Introduction to Statistical Quality Control Douglas C. Montgomery Chapters 1, 2 and 3 Introduction to Statistical Quality Control Douglas C. Montgomery Presentation by Mikey Awbrey

Chapter 1: Introduction KEY POINTS Quality Deming’s 14 points PDCA

Chapter 1 - Quality Quality is a factor of Multiple dimensions Performance Reliability Durability Serviceability Aesthetics Features Perceived Quality Conformance to Standards

Chapter 1 – Deming’s 14 points W. Edwards Deming was an engineer who wanted to improve business practices. He studied in the USA and Japan to create his philosophy based around 14 key points. Create a constancy of purpose focused on the improvement of products and services Adopt a new philosophy that recognizes we are in a different economic era Do not rely on mass inspection to “control” quality Do not award business to suppliers on the basis of price alone, but also consider quality Focus on continuous improvement

Deming’s 14 points cont’d Practice modern training methods and invest in on-the-job training for all employees Improve leadership, and practice modern supervision methods Drive out fear Break down the barriers between functional areas of the business Eliminate targets, slogans, and numerical goals for the workforce Eliminate numerical quotas and work standards Remove barriers that discourage employees from doing their jobs Institute an ongoing program of education for all employees Create a structure in top management that will vigorously advocate the first 13 points

Chapter 1 - PDCA Image from - http://sam4quality.files.wordpress.com/2012/01/pdca1.png

Chapter 2 The DMAIC Process Define Clearly identify opportunity and validate its potential Measure Evaluate and understand the current status of the process Analyze Determine cause and effect relationships and understand variables Improve Problem solve to create changes to improve process performance Control Create a control plan to maintain the improvements and set them in motion

Chapter 3: Modeling Process Quality Key points Variation Discrete vs Continuous Distribution Methods Probability Plots

Chapter 3- Variation Variation - a change or difference in condition, amount, or level, typically with certain limits. (Taken from Google dictionary) Variation can be described in many ways and is the focus of statistical analysis.

Describing Variation Stem and Leaf Histogram Group data together numerically Raw data is exposed Group data together graphically Data is sorted into sets Commonly has bell curve overlay (not required)

Describing Variation Cont’d Stem and Leaf Histogram Image taken from http://www.bbc.co.uk/schools/gcsebitesize/maths/images/hd_crd2_dia_05a.gif Image taken from http://www.mathsisfun.com/data/images/histogram.gif

Describing Variation Cont’d Box Plot Used to represent a number of important features about the data. Image taken from http://www.physics.csbsju.edu/stats/simple.box.defs.gif

Discrete Vs Continuous Distribution The data can only be in certain values, such as integers i.e. 1,2,3,4 The variables can be expressed on a continuous scale. i.e. 1.44565, 4.325, 0.2

Discrete Distributions Bernoulli Trials When a part is pulled form a lot and it either passes or fails. The data collected from this type of trial is a very typical type of discrete data Hypergeometric Distribution Used to predict the probability of selecting a defective part form a sample within the assumptions of pulling a select number from the whole and the parts pulled are not replaced and the number defective are known. Binomial Distribution Similar to hypergeometric, however this assumes the lot from which samples are taken is virtually infinite and uses a percentage for number of defective parts in the lot.

Discrete Distributions Cont’d Poisson Distribution Used to predict the number of defects any given part pulled from a lot might have. Negative Binomial This represents the number of Bernoulli trials to achieve a certain number of successes, rather than the predicted number of failures as it relates to the number of Bernoulli trials performed. Geometric Distribution The number of Bernoulli trials until the first success is acheived

Continuous Distribution Image taken from http://nicedoggie.net/wp-content/uploads/2012/07/Bell-Curve.gif Normal Distribution A symmetrical, unimodal, bell-shaped curve Lognormal Distribution The variables follow an exponential pattern. This describes ln (x) = w which means the natural log of x is normally distributed.

Continuous Distribution cont’d Exponential Distribution The probability distribution of an exponential variable. Used in reliability engineering to model time to failure of a component. Image taken from http://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Exponential_pdf.svg/325px-Exponential_pdf.svg.png Gamma Distribution This reduces the exponential distribution it terms of λ, the result of the exponential distribution. This gives the curve a larger variety of potential shapes. Image taken from http://upload.wikimedia.org/wikipedia/commons/f/fc/Gamma_distribution_pdf.png

Continuous Distribution cont’d Weibull Distribution This is the most flexible distribution with the widest variety of applications in reliability engineering. The exponential distribution is reduced with 1/θ where θ>0 is the scale parameter. Image taken from http://upload.wikimedia.org/wikipedia/commons/5/58/Weibull_PDF.svg

Probability Plots Probability plotting is a graphical method to check if the data is suitable for probability modeling. The data is placed on a special graph and plotted. This can then be evaluated with a subjective visual examination to determine if the data fits the hypothesized model. Image taken from http://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Normprob.png/350px-Normprob.png

Final Notes of Importance It is very important to remember that all of these calculations are approximations. As was apparent in the previous slide, the calculated lines do not fit the data perfectly. Chapter 3 is about using collected data and creating usable predictions from it.