An Introduction to Statistical Process Control Capability Analysis An Introduction to Statistical Process Control Introduction This course is designed to give you a thorough explanation of variation, histograms, and how these fundamentals lead to defining the capability of a product or process. This class is best taught using your company’s specific examples, allowing for interaction among the students Feel free to modify and change this course any way you like. Simply click View  Master  Master Slide to edit the master slide so that all slides show your company logo and name. You may also teach it exactly as it is. We recommend about 4 hours to teach the course. This course is intended to teach an individual or group with basic math skills and little to no prior knowledge of Statistical Process Control. This is the first half of the complete SPC course. Download Stability Analysis to complete the SPC course when it becomes available. We recommend that someone with prior experience and training with SPC teach the course. If not being used as a course, valuable information can still be obtained by following through the presentation and reading the notes section. If you have any questions, please visit or contact us at http://www.biz-pi.com

Cp and Cpk Calculations Pp and Ppk Calculations Examples Review Course Content Course Objectives What is Variation? Seeing Variation Measuring Variation Normal Distribution Cp and Cpk Calculations Pp and Ppk Calculations Examples Review Additional Resources Here is an overview of the course content. Click on one of the topics to go directly to that section.

Upon completion of this course, participants should be able to: Course Objectives Upon completion of this course, participants should be able to: Understand why measuring variation is important Calculate mean, standard deviation, Cp and Cpk Estimate the percent of data beyond the specifications Interpret the results of a capability analysis Understand how to improve the capability of a product or process Upon completion of this course, participants will be able to:

Skewed Distributions mean = median mean median median mean Average class shoe size – No skew A good example where the median and mean differ is when you are looking at data that is skewed to the high or low side. Skewed distributions are typical in housing prices, salaries and most time measurements. The middle curve shows a distribution that does not exhibit skewness. Determining the mean and the median will give you almost the exact same result. Now let’s look at the skewed distributions. As you can see, the median typically determines the middle of the data set that is near the top of the curve. The mean calculates the middle further down the curve, towards the longer tail. Remember, when you have outliers or very large or very small values in your data, the mean calculation gets pulled towards those outliers or values. Conclusion, when using data with a skewed distribution, the median is the more appropriate indicator of the middle of the data. For all other cases, the mean is preferred. Time to drive to work – Skewed right Hours of sleep per week – Skewed left

Standard Deviation Standard Deviation (σ) = the average difference of each value from the mean √ Σ(x - )2 Std dev = n -1 Standard deviation (or sigma) is typically the more accurate estimate of variation. It is calculated by taking the difference of each data point from the average of the data set. Since the standard deviation utilizes every data point, it is a better estimate of the true variability within the data set than the Range. Let’s take a look at an example It is a measure of how spread apart each individual data point is from the mean

What is Cp? Cp is a measure of how well the variation in the data can fit within the tolerance limits If the variation (6σ) is less than the tolerance limits, you have acceptable variation If the variation (6σ) is greater than the tolerance limits, you have unacceptable variation LL UL LL UL Cp is a measure of how well the variation in the data can fit within the tolerance limits. In simple terms, if the spread of variation in the data is less than the limits, you will have good capability. We use an outline curve to estimate what the histogram would look like without having to plot the actual points. On the left is an example of good capability. The right side diagram shows unacceptable capability, as the 6 standard deviations (sigma) in the data exceeds the limits. 6σ 6σ

Predicted failure rate Examples USL Cpk = 0.33 15.87% Predicted failure rate If we look at a process with Cpk = .33, we can determine the percent of fallout we might expect from this process. As you can see, the USL is lined up exactly with the +1 standard deviation mark. To determine the percent beyond the USL, we add the three sections together, which equals 15.87% (13.6 + 2.14 + .135). To conclude, when the specification limit is lined up with the +1 standard deviation line, you can expect about 15.87% fallout from the process. -3 -2 -1 +1 +2 +3

Difference between Cp/Cpk and Pp/Ppk Uses within estimate of standard deviation Estimates potential capability (if outliers removed) Estimates short term variability Pp/Ppk Uses overall standard deviation formula (assumed for this course) Estimates actual capability (includes outliers) Estimates long term variability Cp and Cpk are used for estimating the short term (or within subgroup) variation, which typically is not greatly influenced by outliers. Pp and Ppk are used for estimating the long term (or overall) variation, which is greatly influenced by outliers and unstable processes. If you are unsure, it is safer to use Pp and Ppk, since it will usually be smaller (worse) than Cp and Cpk Unsure? Use Pp and Ppk calculations to be safe

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