1. Prof. Dr. Kadria A. Elkhodairy
Statistics
Prof. Dr. Kadria A. Elkhodairy

2. Learning Objectives to:
Distinguish between controlled and uncontrolled variation
Distinguish between variables and attributes
Determine control limits for several types of control charts
Use graphics to create statistical control charts with Excel
Interpret control charts
Create a Pareto chart

3. Definition Statistics:
the practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

4. Statistical quality control (SQC)
It is the application of statistical tools in the manufacturing process for the purpose of quality control. In SQC technique attempt is made to seek out systematic causes of variation as soon as they occur so that the actual variation may be supposed to be due to the guranted random causes. Statistical quality control refers to the use of statistical methods in the monitoring and maintaining of the quality of products and services

5. Statistica1 quality control (SQC) is the term used to describe the set of statistical tools used by quality professionals. Statistical quality control can be divided into three broad categories:
1. Descriptive statistics:
Are used to describe quality characteristics and relationships. Included are statistics such as the mean, standard deviation, the range, and a measure of the distribution of data.

6. 2. Statistical process control (SPC):
Involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. SPC answers the question of whether the process is functioning properly or not.
3. Acceptance sampling:
Is the process of randomly inspecting a sample of goods and deciding whether to accept the entire lot based on the results. Acceptance sampling determines whether a batch of goods should be accepted or rejected

7. All three of these statistical quality control categories are helpful in measuring and evaluating the quality of products or services. However, statistical process control (SPC) tools are used most frequently because they identify quality problems during the production process.
The quality control tools we will be learning about do not only measure the value of a quality characteristic. They also help us identify a change or variation in some quality characteristic of the product or process.

8. Variations of Statistical Quality Control (SQC):
Variation in the production process leads to quality defects and lack of product consistency
Sources of variation:
1. Common, or random, causes of variation (allowable)
2. Assignable or preventable variation

9. Common causes of variation:
are based on random causes that we cannot identify. These types of variation are unavoidable and are due to slight differences in processing.
An important task in quality control is to find out the range of natural random variation in a process. For example, if the average bottle of a soft drink called Cocoa Fizz contains 16 ounces of liquid, we may determine that the amount of natural variation is between 15.8 and 16.2 ounces. If this were the case, we would monitor the production process to make sure that the amount stays within this range. If production goes out of this range—bottles are found to contain on average 15.6 ounces— this would lead us to believe that there is a problem with the process because the variation is greater than the natural random variation.

10. Assignable causes of variation.
Examples of this type of variation are poor quality in raw materials, an employee who needs more training, or a machine in need of repair.
In each of these examples the problem can be identified and corrected. Also, if the problem is allowed to persist, it will continue to create a problem in the quality of the product.
In the example of the soft drink bottling operation, bottles filled with 15.6 ounces of liquid would signal a problem. The machine may need to be readjusted. This would be an assignable cause of variation. We can assign the variation to a particular cause (machine needs to be readjusted) and we can correct the problem (readjust the machine).

11. Descriptive statistics
Can be helpful in describing certain characteristics of a product and a process. The most important descriptive statistics are measures of central tendency such as the mean, measures of variability such as the standard deviation and range, and measures of the distribution of data.

12. The Mean:
To compute the mean we simply sum all the observations and divide by the total number of observations.
The Range and Standard Deviation:
There are two measures that can be used to determine the amount of variation in the data. The first measure is the range, which is the difference between the largest and smallest observations. In our example, the range for natural variation is 0.4 ounces.

13. Small values of the range and standard deviation mean that the observations are closely clustered around the mean. Large values of the range and standard deviation
mean that the observations are spread out around the mean. illustrates the differences between a small and a large standard deviation for our bottling operation.

14. Normal distributions
There are many types of variation pattern in product quality. The most common pattern of data distribution is the normal curve (symmetrical bell-shaped curve).
● A normal frequency distribution curve is often obtained by plotting the relative frequency of the data obtained from a large number of results along the vertical axis against the magnitude of the measured characteristics, such as tablet weight or chemical assay

16. Distribution of Data
A third descriptive statistic used to measure quality characteristics is the shape of the distribution of the observed data. When a distribution is symmetric, there are the same number of observations below and above the mean. This is what we commonly find when only normal variation is present in the data. When a disproportionate number of observations are either above or below the mean, we say that the data has a skewed distribution.

17. Function of Statistical Quality Control (SQC):
1. Evaluation of quality standards of incoming material, product process and finished product.
2. Judging the conformity of the process to establish standards taking suitable action , when deviation are noted.
3. Evaluation of optimum quality, obtainable under given condition.
4. Improvement of quality and productivity by process control and experimentation.

18. Main purpose of Statistical Quality Control (SQC):
The main purpose of Statistical Quality Control(S.Q.C) is to divide statistical method for separating allowable variation from preventable variation

19. An assignable cause exists when variation within a process can be attributed to a particular cause that is a fundamental part of the process. Once identified, the assignable cause of the errors must be investigated and the process adjusted before other possible causes of variation are examined.

20. STATISTICAL PROCESS CONTROL METHODS
Statistical process control methods extend the use of descriptive statistics to monitor the quality of the product and process.
Using statistical process control we want to determine the amount of variation that is common or normal. Then we monitor the production process to make sure production stays within this normal range. That is, we want to make sure the process is in a state of control. The most commonly used tool for monitoring the production process is a control chart.

21. Developing Control Charts
A control chart (also called process chart or quality control chart) is a graph that shows whether a sample of data falls within the common or normal range of variation. A control chart has upper and lower control limits that separate common from assignable causes of variation. The common range of variation is defined by the use of control chart limits. We say that a process is out of control when a plot of data reveals that one or more samples fall outside the control limits.

22. The different characteristics that can be measured by control charts can be divided into two groups: variables and attributes.
Variable: A product characteristic that can be measured and has a continuum of values (e.g., height, weight, or volume).
Attribute: A product characteristic that has a discrete value and can be counted.

23. A control chart for attributes
Is used to monitor characteristics that have discrete values and can be counted. Often they can be evaluated with a simple yes or no decision. Examples include color, taste, or smell. The monitoring of attributes usually takes less time than that of variables because a variable needs to be measured. An attribut requires only a single decision, such as yes or no, good or bad, acceptable or unacceptable or counting the number of defects.

24. A control chart for variables :
Control charts for variables monitor characteristics that can be measured and have a continuous scale, such as height, weight, volume, or width. When an item is inspected, the variable being monitored is measured and recorded.

25. Where to Use Control Charts
Process has a tendency to go out of control
Process is particularly harmful and costly if it goes out of control
Examples
at the beginning of a process because it is a waste of time and money to begin production process with bad supplies
before a costly or irreversible point, after which product is difficult to rework or correct
before and after assembly or painting operations that might cover defects
before the outgoing final product or service is delivered

26. Quality control charts
Control charts have been employed for various pharmaceutical operations and may be used as an aid in controlling and analyzing physical, chemical, analytical, or biological parameters of product such as:
1- Weight variation of tablets and capsules.
2- Thickness of tablets.
3- Volume of liquid filling in a container
4-The number or percentage of defects in parenteral products.
5- The number of defects in a sample of packages resulting from a storage.

27. Types of quality control charts
A- Control charts by variables:
Variables charts are based on a continuous distribution of measurements that can, in a sense, measure degree of unacceptability.
Generally expressed with statistical measures such as averages and standards deviations
B- Control charts by attributes:
Attribute charts refer to go or no-go situation in which each sample inspected is tested to determine whether it conforms to the requirement.
Attribute data requires larger number of samples than variable inspection to obtain the same amount of statistical information

28. Control Charts
As long as the points remain between the lower and upper control limits, we assume that the observed variation is controlled variation and that the process is in control

29. Cont.
The process is out of control. Both the fourth and the twelfth observations lie outside of the control limits, leading us to believe that their values are the result of uncontrolled variation.

30. Even control charts in which all points lie between the control limits might suggest that a process is out of control. In particular, the existence of a pattern in eight or more consecutive points indicates a process out of control, because an obvious pattern violates the assumption of random variability.

31. Cont.
Control chart makes it very easy for you to identify visually points and processes that are out of control without using complicated statistical tests.
This makes the control chart an ideal tool for the shop floor, where quick and easy methods are needed.

32. A Process Is in Control If
… no sample points outside limits
… most points near process average
… about equal number of points above and below centerline
… points appear randomly distributed

33. A- Control charts by variables
Example 1
● During the automatic filling of a parenteral solution in vials, control of the volume filled during a production run should be established and maintained.
● One vial was taken at random from each of the four needles of the filling machine at designated times, and the average and the range of this subgroup of four was computed.
● The data obtained for the process control record is summarized in table (1) and graphically in figure (1).
● The curves of figure (1) are mean ¯X charts, and the lower curves are range (R)

34. The upper and lower control limits for the average ( UCL and LCL ) of the filled volume were calculated using the following equations:

36. (1)