MBA Statistics 51-651-0 2 COURSE # 5

1. MBAStatistics 51-651-02COURSE #5 Forecasting and Statistical Process Control

2. Part I: Forecasting • Part II: Statistical Process Control

3. Forecasting • Uncertainty means we have to anticipate future events • Good forecasting results from a combination of good technical skills and informed judgement

4. Insulator Sales DataData sets of chapter 10

5. Time Series • Data measured over time is called a time series. • Usually such data are collected at regular time periods. • Aim is to detect patterns that will enable us to forecast future values.

6. Forecasting Process • Choose a forecasting model • Apply the model retrospectively, and obtain fitted values and residuals • Use the residuals to examine the adequacy of the model • If model acceptable, use it to forecast future observations • Monitor the performance of the model

7. Time Series Components • Long term trend • Fundamental rise or fall in the data over a long period of time. • Seasonal effect • Regular and repeating patterns occurring over some period of time • Cyclical effect • Regular underlying swings in the data • Random variation • Irregular and unpredictable variations in the data

8. Identifying the Trend

9. A cycle is a regular pattern repeating periodically with a long period (more than one year).

10. Seasonal effect is similar to cyclical effect but with shorter period (less than 1 year).

11. Random effect • Random variations (also called noise) include all irregular changes not due to other effects (trend, cyclical, seasonal).  • The noise is like a fog, often hiding the other components. • One of the goal is to try to get rid of the effect (using smoothing).

12. Models •  additive model yt = Tt + Ct + St + Rt •  multiplicative model yt = Tt Ct St Rt

13. Illustration: Sales vs Quarter (ts.xls)

14. Moving Averages • Used to smooth data so we can see the trend or seasonality • removes random variation • We can take moving averages of any number time periods (preferable to take an odd number) • How much smoothing? • too little: random variation not removed • too much: trend may also be eliminated

15. Smoothing of Sales

16. Remarks • Considering MA over 3 periods, one can see a linear trend and seasonality of order 4, looking at peaks. • The MA series over 5 periods is too smooth and seasonality almost disappeared. • It is preferable to center the smoothed series with respect to the original one.

17. Smoothing of Sales

18. Exponential Smoothing • Smoothing aims to remove random so as to reveal the underlying trend and seasonality. • Moving averages use only the last few figures, and give them equal weight. We are loosing data. • Exponential smoothing uses all the data giving less and less weight to data further back in time.

19. New Forecast =a ×Latest Actual Value + (1 –a) ×Previous Forecast damping factor Updating Procedure

20. Exponential Smoothing in Excel • In Excel we use the damping factor (1-a) • For a = 0.8, we use 0.2 in Excel • The best value of a is found by trial and error, and is the one that gives the smallest MSE.

21. Exponential smoothing for Sales Data

22. Using Regression for estimating trend and seasonal effects • Can fit a linear regression model to the time series. • Use dummy variables corresponding to seasonality. • More complicated for multiplicative effects. • Desaisonalized series corresponds to residuals + constant!

23. Regression approach • What happens if the only explanatory variable is the quarter? Look at the residuals. • Introduce 3 dummy variables S1, S2, S3, corresponding to the seasonality of order 4. • Look at residuals now. • What are the predictions for the next 10 quarters?

24. Prediction of the next 10 quarters

26. Part II: Statistical Process Control (SPC)

27. Statistical Process Control • Statistical process control (SPC) is a collection of management and statistical techniques whose objective is to bring a process into a state of stability or control • And then to maintain this state • All processes are variable and being in control is not a natural state. • SPC is an effective way to improve product and service quality

28. Plan for Improvement Understand the Process Eliminate Errors Remove Slack Reduce Variation Five Stage Improvement Plan

29. Aspects of SPC • Benefits of reducing variation • Effect of tampering • Common cause highway • Special and common causes • Construction and use of control charts • Establishment and monitoring • Specifications and capability • Strategies for reducing variation

30. People Material Equipment Method Environment People Material Equipment Method Environment Processes PROCESSING SYSTEM INPUTS OUPUTS

31. Collect and analyse data Reduce variation Process Variability Inputs Outputs Process

32. Inputs Outputs Process Collect and analyse data Reduce variation Improved Process: less variability in input => less variability in output

33. Common Cause Highway

34. The Key to Reducing Variation • To distinguish between data that fall within the common cause highway, and data that falls outside the highway. • Common cause variation indicates a systemic problem. • Special cause variation is almost certainly worthy of separate investigation.

35. Epic Video Sales

36. Special Causes of Variation • Localised in nature • Not part of the overall system • Not always present in the process • Abnormalities, unusual, non-random • Contribute greatly to variation • Can often be fixed by people working on the process

37. Common Causes of Variation • In the system • Always present in the process • Common to all machines, operators, and all parts of the process • Random fluctuations • Events that individually have a small effect, but collectively can add up to quite a lot of variation

38. Three Sigma Limits • The arithmetic mean gives the centre line of the common cause highway • The mean plus three standard deviations gives the upper boundary of the highway. This boundary is called the upper control limit (UCL) • The mean minus three standard deviations gives the lower boundary of the highway. This boundary is called the lower control limit (LCL) • If a point falls outside the 3-sigma limits it is almost certainly a special cause.

39. Why 3-Sigma Limits? • In trying to distinguish between common and special causes there are two mistakes that we can make. • Interfering too often in the process. Thinking that the problem is a special cause when in fact it belongs to the system. • Missing important events. Saying that a result belongs to the system when in fact it is a special cause. too narrow; 2-sigma too wide; 4-sigma

40. Patterns • Specific patterns on a control chart also indicate a lack of randomness • We need rules to help us decide when we have a pattern • to avoid seeing patterns when none really exist • A pattern would indicate that special causes could be present

41. UCL Mean LCL 9 Points Below the Mean

42. ? ? ? time ? ? ? ? ? ? ? ? ? ? ? ? ? ? time Stability and Predictability Stable Process Source: Ford Motor Company Unstable process

43. Stability and Predictability • A stable process is predictable in the long run. • In contrast, with an unstable process special causes dominate. • Nothing is gained by adjusting a stable process • A stable process can only be improved by fundamental changes to the system.

44. Implementing SPC • There are two stages involved in implementing SPC • The establishment of control charts • scpe.xls