 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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mytest > help > Part 2. MM4XL Tools > 1. Strategic Tools > Quality Manager > 2. SPC Variable Charts > XRange Control Charts
Quality Manager XRange Control Charts These two charts monitor the location and the variation of a process, respectively. The Xbar chart shows how the process changes according to a central measure of dispersion, the average, and the Range chart shows when the variation of the process changes. For example, they could be used to monitor whether a satisfactory cleanliness level is maintained in 5 restaurants of the same chain throughout the day, or to monitor the sales trend of a product for 4 sales representatives, or to monitor visits to a website with and without payperclick advertising. These charts, however, should be used only when the rate of data collection is slow. In all other cases, the XSigma charts with larger samples are preferrable because the sigma value is more accurate than the range value, due to the fact that the latter is found using only two values of a sample, the largest and smallest one, while sigma uses all values in the range. The picture below shows XR charts drawn with MM4XL's Quality Manager tool. If an input range was not selected in window 1, the XR charts will not be available in the list of chart types and the right side of the window below will be blank. After the desired chart type is selected, the charts will display in the right side of the window as shown below. The result can, of course, be printed in a worksheet. Technical notes The control concept of the XR charts is based on the following assumptions:  The input data has at least 2 observations in each sample.
 The size of the samples is equal for all groups.
 The data are normally distributed or approximate normality. This implies that the data is collected in a short time and there are enough measurements. A common rule of thumb suggests using at least 20 samples and 100 points. If this doesn't approximate normality you should increase the sample size (use the Process Capability tool to verify whether a process approximates normality). When the sample size exceeds 5 units some authors suggest using the XSigma charts instead of the XRange charts.
 All groups have equal weight.
 Observations are collected independently, in order to avoid using autocorrelated data.
 For the Range chart only, betweengroup (sample) variation must be due to special causes, which implies a correct functioning of the process.
Unstable (or out of control) processes run outside of control limits and/or present random patterns of variation, which must be stabilized in order to be correctly analyzed with control charts. Stabilizing a process may require collecting new data. In order to detect a change, the average and the range of the input data are shown in two charts within boundaries as in the picture below. In both charts control limits are placed three standard deviations above and below the central line. Measurements falling outside control limits indicate a change in the process. In practice, 99.7% of normally distributed observations fall within the three standard deviation boundaries, and there are only 27 chances in every 10,000 that it falls outside. Therefore, it is reasonable to conclude that observations outside of the limits show nonconformity in the process, and the analyst should explain why this occurred. When an item goes beyond limits a change has occurred. The change can be bad or good depending on the measurement data. For instance, if the data refer to sales levels falling below the central line, this represents negative performance. When outside the LCL the change is bad and the source of change should be identified and removed from the process. Above the central line the change is good and the source of the change should be made common practice in the process. In general, the rules governing the normal distribution can be used to interpret control charts:  Randomness of data
 Symmetry of the distribution
 99.7% of the observations lie within the 3 standard deviations
 95.5% of the observations lie within the 2 standard deviations
Other rules of thumb to identify variation in the data suggest paying attention to data showing:  7 successive observations on one side of the central line (there is a probability equal to 0.57 or 0.78% of finding such a distribution, and it is reasonable to believe it may be due to a process out of control)
 7 successive observations either increasing or decreasing
 2 successive points placed very close to one of the limits (the probability of two successive normally distributed points lying between two and three standard deviations on one side of the central bar is 0.05%)
Input data The input data for the XR charts require two or more columns of data. The picture below shows a suitable input data in the range B1:F26, mind the hidden rows. Output results The output from the XR charts is made up of two charts and two tables, in accordance with the user selection in the third Quality Manager window (see Introduction to Quality Manager). The first table, shown below, contains basic indexes describing the process. Xdbar is the overall process mean computed on all observations. Rbar is the average Range value of ranges for all groups of observations. StDevBar is the average standard deviation value of standard deviations for all groups of observations. For the sake of brevity, the second table is not shown here. In 10 columns it shows the details of the chart limits by item. The second to fifth columns are used to draw the Range chart and the remaining columns are used to draw the Xbar chart. The XRange Chart shown below refers to an input variable with all observations within confidence limits. Although there has been a slight change in the range chart between the seventh and eleventh sample, this has not altered the system. Also the 5 sequential points in the lower half starting at sample 20 tend to verify that the process is stable and can be used for the purpose of control. The Xbar Chart below confirms a change in average for sample number 10, and also shows a slight negative bump for samples 1921. A joint reading of the two charts helps us to monitor that a given process performs as expected. This implies a thorough knowledge of the process in analysis, in order to explain any cause of variation detected by the charts.
