1. POPULATION VERSUS SAMPLE
Definition
A population consists of all elements – individuals, items, or objects – whose characteristics are being studied. The population that is being studied is also called the target population.
A portion of the population selected for study is referred to as a sample.

2. Figure: Population and sample.

3. POPULATION VERSUS SAMPLE cont.
Definition:
A survey that includes every number of the population is called a census. The technique of collecting information from a portion of the population is called a sample survey.

4. Normally Distributed Curve

5. Skewed Distributions

6. Characteristics of the Normal Distribution
It is symmetrical -- Half the cases are to one side of the center; the other half is on the other side.
The distribution is single peaked, not bimodal or multi-modal
Most of the cases will fall in the center portion of the curve and as values of the variable become more extreme they become less frequent, with “outliers” at each of the “tails” of the distribution few in number.
It is only one of many frequency distributions but the one we will focus on for most of this course.
The Mean, Median, and Mode are the same.
Percentage of cases in any range of the curve can be calculated.

8. Family of Normal Curves

9. 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

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

11. 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

12. 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

13. 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

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

15. X Chart Interval or ratio scaled numerical data
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

16. 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

17. 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)

18. 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.

19. 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

20. R Chart Control Limits
From Tables 18

21. 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

22. 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

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

24. 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.

25. 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.

26. 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

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