2006 Prentice Hall, Inc. S6 – 1 Operations Management upplement 6 – tatistical Process Control 2006 Prentice Hall, Inc. PowerPoint presentation to accompany PowerPoint presentation to accompany Heizer/Render Heizer/Render Principles of Operations Management, 6e Principles of Operations Management, 6e Operations Management, 8e Operations Management, 8e
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PowerPoint presentation to accompanyPowerPoint presentation to accompany Heizer/Render Heizer/Render Principles of Operations Management, 6ePrinciples of Operations Management, 6eOperations Management, 8e Operations Management, 8e
Variations that can be traced to a specific Variations that can be traced to a specific reason (machine wear, misadjusted reason (machine wear, misadjusted equipment, fatigued or untrained workers)equipment, fatigued or untrained workers)
The objective is to discover when The objective is to discover when assignable causes are present and assignable causes are present and eliminate themeliminate them
To measure the process, we take samples To measure the process, we take samples and analyze the sample statistics following and analyze the sample statistics following these stepsthese steps
(a)(a) Samples of the Samples of the product, say five product, say five boxes of cereal boxes of cereal taken off the filling taken off the filling machine line, vary machine line, vary from each other in from each other in weightweight
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WeightWeight
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Each of these Each of these represents one represents one sample of five sample of five
(b)(b) After enough After enough samples are samples are taken from a taken from a stable process, stable process, they form a they form a pattern called a pattern called a distributiondistribution
The solid line The solid line represents the represents the
(c)(c) There are many types of distributions, including There are many types of distributions, including the normal (bell-shaped) distribution, but the normal (bell-shaped) distribution, but distributions do differ in terms of central distributions do differ in terms of central tendency (mean), standard deviation or tendency (mean), standard deviation or variance, and shapevariance, and shape
(d)(d) If only natural If only natural causes of causes of variation are variation are present, the present, the output of a output of a process forms a process forms a distribution that distribution that is stable over is stable over time and is time and is predictablepredictable
(e)(e) If assignable If assignable causes are causes are present, the present, the process output is process output is not stable over not stable over time and is not time and is not predicablepredicable
Constructed from historical data, the Constructed from historical data, the purpose of control charts is to help purpose of control charts is to help distinguish between natural variations distinguish between natural variations and variations due to assignable and variations due to assignable causescauses
Control Charts for VariablesControl Charts for Variables
For variables that have continuous For variables that have continuous dimensionsdimensions Weight, speed, length, strength, etc.Weight, speed, length, strength, etc.
x-charts are to control the central x-charts are to control the central tendency of the processtendency of the process
R-charts are to control the dispersion of R-charts are to control the dispersion of the processthe process
Average range R Average range R = 5.3 = 5.3 poundspoundsSample size n Sample size n = 5= 5From From Table S6.1Table S6.1 D D44 = 2.115, = 2.115, DD33 = 0 = 0
Control Limits for p-ChartsControl Limits for p-Charts
Population will be a binomial distribution, Population will be a binomial distribution, but applying the Central Limit Theorem but applying the Central Limit Theorem
allows us to assume a normal distribution allows us to assume a normal distribution for the sample statisticsfor the sample statistics
UCLUCLpp = p + z = p + zpp^̂
LCLLCLpp = p - z = p - zpp^̂
wherewhere pp ==mean fraction defective in the samplemean fraction defective in the samplezz ==number of standard deviationsnumber of standard deviationspp ==standard deviation of the sampling distributionstandard deviation of the sampling distribution
p-Chart for Data Entryp-Chart for Data EntrySampleSample NumberNumber FractionFraction SampleSample NumberNumber FractionFractionNumberNumber of Errorsof Errors DefectiveDefective NumberNumber of Errorsof Errors DefectiveDefective
Control Limits for c-ChartsControl Limits for c-Charts
Population will be a Poisson distribution, Population will be a Poisson distribution, but applying the Central Limit Theorem but applying the Central Limit Theorem
allows us to assume a normal distribution allows us to assume a normal distribution for the sample statisticsfor the sample statistics
wherewhere cc ==mean number defective in the samplemean number defective in the sample
UCLUCLcc = c + = c + 33 c c LCLLCLcc = c - = c - 33 c c
Patterns in Control ChartsPatterns in Control Charts
One plot out above (or One plot out above (or below). Investigate for below). Investigate for cause. Process is “out cause. Process is “out of control.”of control.”
Patterns in Control ChartsPatterns in Control Charts
Trends in either Trends in either direction, 5 plots. direction, 5 plots. Investigate for cause of Investigate for cause of progressive change.progressive change.
Which Control Chart to UseWhich Control Chart to Use
Using an x-chart and R-chart:Using an x-chart and R-chart: Observations are variablesObservations are variables
Collect Collect 20 - 2520 - 25 samples of n samples of n = 4= 4, or n , or n = = 55, or more, each from a stable process , or more, each from a stable process and compute the mean for the x-chart and compute the mean for the x-chart and range for the R-chartand range for the R-chart
Track samples of n observations eachTrack samples of n observations each
Which Control Chart to UseWhich Control Chart to Use
Using a c-Chart:Using a c-Chart: Observations are attributes whose Observations are attributes whose
defects per unit of output can be defects per unit of output can be countedcounted
The number counted is often a small The number counted is often a small part of the possible occurrencespart of the possible occurrences
Defects such as number of blemishes Defects such as number of blemishes on a desk, number of typos in a page on a desk, number of typos in a page of text, flaws in a bolt of clothof text, flaws in a bolt of cloth