1. PROBABILITY & STATİSTİCS Prof. Dr. Orhan TORKUL Res. Assist. Furkan YENER

2. Probability & Statistics  Many of problems we face daily as industiral engineers have elements of risk, uncertanity, or variabilty associated with them. For example, we cannot always predict what the demand will be for a particular inventory item. We cannot always be sure just how many people will shop at a grocery store and desire to check out during a particular hour. We cannot always be sure that the quality of raw materials from one of our suppliers will be consistent. We are not prophets who can accurately predict results in advance. But we as industrial engineers are educated in the use of applied probability and statistics to make intelligent engineering decisions despite our lack of complete knowledge about future events.

3. Probability of an Event

4. Sample Points Counting Rules

5. Combinations

6. Estimating Probabilites

7. Some Important Probability Distributions 1. Discrete Distribution Properties 2. Binomial Distribution 3. Poisson Distribution 4. Discrete Uniform Distribution 5. Uniform Distribution 6. Normal Distribution 7. Exponential Distribution 8. Rectangular Distribution

8. Normal Distributions

9. Expected Values and Variability

10. Populations and Samples  Much of the work of the applied professions involves the study of only a subset of the total items of interest, in the hope of making statistical inferences about the total. An engineer might collect data on machine utilization for 1 month, hoping to infer from it machines utilization information for many months or years. An automobile manufacturer might test small number of automobiles and then make generalized statements about all the automobiles produced during that model year. An inspection team might use destructive inspection on a small percentage of items in order to infer caracteristics of the total number beng produced. In order to describe this process accurately, we must clearly understand the meaning of population and sample.

11. Population  A population, in the broadest sense, is the total set of elements about which knowledge is desired. Some populations are relatively small, for example, the number of space shuttles; other populations are large, for example, all the electric light bulbs now in existence and to be produced in the future. All elements of a population do not have to be in existence, as the last example indicates. The important thing to remember is that the population must be definable.

12. Sample  A sample is a subset of a population. In extreme situations the sample may be the complete population or it may consist of no elements at all. Of course, this latter sample would yield no information and we shall not consider it further. Remember that the purpose of a sample is to yield inferences about the population from which it was taken.  The two most important futures of a sample are its size and the manner in which it was selected. Much of the study of sampling statistics concerns the determination of these two characteristics. As expected, this determination is based on the specific conditions prescribing the purpose of the sample.

13. Sample Statistics

14. Distribution of Sample Means

15. 0,6-0,250,0625 1,20,350,1225 0,90,050,0025 10,150,0225 0,6-0,250,0625 0,8-0,050,0025 5,10,000,2750 Example

16. Central Limit Theorem

17. THANKS