Patterns on Control Charts (and Other Plots Against Time)"Special Checks"/"Extra Alarm Rules" for Patterns on a Control ChartIE 361 Module 14Patterns on Control Charts and "Special Checks"/Extra Alarm RulesReading: Section 3.4 of Statistical Quality Assurance Methods forEngineersProf. Steve Vardeman and Prof. Max MorrisIow a State UniversityVardeman and Morris (I owa State University) IE 361 Module 14 1 / 17Patterns on Control Charts (and Other Time Plots)To this point, we’ve spoken as if the only use one makes of a Shewhartchart is to compare values of a summary statistic Q to control limits. Ifthat were true, there would be little point in making the plot. Calculationsalone would su¢ ce. But, in fact, people make and examine the plots,looking for interpretable patterns.Under stable process conditions, one expects a sequence of plotted valuesQ thatare without obvious pattern or trend,only on rare occasions fall outside control limits,tend to cluster about the center line, about equally often above andbelow it, buton occasion approach the control limits.When something other than this kind of "random scatter" shows up on acontrol chart, it can be possible to get clues to what physical causes areacting on the process that can be used in process improvement e¤orts.Vardeman and Morris (I owa State University) IE 361 Module 14 2 / 17Patterns on Control ChartsSy ste matic Variation/CyclesSystematic variation/cycles, regular "up then back down again" patternssometimes appear on plots against time. The …gure below is an example.Figure: A Plot of Factory Ambient Temperature vs. TimeIdenti…cation of the period of variation can give hints where to startlooking for physical causes.Vardeman and Morris (I owa State University) IE 361 Module 14 3 / 17Patterns on Control ChartsSy ste matic Variation/CyclesExamples of the kind of factors that can produce cycles are seasonal anddiurnal variables like ambient temperature. And sometimes regular rotationof …xtures or gages or shift changes in operators running equipment ormaking measurements can stand behind systematic variation.While systematic variation is variation of the "second kind," it may notalways be economically feasible to eliminate it. For example, it may bepreferable to live with e¤ects of regular cycles in ambient temperaturerather than try to control the environment in which a process operates.But recognition of its presence at least allows one to intelligently consideroptions regarding remedial measures, and to mentally remove that kind ofvariation from the baseline against which one looks for the e¤ects of otherspecial causes.Vardeman and Morris (I owa State University) IE 361 Module 14 4 / 17Patterns on Control ChartsInstabilityInstability is a word traditionally applied to patterns on control chartswhere many points plot near or beyond control limits. The …gure belowshows two Shewhart ¯x charts. The …rst is "properly behaved" while thesecond shows instability.Figure: Two ¯x Charts, the Second of Which Shows "Instability"Vardeman and Morris (I owa State University) IE 361 Module 14 5 / 17Patterns on Control ChartsInstabilityStanding behind a pattern of instability can be more or less erratic andunexpected causes, like di¤erent lots of raw material with di¤erentphysical properties mixed as process input. Another important possiblecause is that of unwise operator overadjustment of equipment. Controlcharting is useful both because it signals the existence of conditions thatdeserve physical intervention, and because it tells one to leave equipmentuntouched when it seems to be operating as consistently as possible.Vardeman and Morris (I owa State University) IE 361 Module 14 6 / 17Patterns on Control ChartsChan ges in Level (Sudden)Changes in level sometimes app ear on plots against time; the avera geplotted value seems to move decisively up or down. The change can besudden (as pictured below) and traceable to some basic change at thetime of the shift. (The introduction of new equipment or a clear change inthe quality of a raw material can produce such a sudden change in level.)Figure: A Sudden Change in Level of Part HardnessVardeman and Morris (I owa State University) IE 361 Module 14 7 / 17Patterns on Control ChartsChan ges in Level (Gradual)Or the change can be more gradual (as in the …gure below) andattributable to an important cause starting to act at the beginning of thechange in level, but "gathering steam" as time goes on until its full e¤ectis felt. (For example, e¤ective worker training in machine operation andmeasuring techniques could begin a gradual decrease in level on an Rchart.)Figure: A Gradual Change in Level of Part HardnessVardeman and Morris (I owa State University) IE 361 Module 14 8 / 17Patterns on Control ChartsChan ges in Level (Tr end)Where a gradual change in level does not end with stabilization around anew mean, it is traditional to say that there is a trend on a control chart.Many physical causes acting on manufacturing processes will producetrends if they remain unaddressed. An example is tool wear in machiningprocesses as suggested in the run chart below.Figure: A Run Chart With an Unabate d TrendVardeman and Morris (I owa State University) IE 361 Module 14 9 / 17Patterns on Control ChartsMixturesAnother phenomenon that can produce strange-looking patterns onShewhart control charts is something early users called the occurrence ofmixtures. These are the combination of two or more distinct patterns ofvariation (in either a plotted statistic Q, or in an underlying distribution ofindividual observations leading to Q) that get put together on a singlechart. Where an underlying distribution of observations has two or moreradically di¤erent components, depending upon the circumstances aplotted statistic Q can be either unexpectedly variable or surprisinglyconsistent.Vardeman and Morris (I owa State University) IE 361 Module 14 10 / 17Patterns on Control ChartsMixtures (Large Variation)Consider …rst the possibility of unexpectedly large variation. Whereblunders like incomplete or omitted manufacturing operations orequipment malfunctions lead to occasional wild individual observations andcorrespondingly wild values of Q, the terminology freaks is often used todescribe the mixture of normal and aberrant observations. The next …gureshows both a plot over time and a corresponding histogram of a series ofvalues Q that …t this description.Figure: An Example of a Pattern that Could be