 Part 1. Introduction to MM4XL
 Part 2. MM4XL Tools
 1. Strategic Tools
 BCG Matrix
 Brand Mapping
 Brand Switch
 Decision Tree
 Forecast Manager
 McKinsey Matrix
 Profile Manager
 Quality Manager
 Risk Analyst
 Risk Analyst Expert in a Few Minutes
 Introduction to Decision Analysis
 Introducing Risk Analyst with an example
 1. How to run Risk Analyst
 2. Simulation Never heard of it
 3. Examples
 4. Functions
 1. Property Functions
 2. Utility Functions
 3. Distribution Functions
 mmBETA (Scale, Shape)
 mmBETAGEN (Scale, Shape, [Optional: Lower], [Optional: Upper])
 mmBINOMIAL (Trials, Successes)
 mmCHI2 (Degrees)
 mmDISCRETE (InputRange, Probabilities)
 mmERF (Mean)
 mmERLANG (Scale, Shape)
 mmEXPON (Mean)
 mmEXTVAL (ModalValue, StDeviation)
 mmGAMMA (Scale, Shape)
 mmGAUSSINV (Mean, Scale)
 mmGEO (Trials)
 mmHYPERGEO (Sample, Defects, BatchSize)
 mmINTUNI (Lower, Upper)
 mmLOGISTIC (Mean, StDeviation)
 mmLOGNORMAL (Mean, StDeviation)
 mmNEGBIN (Failures, Successes)
 mmNORMAL (Mean, StDeviation)
 mmPARETO (Location, ModalValue)
 mmPARETO2 (Location, ModalValue)
 mmPERT (Lower, ModalValue, Upper)
 mmPOISSON (Mean)
 mmRANDBETWEEN (Lower, Upper)
 mmRAYLEIGH (ModalValue)
 mmSTUDENT (Degrees)
 mmTRI (Lower, ModalValue, Upper)
 mmUNIFORM (Lower, Upper)
 mmWEIBULL (Life, Shape)
 Probability functions
 Technicalities
 Sources
 2. Analytical Tools
 Business Formulas
 mmBASS, Bass Diffusion Model
 mmBEI, Brand Equity Index
 mmBEP, BreakEven Point
 mmBEPR, BreakEven Point with Fixed Rate of Return
 mmBUYRATE, Purchase Rate Model
 mmCAGR, Compound Annual Growth
 mmCHIp, Chi Squared Test
 mmCODING, Coding of variables
 1. Customer Satisfaction
 2. Database Functions
 mmDHMS, Number to Time
 mmEI, Evolution Index
 mmEXPECT, Expected values
 3. Forecast Errors
 mmGROWTH
 mmGROWTHBACK
 mmGRP, Gross Rating Points
 mmHERF, Herfindahl Index
 mmINTERPOLE, Linear Interpolation
 mmLEARN, Learning Curve
 mmMSAR, Market Share to Advertising Ratio
 4. Opportunity Index
 5. Performance Ranking
 6. Project Management
 mmPREMIUM, Price Premium
 mmPRESS, Product Performance Index
 7. Price Indexes
 8. Queuing Theory
 mmRANGE
 mmREBUY, Repeat Purchase Rate
 mmREBUYS, Estimated Number of RePurchases
 mmRELATIVE
 mmSAMPLE, Sample Size
 mmSAMPLEMIN, Minimum Sample for Significant Values
 mmSEASON, Seasonality Indexes
 mmSHARE
 mmSIGNIF, Significance Test
 mmVARc, Coefficient of Variation
 Cluster Analysis
 CrossTab
 Descriptive Analyst
 Gravitation Analysis
 Proportion Analyst
 Sample Manager
 Segmentation Tree
 Variation Analyst
 3. Charts and Maps
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 Part 1. Introduction to MM4XL
 Part 2. MM4XL Tools
 1. Strategic Tools
 BCG Matrix
 Brand Mapping
 Brand Switch
 Decision Tree
 Forecast Manager
 McKinsey Matrix
 Profile Manager
 Quality Manager
 Risk Analyst
 1. How to run Risk Analyst
 2. Simulation Never heard of it
 3. Examples
 4. Functions
 1. Property Functions
 2. Utility Functions
 3. Distribution Functions
 mmBETA (Scale, Shape)
 mmBETAGEN (Scale, Shape, [Optional: Lower], [Optional: Upper])
 mmBINOMIAL (Trials, Successes)
 mmCHI2 (Degrees)
 mmDISCRETE (InputRange, Probabilities)
 mmERF (Mean)
 mmERLANG (Scale, Shape)
 mmEXPON (Mean)
 mmEXTVAL (ModalValue, StDeviation)
 mmGAMMA (Scale, Shape)
 mmGAUSSINV (Mean, Scale)
 mmGEO (Trials)
 mmHYPERGEO (Sample, Defects, BatchSize)
 mmINTUNI (Lower, Upper)
 mmLOGISTIC (Mean, StDeviation)
 mmLOGNORMAL (Mean, StDeviation)
 mmNEGBIN (Failures, Successes)
 mmNORMAL (Mean, StDeviation)
 mmPARETO (Location, ModalValue)
 mmPARETO2 (Location, ModalValue)
 mmPERT (Lower, ModalValue, Upper)
 mmPOISSON (Mean)
 mmRANDBETWEEN (Lower, Upper)
 mmRAYLEIGH (ModalValue)
 mmSTUDENT (Degrees)
 mmTRI (Lower, ModalValue, Upper)
 mmUNIFORM (Lower, Upper)
 mmWEIBULL (Life, Shape)
 Probability functions
 Risk Analyst Expert in a Few Minutes
 Introduction to Decision Analysis
 Introducing Risk Analyst with an example
 Technicalities
 Sources
 2. Analytical Tools
 Business Formulas
 1. Customer Satisfaction
 2. Database Functions
 3. Forecast Errors
 4. Opportunity Index
 5. Performance Ranking
 6. Project Management
 7. Price Indexes
 8. Queuing Theory
 mmBASS, Bass Diffusion Model
 mmBEI, Brand Equity Index
 mmBEP, BreakEven Point
 mmBEPR, BreakEven Point with Fixed Rate of Return
 mmBUYRATE, Purchase Rate Model
 mmCAGR, Compound Annual Growth
 mmCHIp, Chi Squared Test
 mmCODING, Coding of variables
 mmDHMS, Number to Time
 mmEI, Evolution Index
 mmEXPECT, Expected values
 mmGROWTH
 mmGROWTHBACK
 mmGRP, Gross Rating Points
 mmHERF, Herfindahl Index
 mmINTERPOLE, Linear Interpolation
 mmLEARN, Learning Curve
 mmMSAR, Market Share to Advertising Ratio
 mmPREMIUM, Price Premium
 mmPRESS, Product Performance Index
 mmRANGE
 mmREBUY, Repeat Purchase Rate
 mmREBUYS, Estimated Number of RePurchases
 mmRELATIVE
 mmSAMPLE, Sample Size
 mmSAMPLEMIN, Minimum Sample for Significant Values
 mmSEASON, Seasonality Indexes
 mmSHARE
 mmSIGNIF, Significance Test
 mmVARc, Coefficient of Variation
 Cluster Analysis
 CrossTab
 Descriptive Analyst
 Gravitation Analysis
 Proportion Analyst
 Sample Manager
 Segmentation Tree
 Variation Analyst
 3. Charts and Maps
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Part 2. MM4XL Tools > 1. Strategic Tools > Quality Manager > 1. SPC Attribute Charts > NPChart
Quality Manager NPChart The nPchart works the same way as the Pchart (read the corresponding chapter as well), but it is used to control nonconformities in lots of fixed size only, and it plots the number of nonconformities rather than the proportion of nonconformities. Plotting the number rather than the proportion of defectives makes the nPchart simpler to use than the Pchart. However, the nPchart can only plot data from fixed size lots, which is a substantial limitation to its application, and for this reason the Pchart is more widely applied than the nPchart. Tip: Read also the material in this help file concerning Pcharts in order to get a clear view of how the nPchart works and what assumptions it sets. User selections The picture below shows an nPchart drawn with MM4XL's Quality Manager tool. After selecting Chart type, as shown in the following picture, if you have selected a range with more than one variable (column) in input, choose the variable to analyze for Num defectives, otherwise, the tool will automatically show the data of the first series available. If an input range was not selected in window 1, the nPchart will not be available in the list of chart types and the right side of the window below will be blank. Click on Next to go to the window where you select options for printing the results on sheet. Technical notes The control limits are placed at three standard deviations (see field Z in the window) above and below the average (nPbar) of nonconformities. Measurements falling outside control limits indicate a change in the process. Input data The input data for the nPchart requires one column of counts. The picture below shows a suitable data series in the range A1:A35, mind the hidden rows. These can be negative or positive nonconformities. Simulation data When checked, the feature Simulate comparison data in window 2 displays a new data series on the left side of the Attribute charts called Simulated data. These are points produced according to the distribution function characterizing the chart, for instance Binomial for nPcharts, and they are useful for confirming through a visual inspection the stability of the user input data. If the shape of the user data is remarkably different from that of the simulated data one can reasonably conclude that the user data could be influenced by some kind of external force. That is, the impact on the input data should be removed and a new analysis should be run. Tip: In order to speed up the tool, uncheck the simulation option when working with long data series. Output results The nPchart can generate as output two charts and two tables, depending on the user selection in the third window (see section Introduction to Quality Manager). The first table, in the picture below, contains indexes that describe the input data in terms of:  Size of the variable: Max, Min, Sum, Range and Counts
 Central tendency: Average, Median, Mode and Standard deviation (of a variable)
 Chart limits: Upper Control Limit (UCL), Pbar, Lower Control Limit (LCL)
 Z stands for the number of standard deviations where control limits should be placed
 Sigma is the standard deviation of a subgroup
For the sake of brevity, the second table is not shown here. In 5 columns it shows the details of the chart limits by item. In the picture below, the small, red triangle in the upper right corner of the first column label is a Comment that displays a short message. A number of comments are created by Quality Manager. Place the mouse pointer on the red triangle to display the message. The nPChart in the picture below refers to an input variable (thick blue line) presenting one observation outside of the UCL while all other points lie within limits. The thin green line on the left side refers to simulated random data produced by Quality Manager, in our example, according to the Binomial probability distribution function. Comparing the random data to the user input data can help you get a visual understanding of the departure of the input data from normality. In our example, both simulated and user data take a shape that does not indicate any particular sign of an existing trend. Therefore, we could conclude that the input data is stable and can be used for the purpose of control. For a better way to assess normality read the material on the Process Capability tool available in Quality Manager. The histogram in the picture below shows two series:  The blue bars refer to the observed frequency of count classes in the input data. The first bar, for instance, tells us that there are 2 counts for zeros in the data. The second bar shows 4 counts for ones. And so on for all bars.
 The bellshaped red line shows the expected normal curve for a variable with the same range as the input data, and it helps to verify with a quick visual inspection whether the input data follow a normal distribution or not. nPcharts, however, follow the Binomial distribution that they tend to approximate normality only with a large number of observations.
Tip: When working with P and NP charts, sometimes it is necessary to adjust the Pbar value in order to align the central line (Pbar) of simulated and user data. When the two lines lie roughly at the same level one can safely assume the simulated data reflect the shape of the data input by the user. For P charts, the Pbar value is shown in the lower right area of the window among the statistics. An estimate of the NPbar can be found by first running a P chart with fixed lot, and then applying the Pbar to the NP chart. 