c-Charts  c-chart: A chart used for controlling the number of defects when more than one defect can be present in a service or product.  The underlying sampling distribution for a c-chart is the Poisson distribution.  The mean of the distribution is c  The standard deviation is c  A useful tactic is to use the normal approximation to the Poisson so that the central line of the chart is c and the control limits are UCLc = c+z c © 2007 Pearson Education and LCLc = c−z c
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ISR Test Roles & Responsibilities Stakeholders involved in the defect management process should be aware of their respective roles and responsibilities, as indicated below, to ensure that key activities within the defect management process are accounted for. Roles General Responsibilities System Owner /Tester      Execute test cases Raise issues and document defects found during testing Communicate upstream and downstream defect consequences Proactively participate in defect triage meetings and track defect status Certify System Remediated Quality Assurance (QA)     Review the defects logged for validity and severity Report the defect status on a daily basis to Test Lead Coordinate the execution of daily scheduled test events Coordinate defect triage meetings and monitor defect resolution progress Impacted Systems Remediation Point of Contact (ISR POC)  Support System Owner Testers with defining and documenting defects  Responsible for overseeing defect fix progress among Test team, Technical team, and Functional team  Manage ALM test execution and defect status for respective ISR system  Proactively participate in defect triage meetings and tracking defect status Technical / Functional Support Teams  Support execution and validation of test scenarios  Review, fix, and/or reject defects  Proactively participate in defect triage meetings and tracking defect status -5-
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OTHER CHARTS AVAILABLE FROM GOOGLE CHARTS Traditional Graphs Diagrams Area Charts (Traditional and Stepped) Bubble Charts Bar Charts Box and Whisker Plots (Candlestick Charts) Column Charts Calendar Charts Combo Charts Gauge Charts Histograms Geographic Charts Intervals Organizational Charts Line Charts Tables Pie Charts Timelines Scatter Charts Tree Map Charts Time Series (Annotated) Word Trees Trend lines **User created community charts are also available**
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Woodland Paper Company Example 6.4 In the Woodland Paper Company’s final step in their paper production process, the paper passes through a machine that measures various product quality characteristics. When the paper production process is in control, it averages 20 defects per roll. a) Set up a control chart for the number of defects per roll. Use twosigma control limits. b) Five rolls had the following number of defects: 16, 21, 17, 22, and 24, respectively. The sixth roll, using pulp from a different supplier, had 5 defects. Is the paper production process in control? c = 20 z=3 © 2007 Pearson Education UCLc = c+3 c = 20 + 3 20 = 33.42 LCLc = c−3 c = 20 - 3 20 = 6.58
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 The sampling distribution of    When    we choose many SRSs from a population, the sampling distribution of the sample mean is centered at the population mean µ and is less spread out than the population distribution. Here are the facts. MEAN AND STANDARD DEVIATION OF A SAMPLE MEAN Suppose that is the mean of an SRS of size drawn from a large population with mean and standard deviation . Then the sampling distribution of has mean and standard deviation . We say the statistic is an unbiased estimator of the parameter . Because it’s standard deviation is , the averages are less variable than individual observations, and the results of large samples are less variable than the results of small samples. SAMPLING DISTRIBUTION OF A SAMPLE MEAN If individual observations have the distribution, then the sample mean of an SRS of size has the distribution.
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Standard Deviation = SD • Standard Deviation uses all the data points, not just some like Range and Interquartile Range • Standard Deviation does not have squared units (like Variance) and is thus easier to interpret • Standard deviation has the same units as the data!! • The sample standard deviation is a point estimator of the population standard deviation • Interpretation of Standard Deviation: • • • • • • • A Numerical Measure that says how much variability there is in the data points Standard Deviation Is Like An Average Of The Deviations Standard Deviation tells us how fairly the mean represents its data points Standard Deviation tells us how clustered the data points are around the mean For financial assets standard deviation is a measure of risk or fluctuation in asset value Use STDEV.P function for population data Use STDEV.S for sample data. 56
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role of the Central Limit Theorem in finding a confidence interval for  The Central Limit Theorem tells us that when a random sample of size n is taken from a population that has a normal distribution with mean  and standard deviation , then the sampling distribution of x has a normal distribution with mean   and standard deviation —— . This is even true when the population does not n have a normal distribution, as long as the sample size n is sufficiently large. called the standard error of estimate or standard error of the mean There is a 95% chance that x will be within 2 (more precisely, 1.960 standard errors of . ) There is a (1 – )100% chance that x will be within z/2 standard errors of . That is, we can be (1 – )100% confident that population mean  will lie between   x – z/2 —— and x + z/2 —— . n n s Not knowing the value for , we estimate the standard error with —— . n With this estimated standard error of the mean, we must use a t distribution in place of a normal or z distribution.
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Measurement Data & Metrics Base Metrics # & Type of Defects found (major, minor) For each defect, who found # of pages inspected, preparation time (per inspector), inspection time Measures Preparation rate = # pages / average preparation time Inspection rate = # pages / inspection time Inspection defect rate = # major defects / inspection time Defect density = # estimated defects / # of pages Inspection yield = # defects / # estimated defects (individual & team) SRS Phase Defect Containment (%) = 100% * # Defects removed @ step / ( Incoming defects + Injected defects) 6/12/2007 2007_06_12_Rqmts.ppt 28
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Measurement Data & Metrics Base Metrics # & Type of Defects found (major, minor) For each defect, who found # of pages inspected, preparation time (per inspector), inspection time Measures Preparation rate = # pages / average preparation time Inspection rate = # pages / inspection time Inspection defect rate = # major defects / inspection time Defect density = # estimated defects / # of pages Inspection yield = # defects / # estimated defects (individual & team) SRS Phase Defect Containment (%) = 100% * # Defects removed @ step / ( Incoming defects + Injected defects) 6/19/2007 SE 652- 2007_06_19_Overview_Inspections.ppt 17
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The Sampling Distribution of x 12 When we choose many SRSs from a population, the sampling distribution of the sample mean is centered at the population mean µ and is less spread out than the population distribution. Here are the facts.   The Sampling Distribution of Sample Means Suppose that x is the mean of an SRS of size n drawn from a large population with mean  and standard deviation s . Then : The mean of the sampling distribution of x is x =     The standard deviation of the sampling distribution of x is s sx = n Note: These facts about the mean and standard deviation of x are true no matter what shape the population distribution has.   If individual observations have the N(µ,σ) distribution, then the sample mean of an SRS of size n has the N(µ, σ/√n) distribution regardless of the sample size n.
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