Quality Progress - June 2014 - (Page 72)

BACK TO BASICS BY DAVID PHILLIPS Curve Your Enthusiasm How to plot OC curves in Excel SAMPLING PLANS are valuable in many number of nonconforming units that may quality control applications. But it can be be found in the sample for lot acceptance. difficult to explain the benefits of different To put it another way, the lot would be plans to colleagues who are unfamiliar with rejected if c + 1 or more samples are non- the terminology. It is useful to show operat- conforming. In the example spreadsheet in ing characteristic (OC) curves to facilitate Figure 2, the user would enter values for n those discussions. Many sources of OC Part of spreadsheet that created Figure 1 / FIGURE 2 and c in cells B2 and B3 respectively. curve images are inconvenient ("my books The x axis lists possible values with are on my desk"), or they are not relevant to the actual percentage of nonconforming the situation at hand (a published curve for parts in the lot. In Figure 2, values for the a sample size of 70, but not for 68 or 75). x axis are in column A, starting in row six. Smaller percentages are closer together to Fortunately, Microsoft Excel includes draw a smoother curve. built-in functions that make drawing OC curves easy. In this column, we'll focus on Y axis values for the OC curve are attribute (pass/fail) single sampling plans in column B, starting in row six. These that can be modeled with the binomial values represent the probability of ac- distribution, such as ANSI/ASQ Z1.4:2008. cepting the lot given n, c and the actual Excel can be used for other distributions, percentage of nonconforming parts (from such as Poisson and hypergeometric, in a column A). The probability to accept the similar manner. lot comes from the binomial distribution. nonconforming also must be converted to In Excel, the function to calculate this is: a proportion (by dividing by 100) for the Figure 1 shows an example OC curve. It shows the probability of the sampling plan =BINOMDIST(c, n, actual % non-conforming, TRUE) accepting the lot (on the y axis) based on the actual (and usually unknown) percent- table by copying cell B6 down to match You can substitute the cell references using cell B6 as an example: age of nonconforming items in the lot (on function to work correctly. Complete the the length of column A. Then, draw the OC curve by creating an xy chart using the x axis). Two values are required to draw =BINOMDIST($B$3,$B$2,(A6/100),TRUE) columns A and B (both starting in row the curves: sample size (n) and accept num- Because the values for c and n will six). Remember that the y axis is shown as ber (c). The accept number is the maximum always be in cells B3 and B2, $ symbols are used to fix those cell Example OC curve (n = 75, c = 2) / FIGURE 1 a proportion, not a percentage. OC curves provide a graphical method of comparing various plans in a way that not change when cell is easy to explain. Excel makes it simple 1.0 B6 is copied down to to create custom plans to meet specific re- 0.9 complete the table. The quirements. Online Figure 1, for example, 0.8 reference for the actual compares plans designed to allow lots that 0.7 p (accept) references so they will percentage nonconform- are 8% nonconforming to be accepted no 0.6 ing (A6) does not need more than 10% of the time. QP 0.5 the $ because it must 0.4 change for every row 0.3 (for example, in row 0.2 seven it needs to be A7 0.1 0.0 0.00 instead of A6). 2.00 4.00 6.00 8.00 10.00 12.00 % non-conforming 72 QP * www.qualityprogress.com 14.00 16.00 18.00 20.00 The percentage DAVID PHILLIPS is a senior quality engineer at Dentsply Caulk in Milford, DE. A senior member of ASQ, Phillips is a certified quality engineer and a Six Sigma Black Belt. He holds a bachelor's degree in mechanical engineering from Grove City College in Pennsylvania. http://www.qualityprogress.com

Table of Contents for the Digital Edition of Quality Progress - June 2014

Up Front
LogOn
Expert Answers
Keeping Current
Mr. Pareto Head
No Weak Links
Need for Speed
Solid Base
Insurance Policy
3.4 per Million
Quality in the First Person
Career Corner
Statistics Roundtable
2014 Software Showcase and Directory
QP Toolbox
QP Reviews
Back to Basics

Quality Progress - June 2014

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