OPERATIONS MANAGEMENT Chapter 6S Statistical Process Control中南财经政法大学 工商管理学院 刘大明OPERATIONS MANAGEMENTChapter 6SStatistical Process Control*中南财经政法大学 工商管理学院 刘大明BetzDearborns QA Lab.中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Testing the stress tolerance on the fabric 中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Laser Tracking Device中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明SPC Charts Prepared by Hand中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Statistical Quality Control (SPC)Measures performance of a processUses mathematics (i.e., statistics)Provide statistical signal when assignable causes of variation are presentDetect and eliminate assignable causes of variation中南财经政法大学 工商管理学院 刘大明*Points that might be emphasized include:Statistical process control measures the performance of a process; it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance.Statistical process control requires the collection and analysis of datatherefore it is not helpful when total production consists of a small number of unitsWhile statistical process control cannot help identify a “good” or “bad” unit, it can enable one to decide whether to accept an entire production lot. If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot. The issue of rejecting a lot that was actually good can be raised here, but is probably better *中南财经政法大学 工商管理学院 刘大明Variability is inherent in every processNatural or common causes: Random variationsAssignable or special causes: Correctable variationsVariations中南财经政法大学 工商管理学院 刘大明*This slide introduces the difference between “natural” and “assignable” causes.The next several slides expand the discussion and introduce some of the statistical issues. *中南财经政法大学 工商管理学院 刘大明Also called common causesAffect virtually all production processesExpected amount of variationOutput measures follow a probability distributionFor any distribution there is a measure of central tendency and dispersionIf the distribution of outputs falls within acceptable limits, the process is said to be “in control”Natural Variations中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Also called special causes of variationGenerally this is some change in the processVariations that can be traced to a specific reasonThe objective is to discover when assignable causes are presentEliminate the bad causesIncorporate the good causesAssignable Variations中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Natural and Assignable VariationFigure S6.1中南财经政法大学 工商管理学院 刘大明*Students should understand both the concepts of natural and assignable variation, and the nature of the efforts required to deal with them.*中南财经政法大学 工商管理学院 刘大明Natural and Assignable VariationFigure S6.1To measure the process, we take samples and analyze the sample statistics following these steps(a)Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Natural and Assignable VariationFigure S6.1To measure the process, we take samples and analyze the sample statistics following these steps(b)After enough samples are taken from a stable process, they form a pattern called a distribution中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Natural and Assignable VariationFigure S6.1To measure the process, we take samples and analyze the sample statistics following these steps(c)There are many types of distributions, including the normal (bell-shaped) distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shape中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Natural and Assignable VariationFigure S6.1To measure the process, we take samples and analyze the sample statistics following these steps(d)If only natural causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Natural and Assignable VariationFigure S6.1To measure the process, we take samples and analyze the sample statistics following these steps(e)If assignable causes are present, the process output is not stable over time and is not predicable中南财经政法大学 工商管理学院 刘大明*中南财经政法大学 工商管理学院 刘大明Central Limit TheoremRegardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curveThe mean of the sampling distribution (x) will be the same as the population mean mThe sta