ITED 434 Quality Organization & Management Ch 10 & 11Chapter OverviewStatistical FundamentalsSlide 4Slide 5Statistical FundamentalsSlide 7Slide 8Slide 9Slide 10Standard normal distributionSlide 12Applying the formulaArea under a portion of the normal curve - Example 1Example 2Slide 16Slide 17Slide 18Sampling DistributionsSlide 20Slide 21Slide 22Slide 23Slide 24Sampling Distribution of the meanSlide 26SpreadSlide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Hypothesis TestingClassical ApproachSlide 38P-Value ApproachP-Value Approach (Cont’d)Slide 41Process Control Charts Slide 1 of 37Process Control Charts Slide 2 of 37Process Control Charts Slide 3 of 37Process Control Charts Slide 4 of 37Process Control Charts Slide 5 of 37Process Control Charts Slide 6 of 37Process Control Charts Slide 7 of 37Process Control Charts Slide 8 of 37Process Control Charts Slide 9 of 37Process Control Charts Slide 10 of 37Process Control Charts Slide 11 of 37Process Control Charts Slide 12 of 37Process Control Charts Slide 13 of 37Process Control Charts Slide 14 of 37Process Control Charts Slide 15 of 37Process Control Charts Slide 16 of 37Process Control Charts Slide 17 of 37Process Control Charts Slide 18 of 37Process Control Charts Slide 19 of 37Process Control Charts Slide 20 of 37Process Control Charts Slide 21 of 37Process Control Charts Slide 22 of 37Process Control Charts Slide 23 of 37Process Control Charts Slide 24 of 37Process Control Charts Slide 25 of 37Process Control Charts Slide 26 of 37Process Control Charts Slide 27 of 37Process Control Charts Slide 28 of 37Process Control Charts Slide 29 of 37Process Control Charts Slide 30 of 37Process Control Charts Slide 31 of 37Process Control Charts Slide 32 of 37Process Control Charts Slide 33 of 37Process Control Charts Slide 34 of 37Process Control Charts Slide 35 of 37Process Control Charts Slide 36 of 37Process Control Charts Slide 37 of 37Process Capability Slide 1 of 4Process Capability Slide 2 of 4Process Capability Slide 3 of 4Process Capability Slide 4 of 4Slide 83Slide 84ITED 434Quality Organization & Management Ch 10 & 11Ch 10: Basic Concepts of Statistics and ProbabilityCh 11: Statistical Tools for Analyzing DataChapter OverviewStatistical FundamentalsProcess Control ChartsSome Control Chart ConceptsProcess CapabilityOther Statistical Techniques in Quality ManagementStatistical 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.Statistical 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.Statistical 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.”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.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.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.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.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 FundamentalsThe standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Normal distributions can be transformed to standard normal distributions by the formula:X is a score from the original normal distribution,  is the mean of the original normal distribution, and  is the standard deviation of original normal distribution. Standard normal distributionStandard normal distributionA z score always reflects the number of standard deviations above or below the mean a particular score is. For instance, if a person scored a 70 on a test with a mean of 50 and a standard deviation of 10, then they scored 2 standard deviations above the mean. Converting the test scores to z scores, an X of 70 would be:So, a z score of 2 means the original score was 2 standard deviations above the mean. Note that the z distribution will only be a normal distribution if the original distribution (X) is normal.Applying the formulaApplying the formula will always produce a transformed variable with a mean of zero and a standard deviation of one. However, the shape of the distribution will not be affected by the transformation. If X