Scientific Method in Quality Control:
Statistical methods and scientific principles play a vital role in achieving high quality and low-cost production. The democratization of simple science enables widespread use of scientific methods.

Economic Consequences of Poor Quality:
The United States has experienced significant market share losses in industries like automobiles, cameras, and stereo components due to foreign competition. U.S. companies have struggled to match the quality and cost-effectiveness of foreign competitors.

Examples of Quality Issues:
Records indicate that the number of times a car is returned within the first six months of its life remained relatively stable for American car manufacturers, while Japanese cars showed a significant decrease in returns. This comparison highlights the need for U.S. companies to address quality issues.

Importance of Learning:
The use of scientific methods in quality control allows manufacturers to learn about their products and processes, leading to improvements.

Research Problems:
Research opportunities exist in developing new methods for quality control and improving the use of existing methods.

Background of Discovery:
Scientific discoveries often rely on critical events and perceptive observers. The discovery of champagne, for example, required both a critical event (second fermentation of wine) and a perceptive observer (the French monk).

Scientific Method and Technological Change:
The introduction of the scientific method 300 years ago led to a significant increase in technological change. The scientific method involves two key approaches: Informed Observation: Bringing naturally occurring informative events to the attention of perceptive observers. Directed Experimentation: Inducing the occurrence of informative events to increase the probability of discovering new knowledge.

Informed Observation:
Quality control charts are an example of informed observation, where naturally occurring potentially informative events are monitored and analyzed.

Directed Experimentation:
Benjamin Franklin’s kite experiment is an example of directed experimentation, where an experiment is conducted to elicit a specific informative event.

Effectiveness of Methods:
There is a trade-off between the effectiveness and complexity of methods. While fancy techniques can be effective, simpler methods may be more practical for widespread use in a quality revolution involving everyone in an organization.

Observing What Happens:
Observing what happens is the first step in discovering new knowledge and improving quality.

What is a Process?:
A process is not just limited to manufacturing processes. It can also include drafting, invoicing, computer service, hospital admission, getting a ticket to fly, and more.

The Seven Tools of Quality Control:
Ishikawa’s seven tools for quality control include Pareto charts, causal effect diagrams, check sheets, histograms, and others. These techniques are simple and can be used by the workforce, not just by highly educated individuals.

Pareto Chart:
A Pareto chart is a visual representation of the frequency of different types of defects or errors in a process. It helps identify the most common defects or errors, allowing teams to focus on addressing the most impactful issues first.

Histogram:
A histogram is a visual representation of the distribution of data. When split into multiple parts, it can help identify differences between different categories or groups of data.

Quality Man as Detective:
Instead of being a policeman, the quality man should be a detective, following a trail of evidence to identify the root causes of problems and improve the process.

Understanding Fractional Factorial Designs:
Fractional factorial designs have been used for a long time in industry, with the first being employed by Tippett in 1933. Plackett and Berman, along with Dr. Rao, introduced orthogonal arrays, which are not fractional factorials.

Rationale for Using Fractional Factorials:
Symmetric filling of experimental space: Provides a balanced design, ensuring equal representation of factor combinations. Prior knowledge of important interactions: Allows for designing experiments around these interactions, estimating only the significant ones. Projective properties of design in expectation of a Pareto effect: Assumes that only a few factors have important effects, allowing for efficient screening.

Critique of Rationales:
Questioning the second rationale: Argues that knowing which factors have second-order effects while being unaware of first-order effects is illogical. Emphasis on the projective rationale: Believes that the projective rationale is the most significant, providing complete factorials in lower dimensions.

Center for Quality and Productivity Research:
Established at Madison, focusing on research related to quality and productivity. Published 23 research reports on various aspects of quality and productivity.

Simultaneous Consideration of Mean and Variance:
Importance of adjusting both the mean and variance of a process for optimal quality. Challenges in conducting large experiments with multiple repeat runs.

Fractional Designs for Dispersion Effects:
Explored the potential of using fractional designs to study dispersion effects. Examined an experiment on welding with nine variables in a 16-run fractional factorial design.

Identifying Important Factors in a Welding Process:
Plotting the effects on normal probability paper reveals two significant factors, drying method (B) and material (C), while other factors appear less influential.

Material Variation and Dispersion Effects:
Further analysis suggests that material (C) affects not only the mean (location effect) but also the variance (dispersion effect) of tensile strength.

Aliasing between Location and Dispersion Effects:
Dispersion effects are aliased with column effects in fractional designs, leading to potential misinterpretation of results.

Estimating Location and Dispersion Effects Simultaneously:
By taking residuals and analyzing from that, it is possible to estimate location and dispersion effects simultaneously.

Iterative Method for Identification:
An iterative method originally proposed by Vijay Nair and David Pagabon can be used to identify dispersion effects from fractional design.

Iterative Process and Long-Term Investigations:
George E. P. Box emphasizes that statistics is not just about making one-shot decisions but is part of a long-term iterative investigation process. The focus is on collecting clues and identifying the next worthwhile step, rather than drawing definitive conclusions from a single experiment.

Checking Hypotheses and Focusing Attention:
Statistical analysis helps suggest the presence of effects (e.g., location or dispersion effects) without claiming definite proof. This allows researchers to concentrate attention on specific factors for further investigation in subsequent experiments.

Economizing Experimentation and Normal Plotting Methods:
In fractional factorial designs, where the number of experiments is limited, Cuthbert Daniel’s normal plotting methods provide a way to analyze data without feeling guilty about pulling small mean squares. Normal plots help identify potentially important variables and interactions.

Bayesian Model for Effect Sparsity:
Box and Dan developed a Bayesian model that incorporates prior assumptions of effect sparsity, reflecting the idea that many effects are likely to be small or negligible. This model estimates the probability of an effect being purely noise or a combination of noise and a real effect.

Calculating Posterior Probability of Active Factors:
The Bayesian model allows for the calculation of the posterior probability of each factor being an active factor. This provides a more nuanced assessment of factor importance compared to traditional significance testing.

Factorial Effects and Noise:
By analyzing fractional factorials, one can estimate the effects of factors and the level of noise in the data.

Estimating Alpha and Kappa:
Alpha and Kappa are parameters used in the analysis. Alpha represents the proportion of effects that are active, and Kappa represents the number of effects per factor. Estimates for alpha and Kappa can be obtained by examining past examples of fractional factorials.

Interpreting the Results:
The analysis provides probabilities associated with each factor and interaction, indicating their likelihood of being active. A sensitivity analysis can be conducted to assess the impact of varying alpha and Kappa within reasonable ranges.

Robustness of Conclusions:
The conclusions drawn from the analysis are generally robust to variations in alpha and Kappa. Factors that are identified as being very active tend to remain so, while the probabilities of less active factors may vary.

Application and Future Work:
This method has been applied in numerous examples and has proven useful in analyzing fractional factorials. A paper is forthcoming in a volume honoring Cuthbert Daniel, discussing how to modify this method to account for possible faulty observations.