1. Statistical Process Control

2. What is a process? Inputs PROCESS Outputs
A process can be described as a transformation of set of inputs into desired outputs.

3. Types of Measures
Measures where the metric is composed of a classification in one of two (or more) categories is called Attribute data.
_ Good/Bad
Yes/No
Measures where the metric consists of a number which indicates a precise value is called Variable data.
Time
Miles/Hr
Use Minitab to have students record the results and have the students display using Graph..Histogram
Note how “rough” the graph looks
Redo using Basic Statistics …. Descriptive Statistics and display using the Graphical Summary. Walk through the normal curve transform:
Mean (Arithmetic Average)
Standard Deviation
Skew (How off center the data is skewed -=left)
Kurtosis (How flat or peaked the data is -=flat)
Show the Box Plot:
Quartile (25% of the Data Points)
Median (50% of the Data Points on Each Side)
Show the 95% Confidence Interval and Explain how it relates to the data.
January 16, 2019

4. A sample is just a subset of all possible values
Population Vs. Sample (Certainty Vs. Uncertainty)
A sample is just a subset of all possible values
population
sample
Since the sample does not contain all the possible values, there is some uncertainty about the population. Hence any statistics, such as mean and standard deviation, are just estimates of the true population parameters.
January 16, 2019

5. WHY STATISTICS? THE ROLE OF STATISTICS ………
Statistics is the art of collecting, classifying, presenting, interpreting and analyzing numerical data, as well as making conclusions about the system from which the data was obtained.
January 16, 2019

6. Descriptive Statistics
Descriptive Statistics is the branch of statistics which most people are familiar.
It characterizes and summarizes the most prominent features of a given set of data (means, medians, standard deviations, percentiles, graphs, tables and charts.
January 16, 2019

7. Inferential Statistics
Inferential Statistics is the branch of statistics that deals with drawing conclusions about a population based on information obtained from a sample drawn from that population.
January 16, 2019

8. WHAT IS THE MEAN? å The mean is simply the average value of the data.
ORDERED DATA SET -5 -3 -1 1 3 -6 -4 -2 2 4 5 6
The mean is simply the average value of the data.
n=12 x i = - å
mean n 12 17 .
Mean
January 16, 2019

9. WHAT IS THE MEDIAN?
ORDERED DATA SET -5 -3 -1 1 3 -6 -4 -2 2 4 5 6
If we rank order (descending or ascending) the data set ,we find the value half way (50%) through the data points and is called the median value.
Median Value
Median
50% of data points
January 16, 2019

10. WHAT IS THE MODE?
ORDERED DATA SET -5 -3 -1 1 3 -6 -4 -2 2 4 5 6
If we rank order (descending or ascending) the data set We find that a single value occurs more often than any other. This is called the mode. .
Mode
January 16, 2019

11. WHAT IS THE RANGE? x = - 9 ( ) The range is a very common metric .
ORDERED DATA SET -5 -3 -1 1 3 -6 -4 -2 2 4 5 6
The range is a very common metric .
To calculate the range simply subtract the minimum value in the sample from the maximum value.
Range
Max
Min x
MAX
MIN = - 9 ( )
January 16, 2019

12. ( ) å WHAT IS THE VARIANCE/STANDARD DEVIATION? s X n 1 61 67 12 5 6 =
The variance (s2) is a very robust metric .
The standard deviation(s) is the square root of the variance and is the most commonly used measure of dispersion. ( ) s X n i 2 1 61 67 12 5 6 = - å .
DATA SET -5 -3 -1 3 -6 -4 -2 4
-.17
-5-(-.17)=-4.83
-3-(-.17)=-2.83
-1-(-.17)=-.83
0-(-.17)=.17
1-(-.17)=1.17
3-(-.17)=3.17
4-(-.17)=4.17
(-4.83)2=23.32
(-2.83)2=8.01
(-.83)2=.69
(.17)2=.03
(1.17)2=1.37
(3.17)2=10.05
(4.17)2=17.39
61.67
January 16, 2019

13. Statistical Process Control (SPC)
Measures performance of a process
Uses mathematics (i.e., statistics)
Involves collecting, organizing, & interpreting data
Objective: Regulate product quality
Used to
Control the process as products are produced
Inspect samples of finished products 4

14. Functions of a Process Control System are
CONTROL CHART
Functions of a Process Control System are
To signal the presence of assignable causes of variation
To give evidence if a process is operating in a state of statistical control

15. Essential features of a control chart
Upper Control Limit
Central Line
Variable Values
Lower Control Limit
Time

16. Control Chart Purposes
Show changes in data pattern
e.g., trends
Make corrections before process is out of control
Show causes of changes in data
Assignable causes
Data outside control limits or trend in data
Natural causes
Random variations around average 9

17. Quality Characteristics
Variables
Attributes
1. Characteristics that you measure, e.g., weight, length
2. May be in whole or in fractional numbers
3. Continuous random variables
1. Characteristics for which you focus on defects
2. Classify products as either ‘good’ or ‘bad’, or count # defects
e.g., radio works or not
3. Categorical or discrete random variables 6

18. Types of Control Charts for Attribute Data
Description
Type
Sample Size
Control Chart for proportion non conforming units
p Chart
May change
Control Chart for no. of non conforming units in a sample
np Chart
Must be constant
Control Chart for no. of non conformities in a sample
c Chart
Control Chart for no. of non conformities per unit
u Chart
May Change

19. Control Chart Types Control Charts Variables Attributes Charts Charts` X P C
Chart
Chart
Chart
Chart 13

20. X Chart Type of variables control chart
Interval or ratio scaled numerical data
Shows sample means over time
Monitors process average and tells whether changes have occurred. These changes may due to Tool wear
2. Increase in temperature
3. Different method used in the second shift
4. New stronger material
Example: Weigh samples of coffee & compute means of samples; Plot 15

21. R Chart Type of variables control chart
Interval or ratio scaled numerical data
Shows sample ranges over time
Difference between smallest & largest values in inspection sample
Monitors variability in process, it tells us the loss or gain in dispersion. This change may be due to:
1. Worn bearing
2. A loose tool
3. An erratic flow of lubricant to machine
4. Sloppiness of machine operator
Example: Weigh samples of coffee & compute ranges of samples; Plot 17

22. Construction of X and R Charts
Step 1: Select the Characteristics for applying a control chart.
Step 2: Select the appropriate type of control chart.
Step 3: Collect the data.
Step 4: Choose the rational sub-group i.e Sample
Step 5: Calculate the average ( X) and range R for each sample.
Step 6: Cal Average of averages of X and average of range(R)

23. Construction of X and R Charts
Steps 7:Cal the limits for X and R Charts.
Steps 8: Plot Centre line (CL) UCL and LCL on the chart
Steps 9: Plot individual X and R values on the chart.
Steps 10: Check whether the process is in control (or) not.
Steps 11: Revise the control limits if the points are outside.

24. X Chart Control Limits From Tables
Sub group average X = x1 + x2 +x3 +x4 +x5 / 5
Sub group range R = Max Value – Min value 16

25. R Chart Control Limits
From Tables 18

26. Problem8.1 from TQM by V.Jayakumar Page No 8.5

27. p Chart for Attributes Type of attributes control chart
Nominally scaled categorical data
e.g., good-bad
Shows % of nonconforming items
Example: Count # defective chairs & divide by total chairs inspected; Plot
Chair is either defective or not defective 19

28. p Chart
p = np / n where p = Fraction of Defective
np = no of Defectives
n = No of items inspected in sub group
p= Avg Fraction Defective = ∑np/ ∑n = CL

29. p Chart Control Limits
z = 3 for 99.7% limits 20

30. Purpose of the p Chart Identify and correct causes of bad quality
The average proportion of defective articles submitted for inspection,over a period.
To suggest where X and R charts to be used.
Determine average Quality Level.

31. Problem
Problem 9.1 Page no 9.3 TQM by V.Jayakumar

32. np CHART P and np are quiet same
Whenever subgroup size is variable,p chart is used. If sub group size is constant, then np is used.
FORMULA: Central Line CLnp = n p
Upper Control Limit, UCLnp = n p +3√ n p (1- p )
Lower Control Limit, LCLnp = n p -3 √ n p (1- p )
Where p = ∑ np/∑n =Average Fraction Defective
n = Number of items inspected in subgroup.

33. Problem
Problem No 9.11 page No 9.11 in TQM by V.Jayakumar

34. c Chart Type of attributes control chart Discrete quantitative data
Shows number of nonconformities (defects) in a unit
Unit may be chair, steel sheet, car etc.
Size of unit must be constant
Example: Count no of defects (scratches, chips etc.) in each chair of a sample of 100 chairs; Plot 21

35. c Chart Control Limits
Use 3 for 99.7% limits 22