PTTE 434 Quality Organization & Management J. R. Wixson - InstructorClass ObjectivesChapter OverviewStatistical FundamentalsSlide 5Slide 6Statistical FundamentalsSlide 8Slide 9Slide 10Slide 11Sampling DistributionsSlide 13Slide 14Slide 15Slide 16Slide 17Sampling Distribution of the meanSlide 19SpreadStandard normal distributionSlide 22Applying the formulaArea under a portion of the normal curve - Example 1Example 2Example 2 Cont’dExample 3Slide 28Slide 29Slide 30Slide 31PowerPoint PresentationSlide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Standard Error in Relation to Sample SizeSlide 46Slide 47Central Limit TheoremSlide 49Central Limit Theorem (Cont’d)Hypothesis TestingClassical ApproachWhy not accept the null hypothesis?Slide 54P-Value Approach (Cont’d)Slide 56Slide 57Slide 58Steps to Hypothesis TestingSlide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74P-Value ApproachSlide 76Slide 77PTTE 434Quality Organization & ManagementJ. R. Wixson - InstructorCh 10: Basic Concepts of Statistics and ProbabilityThe University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonClass ObjectivesLearn about the standard normal distributionDiscuss descriptive and inferential statisticsLearn how to calculate proportions under the normal curve.Discuss sampling distributionsLearn how to calculate sample size from a normal distributionDiscuss Hypothesis Testing 2 approaches:–Classical method–P-value methodThe University of Idaho - Industrial Technology Department, PTTE 434, J. R. Wixson Chapter OverviewStatistical FundamentalsProcess Control ChartsSome Control Chart ConceptsProcess CapabilityOther Statistical Techniques in Quality ManagementThe University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonStatistical FundamentalsStatistical Thinking–Is a decision-making skill demonstrated by the ability to draw to conclusions based on data. Why Do Statistics Sometimes Fail in the Workplace?–Regrettably, many times statistical tools do not create the desired result. Why is this so? Many firms fail to implement quality control in a substantive way.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonStatistical FundamentalsReasons for Failure of Statistical Tools–Lack of knowledge about the tools; therefore, tools are misapplied.–General disdain for all things mathematical creates a natural barrier to the use of statistics.–Cultural barriers in a company make the use of statistics for continual improvement difficult.–Statistical specialists have trouble communicating with managerial generalists.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonStatistical FundamentalsReasons for Failure of Statistical Tools (continued)–Statistics generally are poorly taught, emphasizing mathematical development rather than application.–People have a poor understanding of the scientific method.–Organization lack patience in collecting data. All decisions have to be made “yesterday.”The University of Idaho - Industrial Technology Department, PTTE 434, J. R. Wixson Statistical FundamentalsReasons for Failure of Statistical Tools (continued)–Statistics are view as something to buttress an already-held opinion rather than a method for informing and improving decision making.–Most people don’t understand random variation resulting in too much process tampering.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. Wixson Statistical FundamentalsUnderstanding Process Variation–Random variation is centered around a mean and occurs with a consistent amount of dispersion. –This type of variation cannot be controlled. Hence, we refer to it as “uncontrolled variation.”–The statistical tools discussed in this chapter are not designed to detect random variation.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. Wixson Statistical FundamentalsUnderstanding Process Variation (cont.)–Nonrandom or “special cause” variation results from some event. The event may be a shift in a process mean or some unexpected occurrence.Process Stability–Means that the variation we observe in the process is random variation. To determine process stability we use process charts.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. Wixson Statistical FundamentalsSampling Methods–To ensure that processes are stable, data are gathered in samples.•Random samples. Randomization is useful because it ensures independence among observations. To randomize means to sample is such a way that every piece of product has an equal chance of being selected for inspection.•Systematic samples. Systematic samples have some of the benefits of random samples without the difficulty of randomizing.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonSampling Methods–To ensure that processes are stable, data are gathered in samples (continued)•Sampling by Rational Subgroup. A rational subgroup is a group of data that is logically homogenous; variation within the data can provide a yardstick for setting limits on the standard variation between subgroups. Statistical FundamentalsThe University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonSampling DistributionsThe University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonSampling DistributionsIf you compute the mean of a sample of 10 numbers, the value you obtain will not equal the population mean exactly; by chance it will be a little bit higher or a little bit lower. If you sampled sets of 10 numbers over and over again (computing the mean for each set), you would find that some sample means come much closer to the population mean than others. Some would be higher than the population mean and some would be lower. Imagine sampling 10 numbers and computing the mean over and over again, say about 1,000 times, and then constructing a relative frequency distribution of those 1,000 means.The University of Idaho - Industrial Technology Department, PTTE 434, J. R. WixsonSampling DistributionsThe distribution of means is a very good approximation to the sampling distribution of the mean. The sampling distribution of the mean is a