notes for my DAD6S1 and JF608_ST students

1. JF 608 QUALITY CONTROL
NORAZMIRA WATI AWANG
norazmira@psmza.edu.my

2. ON TARGET
CHAPTER THREE – CONTROL CHART FOR VARIABLES
Understand control chart for variables
TOPICS
CHAPTER 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

3. ON TARGET
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.

4. ON TARGET
CHAPTER ONE
BASIC STATISTIC

5. ON TARGET
INT RODUC T ION
This note will cover the basic
statistical functions of mean,
median, mode, standard deviation
of the mean, weighted averages
and standard deviations

6. ON TARGET
WH 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.

7. ON TARGET
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)

8. ON TARGET
WH Y S TAT I S T I C ?
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.

9. ON TARGET
-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.

10. ON TARGET
TYPES OF DATA
QUANTITATIVE 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
QUALITATIVE 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.

11. ON TARGET
Qualitative and quantitative variables may be
further subdivided:
Nominal
Qualitative
Ordinal
Variable
Discrete
Quantitative
Continuous

12. ON TARGET
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

13. ON TARGET
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.

14. ON TARGET
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

15. ON TARGET
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”.

16. ON TARGET
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.

17. ON TARGET
Analysis of Data
Min 25th Mean or Mode 50th Max
17
6
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

18. ON TARGET
Histograms
Histogram – graphical summary of a frequency table.
Uses bars to plot the data classes versus the class frequencies.

19. ON TARGET
MEAN- UNGROUPED DATA
The arithmetic mean is defined as the sum of the observations divided by
the number of observations
 
x
12-19
where
n
x
= the arithmetic mean calculated from a sample pronounced ‘x-bar’)
x
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

20. ON TARGET
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:
 
12-20
where
fx
Σf = the sum of the frequencies
Σfx = the sum of each observation multiplied by its
frequency

f
x

21. ON TARGET
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

22. ON TARGET
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.

23. ON TARGET
12-23
MODE
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.
Number of houses sold F
1 2
2 4
3 3
4 6
Total 15
The observation with the largest frequency (6) is 4. Hence the mode
of these data is 4.

24. ON TARGET
MODE
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
d
d d
Mo L
 
12-24
Where
i
1

1 2
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

25. ON TARGET
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,
~ n  1
x 
2
n
If n is even, the median is the mean of the th observation


n
and the th observation
2




 1
2

26. ON TARGET
Example
Number of pieces Frequency f Cumulative frequency
1 10 10
2 12 22
3 16 38
f  38
12-26
MEDIAN
Calculation of the median from a frequency distribution
This involves constructing an extra column (cf) in which the frequencies are
cumulated
cf
Since n is even, the median is the average of the 16th and 17th
observations
From the cf column, the median is 2

27. ON TARGET
~ L
 
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
x
= the median
i

f






C
n
2
x ~
L = the real lower limit of the median class
n = Σf = the total number of observations in the set
C = the cumulative frequency in the class immediately before the median
class
f = the frequency of the median class
i = the length of the real class interval of the median class

28. ON TARGET
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

29. ON TARGET
VARIANCE AND STANDARD DEVIATION

30. ON TARGET
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

31. ON TARGET

32. ON TARGET
Analysis of Data
32
6
Descriptive Analysis
 Frequency distribution
- A table that shows a body of your data grouped according
to numerical values
Example:

33. ON TARGET
Analysis of Data
Descriptive 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
= ퟏퟕퟓ.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

34. ON TARGET
Normal Distribution
Symmetric distribution of values around the mean of a variable
(Bell-shape distribution)
s.d (s or σ) = 24
s.d (s or σ) = 40
s.d (s or σ) = 19
Mean (푋 or μ)=30 Mean (푋 or μ)=70) Mean (푋 or μ)=10

35. ON TARGET
6
Normal distribution: Mean, Median, Mode
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

36. ON TARGET
Standard Deviation (σ)
9/14/2010
99%
95%

37. ON TARGET
The skewness of a distribution is measured by comparing
the relative positions of the mean, median and mode
Distribution is symmetrical
Mean = Median = Mode
Distribution skewed right
Median lies between mode and mean, and mode
is less than mean
Distribution skewed left
Median lies between mode and mean, and mode
is greater than mean

38. ON TARGET
6
SKEWEDNESS
Left-tail is longer Right-tail is longer
Means are distorted by extreme values, or outliers
1. Using median instead of mean
2. If necessary, transform to normality, especially in regression analysis

39. ON TARGET
EXAMPLE Normal distribution
A radar unit is used to measure speeds of cars on a motorway.
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?
Solution:

40. ON TARGET
The following table shows the grouped data, in
classes, for the heights of 50 people.
height (in cm) -
classes
frequency
120 - 130 2
130 - 140 5
140 - 150 25
150 - 160 10
160 - 170 8
a) Calculate the mean of the salaries of the 20 people.
b) Calculate the standard deviation of the salaries of
the 20 people.

41. ON TARGET
THANK YOU