AMERICAN 0,01Eftkiii_714V4iTy cowl-Rix

CHAIR'S MESSAGE by Conrad Fung

How was your summer? I served on a jury for a rather long trial. It was a grat-ifying experience. Statistical principles were in action everywhere, from my being randomly selected by a computer, to the exhaustive questioning of expert witnesses on whether events in the case were surprising or commonplace (you got it—special causes or common causes). While locked up for deliberation, we used graphical dis-plays on the blackboard to understand the variation in our opinions. The graphs showed at a glance where every juror was coming from, and helped us ultimately to reach agreement.

Statistics and due process go together. Understanding variation and common causes is crucial to responsible decision-making. Even the question of "reasonable doubt" raises a statistical issue—is it one in a hundred? One in a thousand? A hat tip to John Gurland at UW for asking this.

Statistical thinking is natural! Everyone does it all the time in everyday life. So why does it seem so novel to apply it in our jobs? I think my jury experience holds part of an answer to this. Intentionally chosen at ran-dom to assure a diversity of backgrounds, our group nat-urally had a diversity of personalities—including a handful of dominant executive types, and a few who were hesitant in the extreme to offer any opinion at all. But an incredible transformation took place in the jury room. Everyone embraced statistical approaches to sum-marizing and displaying information (of course we didn't call it statistics—the word carries a lot of baggage, as Ron Snee says). The outspoken characters accepted a round-robin style of discussion, and the unassertive members became equally as vocal as the others.

Democracy worked in the sheltered world of our jury room, I am convinced, because of a fortunate conjunction of two essential things: (1) we were equally empowered, and (2) we had data. Legitimized by an external authori-ty to take responsibility, even the quietest members said their piece. Armed with no more power than anyone else, the dominant characters managed to set aside personal agendas and acknowledged the higher task of making a responsible decision. Facing down an endless parade of

graphs on the blackboard, we worked from facts rather than emotion. Data as equalizer! What a concept.

As to why statistical thinking doesn't happen more often in our jobs, a quote from one of my students' home-work papers explains a lot (and fits my jury theory): "I talked to an engineer who works for a major manufac-turer that claims to be using the Total Quality approach. The engineer was told by his manager that he relied too much on numbers, and needed to use his gut instinct more often." The requirement for equal empowerment went out the window in this incident, and the data went out with it. Another student's remark is telling too: "It is sometimes amazing how slowly such critical issues spread through American society. I have no doubt that 80% of all Americans could identify Bart Simpson, but who is this Deming fellow?" Such wisdom from young students. Thanks to John Hallinan and Dave Hasseler, respectively.

My time on the jury was a life-affirming experience. Maybe our group was lucky. But I have come away dou-bly impressed by the power of collective decision making.

In the Statistics Division Council, we endeavor to work collectively as much as possible, with as much input from Division members as we can get. The mem-bership survey mentioned in the summer Newsletter is now well underway. Its outcomes will provide vital direc-tion to our future efforts. We'll publish the results in the next Newsletter.

I want to close by thanking a few Division members who work tremendously hard throughout the year to organize sessions at the Annual Quality Congress and the Fall Technical Conference, our main "in-person" opportunities to serve the Society. Rick Schleusener did a yeoman's job as the Division's 1991 AQC Program Representative. Greg Gruska has been working hard all summer to organize the Division's 1992 AQC sessions. Andy Palm's sure hand helped forge 1991's excellent FTC program. And I want to welcome Ralph St. John as Statistics Division's program representative for the 1992 and 1993 FTC's.

All of our officers, council members, regional coun-cilors, and committee members are volunteers who com-mit tremendous personal energy to the success of the Division. As ever, I am grateful for your help.

LETTERS TO THE EDITOR Dear Ms. Baxter,

We are writing in regard to the mini paper "STOP LIGHT CON-TROL - Revisited" by Gruska and Heaphy that appeared in the sum-

ASQC STATISTICS DIVISION OFFICERS

Chair Conrad A. Fung Center for Quality and Productivity Improvement

University of Wisconsin WARF/1109B 610 Walnut Street Madison, WI 53705 (608) 263-2652

Chair-Elect Joseph G. Voelkel Rochester Inst. of Technology Center for Quality and Applied Statistics 1 Lomb Memorial Dr., Bldg.18 P.O. Box 9887 Rochester, NY 14623-0887 (716) 475-2231

Secretary Galen C. Britz 3M Consumer Products Plant Highway #22 South Hutchinson, MN 55350 (612) 234-4000, Ext. 1462

Treasurer Richard A. Lewis Monsanto Chemical Company 800 N. Lindbergh Boulevard St. Louis, MO 63167

(314) 694-7735

MISSION • Promote Statistical Thinking for quality and productivity improvement. • Serve ASQC, business and industry, academia, and govern-ment as a resource for effective use of statistical methods for quality and productivity improvement. • Provide a focal point within

ASQC for problem-driven devel-opment and effective use of new statistical methods. • Support the growth and devel-opment of Division members.

mer issue of the Statistics Division Newsletter. We feel that this paper has no place in a newsletter whose mission statement is to foster "effec-tive use of statistical methods for quality and productivity".

This paper represents a tool that is outmoded and long since aban-doned in favor of the more appropri-ate technology of control charts. Let us examine just a few of the miscon-ceptions within this paper.

First, the automobile companies correctly do not want control meth-ods based on tolerances (specifica-tion limits). Attribute control charts are derived from statistical distribu-tions. The automobile companies insist on control limits based on sta-tistical data NOT engineering speci-fications. This has nothing to do with whether the data is of a vari-able or attribute nature. Statistical limits are a prerequisite for distin-guishing between common and spe-cial cause variation.

Second, the example illustrating the process distribution with Cpk 2 shows warning and stop limits for areas based on the distribution. A value that occurs in the warning area or even the stop area is NOT any indication of a special cause. These ideas and concepts are highly misleading and will lead to many type 1 errors (tampering).

Finally, the use of double sam-pling procedures reinforce the con-cept of inspection tables ( in a zone or out of a zone). Drawing two pieces of out of five in the green zone is luck not statistical control.

These three examples do not cover all of the misconceptions in this article, but should have been sufficient to have curtailed its publi-cation in this newsletter. In fact, we see no useful application of the stop-light concept and any benefit is far outweighed by the dangers. Eileen Beachell Statistical Consultant Marilyn Monda Statistical Consultant

RESPONSE: Gregory Gruska and Maureen

Heaphy The writers of the letter have two

major concerns: (1) the appropriate-

ness of material for this newsletter; and (2) technical concepts addrer in the paper. Let us discuss eacL these separately.

(1) The Statistics Division Newsletter is a major communica-tions channel within the division. Since the majority of Statistics Division members are unable to attend division meetings and func-tion, the newsletter keeps them apprised of what the Division and its officers and members are doing. In addition to this, the newsletter also supports the Division's Mission (see page 2) by including short arti-cles that "promote statistical think-ing ... and aid in the professional growth and development of division members." If an article gets mem-bers to think a little more about the tools they are using or gain addi-tional insight into statistical theory then the article was successful. Controversy is not shied away from and neither "political correctness" nor popularity a prerequisite. Control charts were considered "old and outmoded" tools in the 1960'^ and 1970's - "How could th know?". This did not stop them resurgence in the 1980's. We need to have an open mind and understand the strengths and weaknesses of all the tools available to us.

(2-1) With the move to base the decision criteria of control methods on the process not the tolerance, many "traditional" uses of statistical

Continued on next page

EDITOR'S CORNER Deadline for the Winter Issue is 30, November, 1991. Send all letters EXCEPT FOR CHANGE OF ADDRESS to: Nancy Baxter Thomas J. Lipton Co. 800 Sylvan Avenue C-2I0 Englewood Cliffs, NJ 07632

Communications regarding change of address should be sent to ASQC. This will change the address for all publications you receive from ASQC including the newsletter. You can handle this by phone (414) 272-8575 or (800) 248-1946.

PAGE 2

STATISTICS DIVISION NEWSLETTER

FALL, 1991

tools are no longer considered acceptable. The paper took one such tool, stoplight control, and "updated" it to a tool based on process perfor-mance. With this change, the tech-nique also becomes a valid indicator of the occurrences of special causes.

In the Stoplight scenario, the probabilities depend on how we select the categories. If the cate-gories are determined as in the paper (1.5s increments from the pro-cess average) then the probability of getting a single part form a stable process in the red category is approximately 00.135%. The proba-bility of getting a part in a single yellow category is approximately 6.5% and, by pure chance, we will get a yellow once in 7-8 sampled parts (since we have two yellow cat-egories). The probability of getting two sampled parts in yellow cate-gories is 00.4225% (=.065*.065).

Consequently, a single sampled part in the red category or two or more sampled parts in the yellow category ARE indications that some-thing may have changed - a special cause is present.

(2-2) All sampling plans have both Type I (calling a good process bad) and Type II (calling a bad pro-cess good) errors. We could make the Type I error zero by always accepting the process - regardless of our analysis. This unfortunately would drive the Type II error (and Customer DlSsatisfaction)sky high. Alternately, we could make the Type II error effectively zero by having restrictive decision rules; but this leads to tampering. The focus should be to balance both of these errors to maximize value to the customer. This is where statisticians and the subject matter expert earn their money.

Traditionally, Type I error rates are taken to be in the 1% -5% range. The Average and Range charts have a very low false alarm (Type I) rate -00.27% - regardless of the sample size. But, they also have poor sensi-tivity (i.e. high miss rates - Type II error) for small shifts in the mean. It is recommended in the literature that if small shifts (<.5s) need to be detected, alternate approaches such as the Cusum, WA, or EWMA be used in place of the Average and Range charts.

The (2,3) stoplight plan given in

the paper has a false alarm rate of 2.38%; higher than the Average and Range charts but still "respectable". Correspondingly, it has better sensi-tivity to small shifts than an Average and Range chart of sample size 5. The ability to detect large shifts is virtually the same for both plans.Since the risk of making a wrong decision is part of any statis-tical technique, we must understand what these risks are and how they will impact the total process. It is only through full knowledge and understanding of statistical tools and techniques that we can assist industry, education, and govern-ment in the effective use of statis-tics.

(2-3) Finally, the use of sequen-tial sampling is a technique used to minimize the total number of sam-ples required to make a decision. If our process experienced a large shift, we would not need to measure a large sample to be certain some-thing changed. If our process has not changed (i.e. remained in statis-tical control) we do not want to mea-sure a lot of part to verify it. Instead we sample sequentially.

We start off by giving the process the benefit of the doubt - assume that it is in statistical control. If our first sample is consistent with this assumption, we say the process is still in statistical control. If we find a sample that is totally inconsistent with this assumption - a sample in the red category - we say we have proof that the process is out of sta-tistical control. If we find a sample that may or may not support our assumption, we take more sample; i.e. get more information. The num-ber of times we go through this cycle depend on economics and the risks we are willing to accept.

In conclusion, to encourage or dis-courage the use of a technique with-out understanding, without the ben-efit of profound knowledge is subop-timal in the long term. The reputa-tion of all statistical tools, control charts included, suffer from their misapplication, regardless of the motivation or intent. As members of the Statistics Division of ASQC we must always strive to "promote (cor-rect) statistical thinking for quality and productivity improvement".

Nancy, I have been disturbed more than

once by the Editor's Corner block. I have underlined the sentence of con-cern: "Neither I nor the printers are going to sort through over 14,000 label to find yours." Within the qual-ity philosophy we say - satisfy the customer. Sometimes that is not possible. When it is not possible you either say so, find an alternative or you get out of that business.

It appears that you are faced with the 1st alternative - not being able to comply. Fine, but the customer doesn't want to know your problems or your reasons why. I don't appreci-ate you making us (customer of yours) feel like we've inconvenienced you by asking for an address change. After all (as a previous edi-tor myself) that is part of your job. You do offer an alternative - contact ASQC. That is all that is necessary. Put yourself in the reader's shoes and read your block. It paints a pic-ture of you that I'm sure is not wor-thy!

My suggestion: drop the sentence and your customers will survive and do the right thing with their address changes.

Lisa Albitz Lisa,Thanks for the suggestion.

As you will notice, the Editor's Corner has been revised.

Dear Ms. Baxter, This is in response to your "Name

the Newsletter Contest" item in the Statistics Division Newsletter, Summer 1991, page 15. There is an unproved assumption here, namely, that the division members want a different name for the newsletter. Where is the data set supporting this idea?

Wouldn't it have made more sense to survey the membership on this point? Perhaps 75 percent would agree with me that the pre-sent name is just fine. It appears that the plan is to choose a new name from the responses of those who think that there should be a new name!

However, all is not lost. Why not proceed as follows. Screen the entries to yield the 10(?) best. Then present these to the membership along with the choice "no change in

Continued on next page

FALL. 1991

STATISTICS DIVISION NEWSLETTER

PAGE 3

New Technometrics Editor Manuscripts being submitted for the first time after this date should be submitted to Dr. Vardemar the following address:

Department of Statistics, 303 Snedecor Hall, Iowa State University, Ames, IA, 50010.

All previously submitted manuscripts will continue to be handled by the current Editor, Vijay Nair, through the end of 1992. Dr. Vardeman becomes Editor on January 1, 1993, and will then handle all manuscripts.

Steve Vardeman received his Ph.D. in Statistics from Michigan State University in 1975, and taught at Purdue University until 1981. Since then, he has been at Iowa State University, where he is currently Professor of Statistics and Industrial and Manufacturing Systems Engineering. Steve has done extensive teaching and con-sulting on statistical contributions in a wide variety of areas, and has published in journals that include Technometrics, Journal of Quality Technology, Journal of American Statistical Association, Annals Statistics, Journal of Statisti ■ Planning and Inference, and The American Statistician. He has coauthored a hook, Elementary Statistics (1982) and is currently working on a second book, Statistics for Engineering Problem Solving. He is a Fellow of the American Statistical Association, a Senior Member of the American Society for Quality Control, and member of the Institute of Mathematical Statistics.

Dr. Stephen B. Vardeman will be the next Editor of Technometrics. He will assume the position of Editor-Elect on January 1, 1992.

47TH CONFERENCE ON APPLIED STATISTICS Statistics Division will sponsor

two sessions at the 47th Conference on Applied Statistics. This confer-ence will be held December 16-18, 1991 at the Sands Hotel, Atlantic City, New Jersey. Anyone interest-ed in registration material can con-tact: Walter R. Young, Medical Research Division, American Cyanamid, Bldg. 60, Room 203, Pearl River, New York, 10965. (914) 732-3224.

Statistics Division Sponsored Sessions

Regression Analysis By Example Speaker: Professor Samprit

Chatterjee, New York University Principal Component Analysis

with Applications in Quality Control

Speaker: Dr. J. Edward Jackson, Consultant, Rochester, NY

LETTER FROM THE EDITOR

Dear Readers: The mail has been flowing in the

last 2 months. I have received over 125 submissions for the "Name the Newsletter Contest". Thanks to all those who sent along ideas or com-ments about the newsletter. We are just beginning to sort through the entries and plan to reach a decision by the next newsletter.

I have received several submis-sions for the Mini-paper column but I am still looking for submissions for the Basic Tools column. Is there a specific topic you would like to see presented?

You will notice the "This Quarter in JQT" column has taken on a new look. This column will now feature the table of contents for the latest issue of the Journal of Quality Technology.

As much as I enjoy being editor, I plan to move on to other things at the end of the term (July 1). I have found this position to be rewarding and an excellent opportunity for meeting people within ASQC. We are looking for someone who might be interested in serving as editor. A job description appears elsewhere in the newsletter. Please contact myself or one of the division officers if you are interested.

Nancy

Letters to the Editor Continued from 3

name", and ask them to vote. You would then be essentially fully pro-tected against people who carp, like

Yours truly, Lloyd S. Nelson Director of Statistical Methods Nashua Corporation

Lloyd,If we choose to keep the current name of the newsletter, we'll send you the $50.

CHANGE OF ADDRESS Please note the following changes

of address: "How To" Booklet Editor. Edward F. Mykytka Dept. of Operational Sciences Air Force Institute of Technology AFIT/ENS Wright Patterson AFB, OH 45433 (513) 255-3362 Please note the following change

of address for ASQC headquarters. ASQC P.O. Box 3005 Milwaukee, WI 53201-3005 (414) 272-8575 (800) 248-1946

Liaison with ASQC Divisions Joseph J. Pignatiello, Jr. • Texas A&M University Dept. of Engineering Zachary Engineering Center College Station, TX 77843 409-862-2081

Region 9 Councilor Carlos W. Moreno Ultramax Corporation 1251 Kemper Meadow Dr. #900 Cincinnati, OH 45240-1655 513-825-7794

PAGE 4

STATISTICS DIVISION NEWSLETTER FALL, 1991

O.1

14

Figure 1 Stem-and-leaf display for HOUSING: unit — 0.0001

L01-0.0019

5 -1144444 9 -11222 10 -111 14 -018888 22 -0177777777

(23) -0155555555555555544444444 35 -013333333333222222 19 -011111111100 9 01001111 3 01222

Figure 2

Histowas

-ss

HOUSING

Figure 3

st Homing vs MW Esther Roans Cavity limbo*

STATISTICAL GRAPHICS A GREAT TOOL-KIT Edward R. Hansen The Gillette Company, Boston, Mass.

Using any one of many available computer packages, it is possible to analyze data and prepare reports, using graphs to communicate the most important information. Graphs allow readers to understand relationships, data centering and variability very readily. Well-designed graphs contain tremen-dous amounts of information and our minds interpret such "pictures" very easily. But graphs are not a substitute for judgement and expe-rience; like any other tool they must be understood and used correctly. They are particularly useful in "exploratory data analysis," where one is in the initial stages of study-ing a problem, to help plan more formal experiments, etc. This exploratory process is like peeling an onion; as each layer is removed you gain more insight into the pro-cess factor(s). Using graphics, the accompanying tears as you peel the onion will be minimized.

Most current texts on statistical methods emphasize the value of using simple graphs and plots to get an overall view of the data, look for errors, outliers, non-normality, etc. We will see how to do this as we proceed.

I have used data from a plastic injection molding process on a char-acteristic, "Housing," to illustrate a graphical approach to data analysis and reporting. Our objective is to run experiments to judge the capa-bility of the process and to prepare a report with our conclusions and recommendations. Graphs are par-ticularly useful in this situation because of the complexity of the molding process due to the multiple sources of variation.

The first stage in our plan is to take a sample of 10 complete shots taken over one shift of production. (A "shot" is one piece from each cav-ity taken during one cycle of the molding press.) Figure 1 shows measurement data from this sample of the housing dimension, displayed as a "Stem-and-Lear diagram. (This technique is explained in the summer issue of the Statistics

Division Newsletter.) Two tentative conclusions can be drawn; one piece at -.0019 may be an "outlier," and the data looks distinctly bi-modal. We have peeled one layer from the onion. Figure 2 is a histogram of the same data so you can compare the two graphical approaches. My pref-erence is the Stem and Leaf dia-gram because it displays every number. The Histogram abbreviates the amount of information by using class intervals based on arbitrary criteria.

Next, let's use a general purpose tool called "stratification," in which we break down the data into levels or strata, to obtain a different per-spective. Fortunately, the data is classified by time of sampling and mold cavity number, two obvious ways of stratifying molding data.

A simple "Multi-Vari" plot gives a "snapshot" of the differences in dimensions of parts from the 8 cavi-ties and 10 shots as we can see from

Figure 3. Further deductions can be made from this chart. The possible outlier is from cavity 4, shot num-ber 9.

Cavity 4 output consistently runs well below the other cavities and cavity 8 is usually the highest. This fact explains the bi- modal appear-ance of the histogram and the Stem-and-Leaf Leaf diagram. Now we have peeled the "onion" down to a more useful level.

It is evident from Figure 3 that the averages of the 8 cavities varied somewhat, but the variability with-in each cavity was about the same. An idea of the variability over one shift of the process can be derived from this graph.

The dimensional variation of parts produced by a plastic molding process has two primary causes.

1. Variation between cavities, as we have seen in Figure 1. These dif-ferences should remain stable, as they are the result of the way the steel in the mold was cut and the mold/process design. This source of variation is visible as the differ-ences in the cavity averages. Thus each cavity is a "mini-process" with it's own average and variation.

2. Variations from cycle-to-cycle of the molding process. This is the result of many small changes in temperatures, pressures, timing and a whole host of other factors. This source of variation effects all cavities on each cycle, although not always in the same amount, due to possible interactions. This variation can be measured by changes in the averages of complete shots of the 8 cavities.

FALL, 1991

STATISTICS DIVISION NEWSLETTER PAGE 5

Figure 5

Notched Bee Plot-Clukre Rod

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Figure 7 Notched Bet Rot-Fleeemcde

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Figure 4 is a very useful type of graph, helpful in stratification, called a "Box Plot," used here to show the variability between cavi-ties explained in #1. Each cavity has its own box, based on the 10 samples measured for the cavity. The explanations for the features of this type of plot are as follows:

1. The center line in the box is at the median value, which splits the ordered data values in half.

2. The rectangular box ends are placed at the 25%ile and the 75%ile of the measurements, called the "Interquartile Range" (IQR), thus splitting each half in half again.

3. The two lines from the box, called "whiskers," extend out to a distance of 1.5 times the IQR beyond the box ends, to the "fence."

4. Points marked with an "*" are beyond the fences and those marked with an "o" are beyond 3 times the IQR and show probable outliers. A "well-behaved" (normal) distribu-tion would have all points inside the fences.

The Box Plot shows at least two and possibly five outliers, which need further investigation. Since all ten shots had been saved, it was possible to recheck these pieces. Three of the outliers were errors in recording and two were measure-ment errors. Another layer has been peeled away.

You will note the analysis so far has calculated no averages, stan-dard deviations or other formal statistics. It is my experience that one should always review the raw data from a skeptical viewpoint using graphs, common sense and process knowledge, before one pro-ceeds to more formal methods. There may be errors or other prob-lems that require "purification" of the data before continuing.

Figure 5 is a "Notched" Box Plot of the data after purification. The notches around the medians allow us to make multiple comparisons between cavities. If the notches of any two cavities do not overlap, we can be approximately 95% confident that the medians are different. We still have one outlier "*," but this one was not a measurement or recording error.

Now we can safely confront a potentially more costly and difficult question. What shall we do about cavities 4 and 8? Both medians are away from the target of -.0004 in., and also from the other cavities.

Let us assume that the decision is to rework these two cavities to bring them closer to target. After the rework, a further sampling of 10 shots is selected over one shift. Figure 6 is a Notched Box Plot that shows the result of this action. Notice that even after reworking cavities 4 and 8 we still have signif-icant differences between cavities, but the range of these differences is much less. Assuming a specification of -.0004 .001, the capability of the process may t acceptable.

To gain further assurance, we resampled the process with 10 com-plete shots randomly taken over a

one week period; Figure 7 shows the result. This confirms the earlier sampling. We find no outliers and the notches overlap on all 10 sarr pies. The process appears well c( tered and capable of meeting cus-tomer requirements as reflected in the specifications.

In investigations of this type, it is important to determine if the data can he classified as "normally dis- tributed," since the use of most sta-tistical techniques requires normal- ity. For instance, if we wanted to make predictions about the capabil-ity of the process with probability limits, normality would be required. Figure 8 is a "Normal Probabili' Plot" that shows a graphic, approach to an evaluation of the normality of the data from the sam-ple used in Figure 7. A normal prob-ability plot is made as follows:

1. The data is ordered and for each point an associated percentile value is calculated.

2. The data is plotted against the Housing dimension on the Y-axis and the cumulative normal per-centiles on the X-axis.

3. Some PC programs convert the percentiles in #1 above to Z values and then plot them against a linear axis of Z values ranging from -3 to +3. The end result is the same in that a straight line fit indicates nor-mality.

Fortunately, PC statistics soft-ware does all this heavy labor with a click of a mouse. If a straight line fits the data "reasonably well," then the we judge the data to be normal- ly distributed. From a graphical standpoint, this approach is superi-or to superimposing a normal curve to a histogram. The eye can judi the fit of the cumulative distribu tion of the data to a straight line more accurately than the bars of a

PAGE 6

STATISTICS DIVISION NEWSLETTER

FALL, 1991

1111 I 111111111111 I 11111111111 I

Figure 8

Cumulative Percent

Morsel Probability Plot a A.M.,

•

1

histogram to a curved line.

Unfortunately, our data distribu-tion seems to have heavy tails, and is not normally distributed. This is not surprising, considering that we have only eight cavities and one high or low would result in 1/8th of the values high or low, giving us the heavy tails. This problem could exist in any multi-stream process, in which the number of streams is small (less than 25).

Another problem which con-tributes to the lack of normality, is that our measurement procedure resolution (.0001in.) is large com-pared to the spread of the data (.0008in.). This raises the question of whether our distribution is "con-tinuous." While it would have been "cleaner" if our work had resulted in a nice, normal distribution, this is more like real life "in the trenches."

I hope our readers will not be too disappointed, but the techniques used here are valid in any case.

More work would have to be done on the measurement system and on "rationalizing" the cavities to center them if we needed to assure nor-mality. Future decisions about the process regarding control proce-dures and estimates of output capa-bility must consider these factors, so clearly shown by Figure 8.

Figure 7 shows a process which meets customer requirements; Figure 8 says "problem!" What should be done? This is a typical question which must be answered. Graphs can help to illustrate the problems; people must make deci-sions.

Results of analysis of data from the study of multi-stream processes, such as this example, are difficult to explain in reports. A table of statis-tics, cavity numbers, percents out of specification, becomes almost over-whelmingly complex, whereas graphs such as Figures 6, 7 and 8 portray the important information very effectively. These three graphs, with appropriate commentary, could form the basis for the final report with conclusions and recom-mendations.

This brief example has shown only a few of the many powerful graphical techniques available. In

recent years, graphical approaches to statistical data analysis and reporting have come to the fore-front, spurred on by the many PC software packages that are avail-able to do the "grunt work." I hope all our readers use these techniques to support their analyses.

Execustat (Copyright 1990 Strategy Plus, Inc.) and SYSTAT (Copyright 1990 SYSTAT Inc.) were used to create the graphs used in this study.

Reference Chambers, J.M., Cleveland, W.S.,

Kleiner, B., and Tukey, P.A., Graphical Methods for Data Analysis, Duxbury Press, Boston, Ma., 1983.

Call for Videotape Reviewers Quality Press is actively seek-

ing authors who might have insight into quality as it relates the health care industry; trans-portation; food, drug, and cosmetic industries; retail sales, utilities and other service industries. For more information, contact Deborah Dunlap, Acquisitions Assistant, Quality Press, American Society for Quality Control, P.O. Box 3005, Milwaukee, WI 53201-9488 or call 414-272-8575, extension 7292. '

QA DAY AT ARGONNE NATIONAL LABORATORIES Quality Assurance Day at

Argonne National Laboratories will take place in April, 1992. Statistics Division sponsors a session at this conference. Basic tools or applied industrial papers are needed for this session. Presentations should be 45 minutes in length. If you are interested, contact Jed Heyes (708) 291-4229, FAX (708) 291-4280.

STATISTICS DIVISION MEMBERS - OPPORTUNITY TO UPGRADE STATUS TO SENIOR MEMBER

If you are currently an ASQC member who meets the following eligi-bility requirements you should apply for Senior Member status. Eligible Members must:

1. Be at least 30 years of age, and actively involved in the quality profession for at least 10 years. Graduation in an approved engineering science, mathematics, or statistics curriculum is considered the equiva-lent of 4 years of professional experience.

and, 2. Qualify under one or more of the following: a. be responsible for important engineering or inspection work involv-

ing quality control for at least 2 years. b. be an instructor of quality control, engineering or statistical

methodologies as applied to quality control for at least 2 years; should be capable of teaching a variety of courses in the quality field.

c. be a professional engineer or member of a technical society of national status in any country for which the qualifications require a standing equivalent to that required for a senior member of ASQC.

All eligible Members interested in upgrading their membership sta-tus should contact the Statistics Division Examining Chair, Bob Perry, at Grand Metropolitan Technology Center, 330 University Avenue S.E., Minneapolis, MN 55414, or at (612) 330-8916.

FALL, 1991

STATISTICS DIVISION NEWSLETTER

PAGE 7

THIS QUARTER IN TECHNOMETRICS The first two articles in the

November 1991 issue were present-ed orally at the Technometrics ses-sion of the 35th Annual Fall Technical Conference held in Lexington,Kentucky, October 24-25, 1991.

The first article is "Using Spatial Considerations in the Analysis of Experiments" by Martin 0. Grondona and Noel Cressie. Classical experimental design is based on the three concepts of ran-domization, blocking, and replica-tion. Randomization attempts to neutralize the effects of (spatial) correlation and yields valid tests for the hypothesis of equal treatment effects. More recently, attempts have been made to use the spatial location of treatment effects to improve the efficiencies of estima-

STATISTICS DIVISION NEWSLETTER EDITOR

JOB DESCRIPTION A new newsletter editor is being

sought. Below are the qualifications and responsibilities. If you are interested please contact the editor or one of the Division officers. Job Qualifications:

* Must be a member of the Statistics Division and a Regular member of ASQC.

* Must be able to commit the time and resources to edit a newsletter once per quarter.

* Must have good spelling, math, and grammatical skills. Responsibilities of Job:

* Receive submissions for the newsletter.

* Remind regular contributors (e.g. Chair) of deadlines for submis-sion.

* Identify possibilities for submis-sion and solicit.

* Proofread all submissions and correct spelling, punctuation, and glaring grammatical errors.

* Organize submissions and coor-dinate logistics with printer.

* Proofread typeset copy and make corrections.

* Participate in the activities of the Statistics Division Council.

There is no specified term of office, although editors should expect to serve at least two years (eight issues).

tors of treatment contrasts. This article shows that a simple, flexible spatial-modeling approach to the analysis of industrial experiments (for example, in wafer fabrication) can yield more efficient estimators of the treatment contrasts than the classical approach. The analysis is based on empirical generalized least squares estimation, in which the spatial- dependence parameters are estimated from resistantly detrend-ed response data.

The second article is "Probability Limits on Outgoing Quality for Continuous Sampling Plans" by Lisa M. McShane and Bruce W. Trumbull. Various quality-control sampling plans have been proposed for monitoring continuous produc-tion processes. This article consid-ers the continuous plan (CSP-1) developed by Dodge (1943). This plan has been incorporated into MIL- STD-1235B and has found many applications. Various modifi-cations and elaboration of CSP-1 have been proposed, yet the plan remains popular perhaps because its simplicity. This article investi-

October, 1991 Journal of Quality Technology ARTICLES Prediction Intervals for Some

Discrete Distributions - Jagdish K. Patel and V.A. Samaranayake

An Optimal Design of CUSUM Quality Control Charts -F.F. Gan

SPC in Low-Volume Manufactur-ing: A Case Study -George F. Koons and Jeffery J. Luner

SPC Q Charts for a Poisson Para-meter X : Short or Long Runs -Charles P. Quesenberry

Reliability Test Plans for One-Shot Devices Based on Repeated Samples - Lee J. Bain and Max Engelhardt

Economic Selection of the Mean and Upper Limit for a Canning Problem - Robert L. Schmidt and Phillip E. Pfeifer

Determining the Optimal Process Mean and Screening Limits for Packages Subject to Compliance Testing -Brian J. Melloy

gates the performance of CSP-1 when production run lengths short or moderate or when input process is not iid Bernoulli. For finite run lengths, methods are presented for computing upper and lower percentage points (probability limits) for the distributions of the outgoing quality and fraction inspected when the input process is Markov. Both rectifying and non-rectifying inspection are considered. Particular attention is paid to the special case of iid Bernoulli assump-tions, including Dodge's average outgoing quality limit (AOQL) for the iid case, and AOQL Markov input, and unrestricted AOQL val-ues. These limits are proposed as new performance measures, intend-ed to supplement the tables in MIL-STD-1235B for use in selecting CSP-1 plans. The article also dis-cusses the problem of interval esti-mation of the incoming and outgo-ing quality from CSP-1 inspection data.

Vijayan N. Nair, Editor

Grubbs-Type Estimators for Reproducibility Variances in an Interlaboratory Test Study - Tilmann Deutler

Control Chart Based on the Hodges-Lehmann Estimator -James A. Alloway, Jr. and M. Raghavachari

DEPARTMENTS Computer Programs FORTRAN Programming Tech-

niques - Ronald Crosier Calculation of Average Run Lengths

for Zone Control Charts with Specified Zone Scores - Chun Jin and Robert B. Davis

Computing the Percentage Points of the Run Length Distribution of an Exponentially Weighted Moving Average Control Chart -F.F. Gan

Technical Aids Additional Critical Values fc

Multiple Comparisons by Clusti Analysis - Lloyd S. Nelson

THIS QUARTER -1N JOT,

PAGE 8 STATISTICS DIVISION NEWSLE11ER FALL, 1991

MIN PAPER

SHAPE-FINDER BOX PLOTS Gordon Conference

Grants for Beginning Researchers

Through a generous donation from the Statistics Division the 1991 Gordon Research Conference in Chemistry and Chemical Engineering was able to provide grants to pay for the registration, lodging, and food for six beginning researchers. The winners of this year's competition were

*Benjamin M. Adams, Assistant Professor, Department of Math Science and Statistics, University of Alabama

*Nadine E. Chase, Graduate Student, Department of Civil Engineering and Operations Research, Princeton University

*Dennis Lin, Assistant Professor, Department of Statistics, University of Tennessee

*Frederik Lindgren, Graduate Student, Department of Organic Chemistry, University of Umea (Sweden)

*Cynthia Lowry, Assistant Professor, Department of Decision Sciences, Texas Christian University

*Derrick Rollins, Assistant Professor, Departments of Chemical Engineering and Statistics, Iowa State University

A Call for Papers has been issued for the 36th Annual Fall Technical Conference to be held October 8-9, 1992 in Philadelphia, PA. The con-ference is co-sponsored by the Chemical and Process Industries Division and Statistics Division of the American Society for Quality Control, and the Section on Physical and Engineering Sciences of the American Statistical Association. The theme for the 1992 conference is "Competitiveness Through Continuous Improvement: A Nation Waking Up".

Applied or expository papers are needed for Statistics, Quality Control, and Tutorial/Case Study sessions. Statistics papers should be

Muhammad Aslam Department of Statistics

University of Karachi, Pakistan

ABSTRACT Since it's introduction by Tukey

(1977), Exploratory Data Analysis (EDA) has attracted a great deal of attention. The authors propose a new modification to the box plot indicating degree of "peakedness" via an estimate of Kurtosis. This estimate becomes a single line added to the interior of the box. The position of the line relative to the theoretical normal (location of the whiskers at the midpoint), repre-sents degree of Kurtosis.

KEYWORDS: Exploratory Data Analysis, Box

Plot, Shape-Finder Box Plot, Kurtosis, Percentiles.

INTRODUCTION Among recent trends in statis-

tics, Exploratory Data Analysis (EDA) has attracted a great deal of attention. Tukey (1977) first pro-posed the use of EDA for visual data displays, and for preliminary

at or below the level of Technometrics, while Quality Control and Tutorial/Case Study papers should be at or below the level of Journal of Quality Technology.Please send the title, one-page abstract, and one-page outline of your paper by January 24, 1992 to Greg Piepel, Battelle-Northwest, P.O. Box 999, Richland, WA 99352. For more information contact any of the program chairs: Greg Piepel of the Section on Physical and Engineering Sciences (509-375-6911), Kymberly Hockman of the Chemical and Process Industries Division (302-999-6634), or Ralph St. John of the Statistics Division (419-372-8098).

Gerald B. Heyes Quality Assurance Department Rank Video Services America

Northbrook, Illinois

evaluation of data prior to subject-ing them to formal analyses. In par-ticular, both Stem-and-Leaf plots and Box-and-Whisker plots display the form of a data set, ie; whether it is skewed, symmetric, unimodal etc. These plots can also help detect clusters, and outliers. For construc-tion and review see Heyes (1985).

The literature records extensive studies on variations of Stem-and-Leaf and Box plots (Ahmed and Aslam 1988, Becketti and Gould 1987, Heyes 1988, Hunter 1988, McGill, Tukey and Larsen 1987). A new box plot modification is pro-posed here which provides addition-al information about the shape or "peakedness" of a data set via a graphic indicator of Kurtosis. The authors suggest the name Shape-Finder Box Plot for this modifica-tion_

THE SHAPE-FINDER BOX PLOT A modification of the convention-

al box-and-whisker plot, the shape-finder box plot is constructed by simply drawing an additional line within the box. The location of this line relative to the center of the box width where the whisker is normal-ly connected, provides a convenient visual indicator of kurtosis.

ESTIMATING KURTOSIS While there is considerable dis-

agreement in the literature regard-ing the definition, meaning and interpretation of Kurtosis, the pre-sent authors prefer the simple defi-nition of Moors. Moors (1986) argues that kurtosis is a measure of dispersion in the middle of the dis-tribution and concentration of observations in the tail of a distri-bution. The concentration in the middle of the distribution may be high or low, consequently the tails are sharp or heavy; hence the distri-

1992 FALL TECHNICAL CONFERENCE CALL FOR PAPERS

Anwer Khurshid Department of Statistics

University of Karachi, Pakistan

FALL, 1991 STATISTICS DIVISION NEWSLETTER PAGE 9

bution may be leptokurtic, mesokurtic or platykurtic respec-tively. Further, the authors have chosen a simple measure of kurtosis which is consistent with other box-plot measures. This measure, K is called the percentile coefficient of kurtosis and is given by:

K=((Q 3- Q 1)/ 2 )/(P9 0 - P1 0 ) where Q1 and Q3 are lower and upper quartiles, or by

K.(HS/2)/(P90-P10) where HS is the Hinge Spread to

be discussed later. P10 and P90 are the 10th and

90th percentiles respectively of the ordered data. A standard value of K=26.3% is obtained for the normal, mesokurtic distribution. Leptokurtic and platykurtic distri-butions obtain K values less than 26.3% or more than 26.3% respec-tively, as shown in Figure 1.

COMPUTING QUANTILES FIGURE 1

iv=

T 3

Box Plot Degrees of Kurtosis

To obtain the necessary hinges, percentiles and median the authors recommend using a stem-and-leaf plot as described in example 1_

EXAMPLE 1 Table 1 shows pulse rate mea-

surements from 45 students. 79 88 97 94 79 94 87 75 81 80 91 88 74 79 80 90 88 68 81 81 87 91 70 80 82 92 92 80 82 83 91 90 64 70 84 92 90 67 79 84 94 90 68 83 90

TABLE Table 2 displays the pulse rate

data in stem-and-leaf format using

double stems (ie: *60 =60 thru 64, while .60 =65 thru 69). Using the stern-and-leaf plot we find the val-ues corresponding to the "depth" of the measures of interest.

TABLE 2

The "depth" of a measure is given by formulas and computed as below. See Freund and Perles 1987 for the d(P) formula.

Sample size N=45

d(M)=Depth of Median =(N+1)/2 =46/2 =23

d(H)=Depth of Hinges .(d(M)+1)/2 =24/2 =12

d(P)=Depth of Percentiles =1+((N-1)/10) =5.4

The values corresponding to the depth of the measures are obtained by counting inward from the largest (or smallest) values in the ordered data. For instance the lower Hinge is located by counting in 12 values from and including, the smallest observa-tion. The 12th value of 79 is easily located from the stem-and-leaf plot in table 2. Table 3 summarizes the depths and corresponding values for the measures in example 1.

TABLE 3

BOX PLOT CONSTRUCTION First draw a simple box plot with

length equal to the interquartile range, IQR =(Q3-Q1 ) or the Hinge Spread HS. The whiskers extend to the highest and lowest values, and

are located outside the box attached to the center. A median line is added inside the box as in Figure 2. Figure 3 shows a box plot of the stu, dent pulse rate data, using hing rather than quartiles.

THE SHAPE-FINDER BOX PLOT MODIFICATION

For the shape finder box plot we will assume a standard K value of 26.3% for the location of the whiskers at the ends of the box. Using Moors' estimate, for example 1 kurtosis is computed as:

K=((UpperH-LowerH)

l2)/(1390-P10) K.(90-79)/2/(92-71.6)

K.(11J2) /20.4 = 5.5/20.4 =26.96% Having calculated K, it may now

be used to create a shape-finder box plot for the student pulse rates. Scaling the end of the box plot enables us to indicate the "per-centile coefficient of Kurtosis" on the box, by comparing it to the theo-retical normal distribution at the whiskers where K=26.3%.

The method of scaling to indicate percentiles on a box plot is derived from Cleveland (1985). First, assign a the standard value of 26.3% to the

location on the x-axis corresponding to the lower whisker location. Next assign an x value of 0 to the side of the box to the left of the whisker Finally the value of 52.6% i assigned to the x location corre-sponding to the right side of the

07

97

97

77

Stem Ordered Leaves No. Leaves Cum. Total

*60 4 1 1 .60 7 8 8 3 4 *70 0 4 2 6 .70 5 8 9 9 9 9 6 12 *80 0 0 0 0 1 1 1 2 2 3 3 4 4 13 25 .80 7 7 8 8 8 .5 30 *90 0 0 0 0 0 1 1 1 2 2 2 4 4 4 14 44 .90 7 1 '45

Measure Depth Value Plot Feature

Median (M) 23 83 Median Line Hinges (H) 12 79,90 Box Length Min, Max 1 64,97 Whisker Ends Percentiles (P) 5.4 71.6,92

PAGE 10

STATISTICS DIVISION NEWSLETTER FALL, 1991

I . 104

• ' a% 213 ci6

. 94

_ 84

. 74

64

BOX-and-WHISKER PLOT

FIGURE 2

box. By this method each side of the box is 26.3% units from the central whisker. For computed values of K greater than 52.6%, simply continue the scale upwards in major incre-ments of 26.3% truncated at the ending value of 100%.

From table 3, the subsequent cal-culation of K, and the x- axis scal-ing, construction of the shape-finder box plot is illustrated in figure 4. In this example, other box plot fea-tures (fences, confidence envelopes etc.), have been omitted to draw attention to the location of the K value line.

F IGURE 4

SHAPE I NOCE ROD/ PECATION

Figure 4 displays the following obvious properties:

FALL, 1991

I)

II)

to

III)

IV)

to

104

94

54

74

64

line

two

the

to be

plot

American Statistician, Vol 40, pp. 283-284. Tukey, J.W. 1977. Exploratory Data

r

Analysis. Addison-Wesley, Reading, MA.

THE AUTHORS Gerald B. Heyes is a senior mem-

ber of the American Society for Quality Control, a C.Q.E., and past member of the American Chemical Society and the American Management Association. Experi-enced in chemical, aerospace and electronics industries, he is Senior Q. A. Engineer for Rank Video Service America, in Northbrook, IL. Mr. Heyes has published numerous articles dealing with the use of statistics in industry and taught classes in SPC and process trou-bleshooting. "Jed" earned a BA (hon-ors) in Biology from Blackburn College in Carlinville, IL.

Muhammad Aslam is a lecturer in the Department of Statistics, University of Karachi, Pakistan. He holds a Masters degree in Statistics from the University of Karachi.

Anwer Khurshid is an Assistant Professor in the Department of Statistics, University of Karachi and a member of the International Association for Official Statistics, ISI, Netherlands.

ADDENDUM The main idea, that of modifying a

box plot with Moor's estimated K value as a line, was presented to Jed Heyes some time ago by co-authors Aslam and Khurshid. Recognizing that the central theme may have some merit, Heyes responded to their request for assis-tance in developing it thus far. Jed would be delighted to hear from read-ers who have comments or suggestions for improvement. Some already made include: (1) Determine the operating characteristics of this K statistic rela-tive to the classic B2 measure. (2) Find the optimum scaling for the ends of the box as opposed to the most convenient and determine it's sensitivity to K val-ues. (3) Alternatively, scale the ends of the box based on computed K values for distributions at the extremes of Kurtosis, ie; the most common lep-tokurtic and platykurtic. (What are these?) (4) Standardize this unusual K value of 26.3% by dividing it by 26.3% thus the standard normal would have a standardized K value of 1.0. (5) How useful is this as a tool?

Editor

relative

whiskers- coefficient

sample

inner/outer

almost

REFERENCES

Digidot

The Median - Location

- Also known There is a - Location the hinges - Relative

of There

data - No values

The data

- Location whiskers - shape of

Ahmed, E. and

STUDS

to X-axis

Confirmed

fences

mesokurtic

Plot. unpublished

FIGURE 3 ME PULSE RAPES

value is of internal

scale from

slight positive of median (box ends)

lengths

skewness are no outliers

exceeding

shape

of K value

M. Aslam

S. and Box Plots:

the stem-and-leaf

about 83 median

Table 3 skew

line relative

of the via computed -0.583

in

computed

appears

line relative

1988. Extended manuscript. W. Gould 1983.

A Note."The "Rangefinder Becketti,

American Statistician, Cleveland, W.S.

Graphing Data. Wadsworth

Vol 1985.

B.M. of

"The 12,

"The

Statistician,

Newsletter

41, p. 149. The Elements 9f

Pub. Monterey,

Perles, 1987. "A Ungrouped Data."

Vol 41, pp. 200-

Box Plot." Quality

CA. pp. 127-144. Freund, J.E.

New Look at Quartiles The American

and

1985.

1988.

202. Heyes, G.B.

Progress, Vol XVIII,No pp. 12-17. Ghost Box

Vol 8, Plot."

No 12,

The 54.

The

Heyes, G.B. ASQC Stat. Div. pp. 10-11.

Hunter, J.S. 1988. "The American Statistician, Vol

Digidot Plot." 42, No. 1, p. and W.A. Larsen.

Box Plots." 32, pp. 12-16. "The Meaning

McGill, R., Tukey, J.W. 1978. "Variations of American Statistician, Vol

of The

Moors, J.J.A. 1986. Kurtosis: Darlington Reexamined."

STATISTICS DIVISION NEWSLETTER PAGE 11

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ASQC STATISTICS DIVISION NEWSLETTER

INSIDE THIS ISSUE:

Chair's Message p. 1 Officers p. 2 Letters to the Editor p. 2-4 Applied Statistics Conference p. 4 New Technometrics Editor p. 4 Basic Tools

"Statistical Graphics - A Great Tool Kit"....p. 5-7 Membership Upgrade••••• MMMMM • MMMMM . MMMMMM ••• MMMMMMMMM • p• 7 Newsletter Editor Job Description P. 8 This Quarter in JQT p. 8 This Quarter in Technometrics p. 8 FTC Call for Papers P. 9 Mini Paper

"Shape-Finder Box Plots" P. 9

STATISTICS DIVISION NEWSLETTER PAGE 12 FALL, 1991