithmetic mean calculated from a sample pronounced ‘x-bar’)
Sx = the sum of the observations
n = the number of observations in the sample
The symbol for the arithmetic mean calculated from a population is the Greek
letter μ
n
xx
x
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12-20
MEAN – GROUPED DATA
Calculation of the mean from a frequency distribution
It is useful to be able to calculate a mean directly from a frequency table
The calculation of the mean is found from the formula:
where
Σf = the sum of the frequencies
Σfx = the sum of each observation multiplied by its frequency
f
fxx
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12-21
MEAN – example
1. Find the mean of 25, 47, 30, 61, 44, 59, 38
2. Find the mean in the following data.
Class Frequency
30-49 6
50-59 9
60-69 12
70-79 13
80-89 8
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12-22
MODE
The mode is number that occurs most frequently in a set of numbers
Data with just a single mode are called unimodal, while if there are two modes the
data are said to be bimodal
The mode is often unreliable as a central measure
Example
Find the modes of the following data sets:
3, 6, 4, 12, 5, 7, 9, 3, 5, 1, 5
Solution
The value with the highest frequency is 5 (which occurs 3 times).
Hence the mode is Mo = 5.
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12-23
Calculation of the mode from a frequency distribution
The observation with the largest frequency is the mode
Example
A group of 15 real estate agents were asked how many houses they
had sold in the past year. Find the mode.
The observation with the largest frequency (6) is 4. Hence the mode
of these data is 4.
Number of houses sold F
1 2
2 4
3 3
4 6
Total 15
MODE
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12-24
Calculation of the mode from a grouped frequency distribution
It is not possible to calculate the exact value of the mode of the original data from a grouped frequency distribution
The class interval with the largest frequency is called the modal class
Where
L = the real lower limit of the modal class
d1 = the frequency of the modal class minus the frequency of the previous class
d2 = the frequency of the modal class minus the frequency of the next class above the modal class
i = the length of the class interval of the modal class
i21
1
dd
dLMo
MODE
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12-25
MEDIAN
The median is the middle observation in a set
50% of the data have a value less than the median, and
50% of the data have a value greater than the median.
Calculation of the median from raw data
Let n = the number of observations
If n is odd,
If n is even, the median is the mean of the th observation
and the th observation
2
1n~ x
2
n
1
2
n
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12-26
MEDIAN
Calculation of the median from a frequency distribution
This involves constructing an extra column (cf) in which the frequencies are cumulated
Since n is even, the median is the average of the 16th and 17th
observations
From the cf column, the median is 2
Number of pieces Frequency f Cumulative frequency
cf
1 10 10
2 12 22
3 16 38
38f
Example
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12-27
MEDIAN
• Calculation of the median from a grouped frequency distribution– It is possible to make an estimate of the median– The class interval that contains the median is called the median class
Where
= the medianL = the real lower limit of the median classn = Σf = the total number of observations in the setC = the cumulative frequency in the class immediately before the median
classf = the frequency of the median classi = the length of the real class interval of the median class
if
x
C2
n
L~
x~
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12-28
Quartiles
Quartiles divide data into four equal parts
First quartile—Q1
25% of observations are below Q1 and 75% above Q1
Also called the lower quartile
Second quartile—Q2
50% of observations are below Q2 and 50% above Q2
This is also the median
Third quartile—Q3
75% of observations are below Q3 and 25% above Q3
Also called the upper quartile
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VARIANCE AND STANDARD DEVIATION
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Example
Find the variance and standard deviation for the following data
Solution:
No. of order f
10-12 4
13-15 12
16-18 20
19-21 14
Total 50
No. of order f x fx fx2
10-12 4 11 44 484
13-15 12 14 168 2352
16-18 20 17 340 5780
19-21 14 20 280 5600
Total 50 832 14216
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Analysis of Data
326
Descriptive Analysis
Frequency distribution- A table that shows a body of your data grouped according
to numerical values
Example:
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Analysis of DataDescriptive Analysis
Mean
arithmetic average of a set of number
Median
the middle observation in a group of data when the data are
ranked in order of magnitude
Mode
the most common value in any distribution
Height
Mean: 170+190+172+180+187+174+174+166+164+182
10= 𝟏𝟕𝟓.9
Median: 174+174
2=174
164 166 170 172 174 174 180182 187 190
Mode: 174
Variance: (170−175.9)2+(190−175.9)2+ ∙ ∙ ∙ +(164−175.9)2+(182−175.9)2
(10−1)
=74.77
Standard deviation: 74.77 = 8.65
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ET Normal Distribution
Symmetric distribution of values around the mean of a variable
(Bell-shape distribution)
Mean ( 𝑋 or μ)=30 Mean ( 𝑋 or μ)=70) Mean ( 𝑋 or μ)=10
s.d (s or σ) = 24
s.d (s or σ) = 40
s.d (s or σ) = 19
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6
Normal distribution: Mean, Median, Mode
Mean: arithmetic average of a set of numberMedian: the middle observation in a group of data when the data are ranked in order of magnitudeMode: the most common value in any distribution
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9/14/2010
Standard Deviation (σ)
95%
99%
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The skewness of a distribution is measured by comparing the relative positions of the mean, median and mode
Distribution is symmetricalMean = Median = Mode
Distribution skewed rightMedian lies between mode and mean, and mode is less than mean
Distribution skewed leftMedian lies between mode and mean, and mode is greater than mean
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SKEWEDNESS
Means are distorted by extreme values, or outliers
1. Using median instead of mean
2. If necessary, transform to normality, especially in regression analysis
Left-tail is longer Right-tail is longer
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The speeds are normally distributed with a mean of 90 km/hr and a standard
deviation of 10 km/hr. What is the probability that a car picked at random is
travelling at more than 100 km/hr?
EXAMPLE Normal distribution
Solution:
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a) Calculate the mean of the salaries of the 20 people.
b) Calculate the standard deviation of the salaries of
the 20 people.
height (in cm) -
classes
frequency
120 - 130 2
130 - 140 5
140 - 150 25
150 - 160 10
160 - 170 8
The following table shows the grouped data, in
classes, for the heights of 50 people.
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THANK YOU