Quality Management
1) I em(Statistics
by John B. Durkee
uestion #l. If all your parts look and feel the same, how do you tell which, if any, are clean? Question #2. If the data coming from your cleaning test show the desired performance, how do you know any of those numbers mean anything? Question #3. If a vat of aqueous cleaning juice always looks gray, feels wet, and smells foul, how do you know when it is spent? Question #4. If your process is running today apparently as it was running yesterday, has anything changed? And, do you care? “Would you like me to quote some statistics?” “En well . ..” “Please, I would like to. They, too, are quite sensationally dull.“1 Answers to those questions are what we intend to cover in this and the March and May 2003 columns. So, today’s subject is information and how to manage it in cleaning operations. Bring your statistics book or spreadsheet. Look up the section on t-tests. We’re going to make this simple!2 On Statistics: “Here we have a game that combines the charm of a Pentagon briefing with the excitement of double-entry bookkeeping.“3 Cleaning development, management, and validation involve small differences among parameters difficult to measure (NVR, particle or defect count, solution concentration, surface thickness, misalignment, and optical quality). It is those differences that define our job performance in cleaning work. If we misunderstand the nature of those differences, we can find ourselves standing in the same line as those who used to work for Enron. “The most misleading assumptions are the ones you don’t even know you’re making.“4 Here is a simple example that illustrates the danger of working with one data point. Suppose we are cleaning small stamped parts. There are about 25 parts in one pound (18.144 g/part). A dirty part has about 250 mg/ft2 of soil (17.35 mg of soil if each part has about 10 in2 area). These values are absolutely typical-they are the data from a client I worked with in June 2002.
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John B. Durkee is President of Creative EnterpriZes, a consulting firm located in Kerrville, Texas. E-mail,
[email protected].
1
Now choose one part and weigh 18.16163 g.
it. It weighs
Run it through the cleaning machine. Weigh it again, It weighs 18.14443 g. So the cleaning machine removed 17.20 mg of soil. (Please note that this is not cleaning data! All we know is how much soil has been removed. We don’t know how much more soil is on the parts. We don’t know if the parts are clean. Unremoved solid could weight another 17 mg, 0.17 mg, or 170 mg. We just don’t know, yet.) Run the part through an extraction process using isopropanol, which is believed to remove all soil. Now it weighs 18.14420 g. An additional 0.23 mg of soil was removed. If we believe that the isopropanol extraction process removes all soil, then the weight of this soil-free part is 18.14220 g. Calculate the percent clean after the cleaning machine as (17.20)/(17.20 + 0.23) = 98.68%. Suppose the standard of performance is to remove at least 98.50% of the soil. Is the cleaning machine meeting that standard? With just this one sample, the answer is “ . . .yes, why do you ask.. .?” Suppose we take additional samples and perform the same test. Then we average (take the mean of) the percent clean data. What we find is listed in Table I. Whoops! With 10 or more samples, we can see that the process is not meeting the standard of performance of 98.50% soil removal. The parts are not clean! What are the chances of that being true? We’ll answer that below (Question C) with the aid of the t-test (see Fig. 1). Errors using inadequate data are much less than those using no data at a11.5 Consider the extraction process may not remove all soil. In that case, we must complete another independent test to learn if the first extraction does remove all soil. This is called validation. Here we are proving or disproving that our cleaning test (the IPA extraction) is a valid test for part cleanliness. Our validation test might be another extraction, using the hexane isopropanol azeotrope to be certain of removing both polar and nonpolar soils. 65
The validation test was completed and the results for the single and multiple samples are shown in Table II. Question A is: “Did the IPA/hexane validation extraction process remove all the soil as expected?” The answer is learned via comparing the right-hand column in Table II with 100%. If they are the same value, then the IPA/hexane validation extraction process did remove all the soil. Question B is: “Did the normally used IPA extraction process remove all the soil as expected?” The answer is learned by comparing the center column with the right-hand column in Table II. If they are the same value then the IPA extraction process did remove all the soil and may be considered a useful cleanliness test. If they are not, another cleaning test must be found. Both questions are answered below, with the aid of the t-test. Truth comes out of error more readily than out of confusion.6
The t-test is useful for deciding if some sort of treatment worked compared to the control group. This is what cleaning professionals do. We want to know if some parts are cleaner than a standard or
J C-
other parts. Familiarity with the t-test is critical for all who work with data, especially those who do parts cleaning. There are some internet sites7 from which you can learn about and use on-line calculators (applets) for the t-test. The primary assumptions for the t-test are: 1. Population data from which the sample data are drawn are normally distributed. 2. The variances of the populations to be compared are equal. Actually, empirical studies8 of the t-test have demonstrated that these assumptions can be violated to an amazing degree without substantial effect on the results. In other words, unless you know that your data are unstable (have some area of operation, which can’t be or always are achieved) or are of two different types (continuous analog or distributed digital), go with the t-test. “If you think it’s expensive to hire a professional do the job, wait until you hire an amateur.“3
to
Fortunately, in 2003 we cleaning folk don’t have to know the details of the t-test calculation. But we do have to know what the results mean and how they can and cannot be used. Today’s spreadsheets do the calculations for us. Both Microsoft’s Excel and Corel’ Quattro-Pro have the same function: Core1 uses the name @TTEST and Microsoft uses the name =TTEST. The parameters for use are the same for both spreadsheets. The output is a fraction. @ or = TTEST (Data Set #l,Data Set #2, 1,l)
Figure l.The “t-test. ” “t” is the difference between the means of two groups of data provided by the combined variability of both groups. A higher ratio occurs when the means are more easily identified-a greater difference or a lower probability of misidentifying one mean for the other.
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When converted to a percent, the output of GZTTESTis the % chance that Data Set #1 is the same as Data Set #2. When converted to a percent the output of (l@ITEST) is the % chance that Data Set #l is different than Data Set #2. “Statistics tain.“lO
means never having
to say you’re
cer-
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Question A: For the raw data that produced Table II, @TEST is 99.9998%. This means that there is a 99.9998% chance that the IPA/hexane extraction data (right-hand column) is the same as 100%. Thus, there is a 99.9998% chance that the IPA extraction process did remove all the soil. The answer to question A is: there is a 99.9998% chance that the extraction test did remove all the soil. Question B: For the raw data that produced Table II, @ITEST is 0.134% or (l-@TTEST) is 87.6%. This means that there is an 87.6% chance that the cleaning process IPA extraction (center column) results are different than the validation (right-hand column) test results. Thus, the answer to question B is: there is only an 87.6% chance that the IPA extraction is a useful cleaning test. That’s not good enough. Another routine cleaning test is needed. Question C: For the raw data that produced Table I, (l-@ITEST) is 99.50% at 10 samples. This means that the 10 results that produced an average in the center column of 98.45% clean are different from the 10 results that produced an average in the righthand column of 98.50% clean. So, if we process 10 samples there is only a l/2%chance that our cleaning work is done to the 98.5% level of soil removal. “The solid wealth of insurance companies and the success of those who organize gambling are some indication of the profits to be derived from the efficient use of chance.“ll
January 2003
Generally, industrial work requires at least a 95% chance that something is or is not equal to something else. Recent emphasis on quality have raised that chance to 97 to 98% and in some cases to 99%. Please review the situation reported in Table I, the cleaning process won’t meet the goal of removing 98.5% of the soil. Sometimes it makes more sense to question the value of meeting a specification. Maybe one slightly less strict would not compromise part use and be achievable. Table III is Table I with the specification changed to 97.5%, an intermediate result at 6 samples. The added colum at right is (l@TTEST) for the individual results, which produced the averages in Table III. So now we know how many samples to process. If we can live with the slightly poorer quality of 97.5% soil removal, we need to take 6 samples to process to be 95% confident and 10 samples of being greater than 99% confident that 97.5% of the soil is removed. “Statistics are like a bikini. What they reveal suggestive, but what they conceal is vital.‘a
is
What can we learn from these exercises in addition and subtraction? 1. We can better know something if we measure it more often. Obviously, if we measure something more often than we need to, we waste the cost of doing so. (Note: Measuring the cleanliness of 25 parts in
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25 separate tests does not produce the same certainty of knowledge as measuring the cleanliness of 25 parts once (assuming we have a balance that can measure the weight of 25 parts to 0.01 mg). The latter is only 1 test, though it may be one with less error.) 2. We often use the average (statisticians use the word mean) of individual cleanliness measurements to collect the information from a series of cleaning tests. 3. In cleaning, we’ll find that much of our time in managing information is spent determining if one average (mean) is different from the average of another kind of measurements. Averages (means) are compared using what statisticians call the “t-test” or the “Student t-test.“13 “What’s one and one and one and one and one and one and one and one and one and one and one and one? ‘I don’t know’said Alice. ‘I lost count.“‘She can’t do addition.' said the Red Queen.“14 So the answer to Question 1 (how do I tell which parts are clean?) is to: 1. Identify your goal for cleanliness
and how cer-
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tain you want to be of meeting that goal. That’s the major part of experimental design. 2. Identify a laboratory process that you are certain will remove all soil (in this case something other than the IPA extraction). 3. Identify a repeatable test to measure soil content of parts (part weight to 0.01 mg in this case) 4. Take a small number of supposedly clean parts. Take 5 parts unless you have a better choice. Perform the soil content test and then the laboratory cleaning process with each part. Calculate the average (mean) of this cleanliness data as we did in Table I. “By a small piece.“15
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5. Use the t-test [(l-TTEST) actually] in your spreadsheet to determine the chance that your cleanliness measurements are different than your cleanliness goal, as we did in Table III. 6. Process a few more samples if you are not meeting your goal of certaintly. 7. Consider reducing the cleanliness goal if the cost of testing exceeds your limits.
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“Consistency requires you to be as ignorant today as you were a year ago.“16 And the answer to Question 2 (how do I know if my cleanliness data are meaningful) is to: 1. Review the results of 6 and 7 above. a. If you reduce the cleanliness goal to a low level so that parts are failing in customer’s operation, your cleanliness goal is meaningless to the use of your parts. This exchange of information is usually done by your marketing department (who control the use of your products in meeting the needs of customers) and your production department (who are responsible for making the product). b. If your confidence of meeting your cleanliness specification is so low that your part reject rate makes the production unprofitable, your level of certainty is meaningless. This exchange of information is usually done by the marketing (who are also responsible for profitability) and your production departments. 2. If you don’t have a cleanliness goal that meets customer needs and a certainty of meeting it
that meets profitability requirements, your cleaning process is meaningless. You should update or replace it. “An expert is a man who has made all the mistakes, which can be made, in a very narrow field.“17 We’ll answer Questions 3 and 4 in the March 2003 column. INTERESTING
NEW STUFF
In the last Cleaning Times, we wrote about the EPA’s SNAP program. Seemingly, within minutes of the column’s completion, a new decision was published in the Federal Register that has some impact on surface cleaning of particles from metal surfaces. This decision is interesting because it shows that the chronological flow of environmental affairs is not always toward environmental management. The manufacturer of HCFC 225 ca/cb (Asahi Glass) supplied new toxicity data based on recent studies. EPA toxicologists considered it, and the EPA supported the manufacturer’s increase of 8-hr time weighted average to 100 ppm. When the product was introduced, around 1994, the TWA was 25 ppm.
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SOME RANDOM
QUESTIONS
Business is lousy right now in the cleaning industries. This is a great time to take a quotation from a supplier and offer then approximately % of the proposed amount. They just might take it. A down market is always a good time to buy. Do your ferrous parts rust after aqueous cleaning? Does the rust inhibitor that you apply cost too much, require additional cleaning, discolor your parts, or make them sticky? Consider one of the dry blast cleaning processes. They bring a different balance of advantages and disadvantages. Is your process for cleaning aluminum performing properly? It is not if the pH is not slight basic. A good target value OS9.0 vs 12+ for steel. If you are still using trichloroethane, are you operating legally? Sure. You can buy imported material, at a high price, as long as you pay the excise tax on it. REFERENCES
Adams, D., “Life, the Universe,
and Everything,” Ballantine Books, New York, 1996 2. Students beware! These articles are not a substitute for courses in statistics. These articles teach how to manage cleaning work using designed experiments and statistical methods. 1.
3. Adams, C., “The Straight Dope,” (http://www.straightdope.com) 4. Adams, D. and M. Carwardine, “Last Chance to See,” Ballantine Books, New York 5. Babbage, Charles 6. Bacon, F., Novum Organum; 1620 7. http://www.graphpad.com/quickcalcs/ttestl.cfm, http://www.bio.Miami.edu/rob/Students_t.html, http:/lwww.stat.sc.edulwebstat/version2.0/ 8. Hays, W.L., “Statistics,” pp. 319-323, Holt, Rinehart and Winston, New York; 1963 9. Adair, R., on his fee for extinguishing oil well fires after the Gulf War 10. Anonymous 11. deBono, E. 12. Levenstein, A. 13. The name Student-test is derived from the pen name of the man (W. Gossett) who developed the test. It has nothing to do with the popularity of this test in introductory courses. His employer (a brewery-the ultimate dream job of every cleaning professional!) had regulations concerning trade secrets that prevented him from publishing his discovery, but in light of the importance of the t distribution, Gossett was allowed to publish under the pseudonym “Student.” 14. Carroll, L., “Through the Looking Glass;” 1872 15. Cervantes (Miguel de Cervantes Saavedra) 16. Berfenson, B., Notebook; 1892 17. Bohr, N.H.D. MF
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