Chapter 6 - Statistical Quality ControlLearning ObjectivesLearning Objectives –con’tThree SQC CategoriesSources of VariationDescriptive StatisticsDistribution of DataSPC Methods-Developing Control ChartsSetting Control LimitsControl Charts for VariablesSlide 11Constructing an X-bar Chart: A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled. If the standard deviation of the bottling operation is .2 ounces, use the below data to develop control charts with limits of 3 standard deviations for the 16 oz. bottling operation.Solution and Control Chart (x-bar)X-Bar Control ChartControl Chart for Range (R)R-Bar Control ChartSecond Method for the X-bar Chart Using R-bar and the A2 FactorControl Charts for Attributes –P-Charts & C-ChartsP-Chart Example: A production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires. Calculate the control limits.P- Control ChartC-Chart Example: The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below.C- Control ChartProcess CapabilityRelationship between Process Variability and Specification WidthComputing the Cp Value at Cocoa Fizz: 3 bottling machines are being evaluated for possible use at the Fizz plant. The machines must be capable of meeting the design specification of 15.8-16.2 oz. with at least a process capability index of 1.0 (Cp≥1)Computing the Cpk Value at Cocoa Fizz±6 Sigma versus ± 3 SigmaAcceptance SamplingAcceptance Sampling PlansOperating Characteristics (OC) CurvesAQL, LTPD, Consumer’s Risk (α) & Producer’s Risk (β)Developing OC CurvesExample: Constructing an OC CurveAverage Outgoing Quality (AOQ)Implications for ManagersSQC in ServicesService at a bank: The Dollars Bank competes on customer service and is concerned about service time at their drive-by windows. They recently installed new system software which they hope will meet service specification limits of 5±2 minutes and have a Capability Index (Cpk) of at least 1.2. They want to also design a control chart for bank teller use.SQC Across the OrganizationChapter 6 HighlightsChapter 6 Highlights – con’tSlide 41Slide 42Chapter 6 Homework Hints© Wiley 2010 1Chapter 6 - Statistical Quality ControlOperations ManagementbyR. Dan Reid & Nada R. Sanders4th Edition © Wiley 2010© Wiley 2010 2Learning ObjectivesDescribe categories of SQCExplain the use of descriptive statistics in measuring quality characteristicsIdentify and describe causes of variationDescribe the use of control chartsIdentify the differences between x-bar, R-, p-, and c-charts© Wiley 2010 3Learning Objectives –con’tExplain process capability and process capability indexExplain the concept six-sigmaExplain the process of acceptance sampling and describe the use of OC curvesDescribe the challenges inherent in measuring quality in service organizations© Wiley 2010 4Three SQC CategoriesStatistical quality control (SQC): the term used to describe the set of statistical tools used by quality professionals; SQC encompasses three broad categories of:1. Statistical process control (SPC)2. Descriptive statistics include the mean, standard deviation, and rangeInvolve inspecting the output from a processQuality characteristics are measured and chartedHelps identify in-process variations3. Acceptance sampling used to randomly inspect a batch of goods to determine acceptance/rejectionDoes not help to catch in-process problems© Wiley 2010 5Sources of VariationVariation exists in all processes.Variation can be categorized as either:Common or Random causes of variation, orRandom causes that we cannot identifyUnavoidable, e.g. slight differences in process variables like diameter, weight, service time, temperatureAssignable causes of variationCauses can be identified and eliminated: poor employee training, worn tool, machine needing repair© Wiley 2010 6Descriptive Statistics Descriptive Statistics include:The Mean- measure of central tendencyThe Range- difference between largest/smallest observations in a set of dataStandard Deviation measures the amount of data dispersion around meanDistribution of Data shapeNormal or bell shaped orSkewednxxn1ii 1nXxσn1i2i© Wiley 2010 7Distribution of DataNormal distributionsSkewed distribution© Wiley 2010 8SPC Methods-Developing Control ChartsControl Charts (aka process or QC charts) show sample data plotted on a graph with CL, UCL, and LCLControl chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, timeControl charts for attributes are used to monitor characteristics that have discrete values and can be counted, e.g. % defective, # of flaws in a shirt, etc.© Wiley 2010 9Setting Control LimitsPercentage of values under normal curve Control limits balance risks like Type I error© Wiley 2010 10Control Charts for VariablesUse x-bar and R-bar charts togetherUsed to monitor different variablesX-bar & R-bar Charts reveal different problemsIs statistical control on one chart, out of control on the other chart? OK?© Wiley 2010 11Control Charts for VariablesUse x-bar charts to monitor the changes in the mean of a process (central tendencies)Use R-bar charts to monitor the dispersion or variability of the process System can show acceptable central tendencies but unacceptable variability orSystem can show acceptable variability but unacceptable central tendencies© Wiley 2010 12xxxxn21zσxLCLzσxUCLsample each w/in nsobservatio of# the is (n) and means sample of # the is )( wherenσσ , ...xxxx xkkConstructing an X-bar Chart: A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled. If the standard deviation of the bottling operation is .2 ounces, use the below data to develop control charts with limits of 3 standard deviations for the 16 oz. bottling operation.Center line and control limit formulasTime 1 Time 2 Time 3Observation 115.8 16.1 16.0Observation 216.0 16.0 15.9Observation 315.8 15.8 15.9Observation 415.9 15.9