The Habitual Collection and Display of Process DataSimple Principles of Engineering and Quality Assurance Data CollectionSimple Statistical Graphics for Quality AssuranceIE 361 Module 9Simple Principles in the Collection of Industrial and Engineering Dataand Simple Statistical Graphics for Quality AssuranceReading: Sections 2.3, 2.4 Statistical Quality Assurance Methods forEngineers(Sections 1.4 and 1.5 of Revised SQAME )Prof. Steve Vardeman and Prof. Max MorrisIow a Stat e UniversityAugust 2008Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 1 / 17The Habitual Collection and Display of Process DataStep #3 in the 6 Step Process-Oriented Quality Assurance Cycle of Table1.1 of SQAME urges the regular collection and summarization of data onprocess performance. Data from a single period serve to give one asnapshot of process performance. Comparison of data sets from multipleperiods allows one to see and act on trends in process performance. Inthis module we make some observations about real world data collectionand then note how e¤ective some of the simplest tools of statisticalgraphics can be in giving one a quick picture of the main features of aprocess performance data set.Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 2 / 17Simple Principles of Engineering and Quality AssuranceData CollectionUseful and informative data don’t just magically appear in a data …le or ona data collection form. They must be gathered by real humans (or"automatic" data collection systems designed and implemented byhumans) and are only as useful as the wisdom, care, and genuine goo d willthat go into their collection. There are technical matters that impact theusefulness of QA data (like exact sample size choices and particularchoices of structure for a data collection plan). But whether data are tobe used to monitor process stability/p erf ormance or to guide changesaimed at process improvement, there are also some simple qualitativeguidelines that are relevant. Among these are the following:There must be usable operational de…nitions of the quantities onwhich data are to be gathered. Where measurements are to be taken,the measurement equipment itself must be stable/well-calibrated.Technicians must be properly trained in the meaning of the de…nitionsand the use of any equipment involved.Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 3 / 17Simple Principles of Engineering and Quality AssuranceData CollectionA small or moderate amount of carefully collected and immediatelyused data will almost always be worth much more than even a hugeamount of thoughtlessly collected or never used data.It is the absolute size (rather than the relative size) of a sample andthe basic process/population variability that dete rmines theinformation content of a sample. (For example, a blanket "take a10% sample" rule will sometimes over-sample and sometimesunder-sample.)The closer that data are taken (in time and space) to an operationwhose performance they are meant to re‡ect, the better. (The ideal isprobably data collection by well-trained process worke rs who haveadequate time for the task.)Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 4 / 17Simple Principles of Engineering and Quality AssuranceData CollectionRoutine data collection should be made as convenient as p oss ible, andwhere feasible, any form used for data collection should make themimmediately useful (without transfer, e.g., to another form ormedium). The point is to get data used, not to make presentationquality displays.In order to be useful in indicating sources of variation in a data set,care needs to be taken to keep track of conditions surrounding eachobservation (e.g. machine number, operator, etc.).One must take into account psychology and politics when assigningdata collection tasks. He or she who is to collect data should beconvinced that their production is a help rather than a threat, andthat faithful representation of a situation (rather than "goodnumbers") is the goal.Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 5 / 17Simple Statistical Graphics for Quality AssuranceOnce data are collected, it is important to get them immediately used.Often, very simple statistical graphics (like those taught in the …rst coupleof lectures of an elementary statistics course like Stat 231) can beamazingly e¤ective in conveying the most important features of a data setand suggesting what is going on in a process (and, sometimes, how itmight be improved).Histograms provide very simple summaries of distribution center, spread,and shape, that are understandable by even very non-quantitative persons.Usually, a (not necessarily symmetric, but) fairly smooth "unimodal" (onehump/"up and then back down again") shape is what one expects to seein a snapshot of process data. When something else appears, there istypically an interpretable cause for that shape that provides valuableinformation for process understanding and improvement.Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 6 / 17Simple Statistical Graphics for Quality AssuranceThe next …gure is a bi modal (two-mode) histogram of measured axeldiameters (in units of inches). Its shape suggests that there are twoversions of some process element upstream ... two fundamentally di¤erentraw materials sources, two (di¤erently adjusted) lathes, two machineoperators with di¤erent understandings of how to run a single lathe, or ...This possibility can produce variation in diameter that might b e a voided(thereby improving quality). Sliding the two "humps" below together andwould reduce the overall spread in measured diameter.Figure: Bimodal Histogram of Some Axle Diameters ( in)Vardeman and Morris (I o wa St at e Un iversity) IE 361 Mod ule 9 A ugust 2008 7 / 17Simple Statistical Graphics for Quality AssuranceBy the way, this notion of eliminating multiple versions of a single processelement is part of what motivates modern trends to reduction of supplierbases. People even go so far as to consider "single sourcing" for parts andcomponents that must be very uniform. Reducing numbers of vendorshelps an organization reduce variability, time and hassles associated withswitch-overs in production between sources, and the overhead involvedwith dealing with more vendors than absolutely necessary. (There arealso, of course, dangers