Introduction of George Box:
Dr. George Box is an expert in statistics with a distinguished career. He was the first chairman of the Statistics Department at the University of Wisconsin in Madison. Dr. Box has received numerous awards for his contributions to the field of statistics.

Historical Context:
Dr. Box and Gwilym Jenkins published a paper in 1962 advocating for the integration of control engineering and statistics. Their work was not widely accepted at the time but has gained traction in recent years.

Rediscovery of Statistical Concepts:
Some statistical concepts have been rediscovered and are now being applied to quality control. This approach can help address issues with standard quality control charts.

Basic Statistical Concepts:
In introductory statistics courses, students often learn about calculating the average (Y bar) and standard deviation (S) of a data set. These statistics are considered sufficient statistics for the normal distribution, meaning they contain all the information about the distribution.

R.A. Fisher’s Work:
R.A. Fisher, a prominent statistician, emphasized the importance of Y bar and S as sufficient statistics. According to Fisher, once these values are known, all that can be known about the normal distribution and the independent observations within it is known.

Plotting Data for Process Data:
Dr. Schuart emphasizes the importance of plotting data, especially for process data, as the order of the data can affect its interpretation.

Non-Independence of Observations:
Data from a process is not a random sample, and observations are often dependent on each other. This affects the validity of statistical methods assuming independence.

Schwarzschild Chart:
A Schwarzschild chart is a plot of the data with lines indicating unusual discrepancies.

Plotting Data as a Valuable Tool:
Plotting data can reveal patterns and trends that might not be evident from summary statistics alone.

Significance of Large Deviations:
When a point deviates significantly from the norm, it is important to consider the distribution of the data and the independence of observations.

The Challenge with Quality Control Charts:
Quality control charts are designed to detect unusual patterns in data, but their effectiveness relies on the assumption of independence among observations.

Assumptions and Violations:
Over 85% of control charts in training manuals for SPC had misplaced control limits. Real-world data often violates the assumptions on which control charts are constructed.

Common Causes and Special Causes:
Common causes are noise below the level of detection that must exist and are not detectable. Special causes are detectable events that cause significant variation.

Problems with Control Chart Data:
Common causes are unlikely to fit nicely into one-hour intervals. Common causes can persist for long periods, such as when a new operator takes over a process.

Muth’s Model:
Muth, an economist, developed a model that described permanent and transitory common causes. Transitory causes are temporary and random, while permanent causes are persistent and systematic.

Central Limit Theorem and Normality:
The central limit theorem states that the sum of many random variables tends to be normally distributed. This means that if multiple random common causes are present, the resulting data will often appear normal.

Stationarity vs. Non-Stationarity:
Stationary processes exhibit a fixed mean and a constant variance over time, making them predictable. Non-stationary processes, however, lack a fixed mean and exhibit a wandering or drifting behavior, making them unpredictable.

Causes of Non-Stationarity:
External factors, such as changes in the environment or economic conditions, can induce non-stationarity in a process. Internal factors, such as feedback loops or inherent instability, can also contribute to non-stationarity.

Implications of Non-Stationarity:
Non-stationary processes challenge traditional statistical methods, which assume a fixed mean and constant variance. Forecasting and control become difficult in the presence of non-stationarity, as the process’s behavior cannot be accurately predicted.

Identifying Non-Stationarity:
Visual inspection of a time series plot can provide initial clues about non-stationarity, such as drifting trends or fluctuating means. Statistical tests, such as the Augmented Dickey-Fuller (ADF) test, can formally assess the stationarity of a time series.

Addressing Non-Stationarity:
Transformation: Applying mathematical transformations, such as differencing or logarithmic transformations, can sometimes induce stationarity in a non-stationary process. Control: Implementing feedback mechanisms or control systems can stabilize a non-stationary process and bring it closer to a stationary state. Modeling: Specialized statistical models, such as autoregressive integrated moving average (ARIMA) models, can explicitly account for non-stationarity and provide more accurate forecasts.

Model Definition:
A good model is an approximation that captures essential features, produces robust procedures, and is easy to use. For non-stationary processes, a reasonable model is a local average with exponentially weighted deviations, plus random noise.

Exponentially Weighted Moving Average (EWMA):
EWMA is a weighted average that gives more weight to recent observations and less weight to older ones. The formula for calculating the next EWMA is: y twiddle t plus 1 = theta * y twiddle t + lambda * y sub t. Theta is the weighting factor (0 ≤ theta ≤ 1), and lambda is the forgetting factor (1 – theta).

Non-Stationary Series and Lambda:
Different values of lambda generate different non-stationary series. Lambda = 0: White noise (stationary). Lambda > 0: Increasingly wobbly series. Lambda ≈ 0.2 or 0.1: More realistic for real processes.

Application in Process Control:
EWMA can be used to monitor and control non-stationary processes. An adjustment chart is used to plot the EWMA until it reaches a certain limit (L). If the EWMA crosses the limit, an adjustment is made to the process. This helps to keep the process within desired limits.

Statistical Process Control Techniques:
Statistical process control (SPC) involves the use of statistical techniques to monitor and control processes, with the goal of improving their performance and reducing variability.

Identifying Special Causes:
SPC techniques help identify special causes of variation, which are non-random events that can significantly impact the process. In the example provided, a sudden shift in the monitoring chart indicated the presence of a special cause.

Adjustment Chart:
The adjustment chart is used to determine whether the process is in control and whether adjustments are needed to maintain control. The adjustment chart plots the difference between the observed value and the exponentially weighted average, which should be white noise if the process is in control.

Monitoring Chart:
The monitoring chart is used to monitor the process over time and identify any shifts or trends that may indicate a special cause of variation.

Using Multiple Charts:
While multiple charts can be used to monitor a process, only the adjustment and monitoring charts are necessary for effective SPC.

Background:
George Box discusses advanced statistical techniques for engineering process control, including exponential weighted moving average (EWMA), Muth’s Transient and Permanent Innovations, and time series analysis.

EWMA for Adjustment Control:
EWMA is a technique for determining when to adjust a process based on the exponential weighted average of past observations. Adjustments are made when the EWMA exceeds a specified threshold. Lambda (λ) is a parameter that controls the sensitivity of the EWMA to changes in the process.

Robustness of EWMA:
EWMA is robust to variations in the value of lambda. Small variations in lambda do not significantly affect the performance of the EWMA control chart.

Selecting the Value of Lambda:
The optimal value of lambda can be determined by minimizing the sum of squared errors between the EWMA and the actual process data. This can be done through a least squares approach.

Options for Adjustment Intervals:
The average adjustment interval can be adjusted by changing the value of L, which is the threshold for making adjustments. Increasing L increases the average adjustment interval, while decreasing L decreases the average adjustment interval. The choice of L depends on the specific process and the desired level of control.

Relationship to Proportional Integral Derivative (PID) Control:
EWMA control is related to PID control, which is a common method of engineering process control. EWMA control is similar to integral control, which adjusts the process based on the integral of past errors. PID control also includes proportional and derivative components, which adjust the process based on the current error and the rate of change of the error, respectively.

Applications and Resources:
Box mentions a paper published in Quality Engineering and an upcoming book, “Physical Control by Monitoring Adjustment, Second Edition,” which provide further details on the discussed techniques. Synergistic control is a concept that combines engineering process control and statistical process control for a more sophisticated approach.

Stationarity in Processes:
George Box believes that stationarity, or the idea that a process remains constant over time, is a non-existent concept. He argues that it is unrealistic to expect any process to remain unchanged indefinitely.

Causes of Drift:
In cases where a process exhibits drift, or a gradual change over time, Box suggests that there may be an underlying cause. However, identifying the exact cause may not always be possible.

Adjusting for Drift:
Box emphasizes that even if the cause of drift is unknown, it is still possible to make adjustments to compensate for it. This can be done by using operating variables that are known to influence the process and adjusting them accordingly.

Practical Approach:
Box advocates for a pragmatic approach to dealing with process drift. He suggests that it is unnecessary to know the specific cause of the drift in order to make adjustments. Instead, one can rely on empirical evidence and experimentation to determine the most effective adjustments.

Randomness and Uncertainty:
Box acknowledges that many things happen in processes for which we cannot pinpoint the exact cause. However, he emphasizes that even in the face of uncertainty, it is still possible to take action and address the issue.

Muth’s Model and Transient and Permanent Innovations:
Muth’s model introduces the concept of transient and permanent innovations to explain the noise or variations in a process. Transient innovations are temporary changes in the process that eventually stop, while permanent innovations are changes that persist over a period of time. Box emphasizes the importance of Muth’s contribution in recognizing that noise is caused by real events and that some of these events are transient while others are permanent.

Common and Special Causes in Moose’s Model:
Common causes are the variations in a process that are inherent to the process itself and cannot be easily identified or eliminated. Special causes are variations that are caused by specific, identifiable events or factors. In Moose’s model, common causes are represented by transient and permanent innovations, while special causes are represented by events that cause sudden changes in the process level.

Data Analysis and Interpretation:
Box highlights the importance of data analysis and interpretation in understanding the behavior of a process. He emphasizes the value of smoothing data to identify trends and patterns, as well as examining the residuals (the part that does not fit the smoothed trend) to detect potential special causes. Box also stresses the importance of plotting the raw data to gain a comprehensive understanding of the process behavior.

Application to Service Industries:
Box acknowledges that his methodology is primarily applicable to continuous processing industries. However, he suggests that some aspects of it could be adapted to service industries such as healthcare and education, where processes involve collecting data and monitoring performance over time.

Limited Innovation and Special Causes:
Box discusses the concept of limiting innovation to special causes. He suggests that in some cases, it may be more practical to focus on identifying and addressing special causes of variation rather than trying to eliminate all variations in the process.

Conclusion:
George Box apologizes for not being able to provide a technical explanation due to his age and limited knowledge of the specific details of processes.

Statement:
He acknowledges that he is close to reaching 90 years old and expresses a desire to reach that milestone. He feels that in order to do so, he needs to stop discussing the system being referred to in the conversation.

Further Apology:
He apologizes again for not being able to understand or respond to a technical question that was asked. He admits that he may not have understood it even if it had been explained to him, due to his lack of expertise in the specific area being discussed.