Capability Analysis An Introduction to Statistical Process Control

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 http: //www. biz-pi. com 2 Capability Analysis

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 http: //www. biz-pi. com 3 Capability Analysis

Skewed Distributions mean = median mean median Average class shoe size – No skew Time to drive to work – Skewed right http: //www. biz-pi. com Hours of sleep per week – Skewed left 4 Capability Analysis

Standard Deviation (σ) = the average difference of each value from the mean Std dev = √ Σ(x - )2 n -1 It is a measure of how spread apart each individual data point is from the mean http: //www. biz-pi. com 5 Capability Analysis

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 LL If the variation (6σ) is greater than the tolerance limits, you have unacceptable variation UL LL 6σ http: //www. biz-pi. com UL 6σ 6 Capability Analysis

Examples USL Cpk = 0. 33 15. 87% Predicted failure rate -3 http: //www. biz-pi. com -2 -1 0 7 +1 +2 +3 Capability Analysis

Difference between Cp/Cpk and Pp/Ppk Cp/Cpk Pp/Ppk -Uses within estimate of standard deviation -Estimates potential capability (if outliers removed) -Estimates short term variability -Uses overall standard deviation formula (assumed for this course) -Estimates actual capability (includes outliers) -Estimates long term variability Unsure? Use Pp and Ppk calculations to be safe http: //www. biz-pi. com 8 Capability Analysis

Additional Resources Business Performance Improvement http: //www. biz-pi. com 9 Capability Analysis