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1、Statistical Quality ControlStatistical Quality Controlby R.B. Clough UNH M. E. Henrie - UAAThe Right Statistical ToolsStatistical Quality ControlBasic StatisticsnDescriptive StatisticsnA straightforward presentation of facts. A survey or summary of a population in which all data are known.nInferenti
2、al StatisticsnDrawing conclusions about a population from a random sampleStatistical Quality ControlInferential StatisticsnInferential statistics is a valuable tool because it allows us to look at a small sample size and make statements on the whole population.nSamples must be pulled RANDOMLY from a
3、 population so that the sample truly represents the population. Every unit in a population must have a equal chance of being selected for the sample to be truly random.nThe distribution or shape of the data is important to know for analytical purposes. nThe most common distribution is the bell shape
4、d or normal distribution.nParameters can be estimated from sample statistics. Two of the most common parameters are the mean and standard deviation.nThe mean (or average, denoted by ) measures central tendencyThis is estimated by the sample mean or xbar. nThe standard deviation ( ) measures the spre
5、ad of the data and is estimated by the sample standard deviationStatistical Quality ControlThree SQC CategoriesnStatistical quality control (SQC) is the term used to describe the set of statistical tools used by quality professionalsnSQC encompasses three broad categories of;nDescriptive statisticsn
6、e.g. the mean, standard deviation, and rangenStatistical process control (SPC)nInvolves inspecting the output from a processnQuality characteristics are measured and chartednHelpful in identifying in-process variationnAcceptance sampling used to randomly inspect a batch of goods to determine accepta
7、nce/rejectionnDoes not help to catch in-process problemsStatistical Quality ControlSources of VariationnVariation exists in all processes.nVariation can be categorized as either;nCommon or Random causes of variation, ornRandom causes that we cannot identifynUnavoidablene.g. slight differences in pro
8、cess variables like diameter, weight, service time, temperaturenAssignable causes of variationnCauses can be identified and eliminatedne.g. poor employee training, worn tool, machine needing repairStatistical Quality ControlTraditional Statistical Tools nDescriptive Statistics includenThe Mean- meas
9、ure of central tendencynThe Range- difference between largest/smallest observations in a set of datanStandard Deviation measures the amount of data dispersion around meannDistribution of Data shapenNormal or bell shaped ornSkewedStatistical Quality ControlDistribution of DatanNormal distributionsnSk
10、ewed distribution Wiley 2010SPC Methods-Control ChartsnControl Charts show sample data plotted on a graph with CL, UCL, and LCLnControl chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, timenControl charts for attributes are used to monitor
11、characteristics that have discrete values and can be counted, e.g. % defective, number of flaws in a shirt, number of broken eggs in a boxAnalysis of Patterns on Control ChartsnWhen do you have a problem with your process?nOne or more points outside of the control limitsnA run of at least seven poin
12、ts (up, down or above or below center line)nTwo or three consecutive points outside the 2-sigma warning limits, but still inside the control limitsnFour or five consecutive points beyond the 1-sigma limitsnAn unusual or nonrandom pattern in the dataFrom Douglas C. Montgomery “Introduction to Statist
13、ical Quality Control”Statistical Quality ControlSetting Control LimitsnPercentage of values under normal curvenControl limits balancerisks like Type I errorHypothesis TestsnResults of hypothesis tests fall into one of four scenarios:Statistical Quality ControlType I ErrorOKOKType II ErrorType I and
14、Type II Error ART and BAFnType I - ART (Alpha, Reject Ho when true)nType II - BAF (Beta, Accept Ho when false)Statistical Quality ControlJury Trial vs. Hypothesis Test Wiley 2007Defendant is InnocentJury TrialHypothesis TestAssumptionStandard of ProofEvidenceDecisionBeyond a reasonable doubtNull hyp
15、othesis is trueFacts presented at trialFail to reject assumption (not guilty) or reject (guilty)Determined by Summary statisticsFail to reject H0 or Reject H0 in favor of HaContext?nWhat does it mean to make a type I error here?nConvict an innocent person of a crime.nWhat does it mean to make a type
16、 II error?nFail to convict a guilty person.nWhat do we usually say about type I and type II error rates in this context?Statistical Quality ControlControl Charts for VariablesnUse x-bar and R-bar charts togethernUsed to monitor different variablesnX-bar n(1) process characterization, n(2) metrology characterization, n(3) capability determination, n(4) optimization or reduction of variability, and n(5) preventive control. The two standard methods
