The post Process Capability with SigmaXL appeared first on Deploy OpEx.

]]>Process capability measures how well the process performs to meet given specified outcome. It indicates the conformance of a process to meet given requirements or specifications. Capability analysis helps to better understand the performance of the process with respect to meeting customer’s specifications and identify the process improvement opportunities.

Process Capability Analysis Steps

- Determine the metric or parameter to measure and analyze.
- Collect the historical data for the parameter of interest.
- Prove the process is statistically stable (i.e. in control).
- Calculate the process capability indices.

Monitor the process and ensure it remains in control over time. Update the process capability indices if needed.

Process capability can be presented using various indices depending on the nature of the process and the goal of the analysis. Popular process capability indices are:

- Cp
- Pp
- Cpk
- Ppk
- Cpm

The Cp index is process capability. It assumes the process mean is centered between the specification limits and essentially is the ratio of the distance between the specification limits to six process standard deviations. Obviously, the higher this value the better, because it means you can fit the process variation between the spec limits more easily. Cp measures the process’ potential capability to meet the two-sided specifications. It does not take the process average into consideration.

High Cp indicates the small spread of the process with respect to the spread of the customer specifications. Cp is recommended when the process is centered between the specification limits. Cp works when there are both upper and lower specification limits. The higher Cp the better, meaning the spread of the process is smaller relative to the spread of the specifications.

Note: Cpm can work only if there is a target value specified.

Data File: “Capability Analysis” tab in “Sample Data.xlsx”

- Select the entire range of data (i.e. the column “HtBk”)
- Click SigmaXL -> Process Capability -> Histograms & Process Capability
- A new window named “Histogram & Process Cap” pops up with the selected range of data appearing in the box under “Please select your data”

- Click “Next>>”
- A new window named “Histograms & Process Capability” appears
- Select “HtBk” as the “Numeric Data Variables”
- Enter 6 in LSL, 6.5 in T and 7 in USL into the boxes for “Lower Spec Limit”, “Target” and “Upper Spec Limit” respectively

- Click “OK”
- The histogram and the process capability analysis results are in the newly generated tab “Hist Cap (1)”

Model summary: With P_{pk} of less than 1.0 we can conclude that the capability of this process is not very good. Anything less than 1.0 should be considered not capable and we should strive for P_{pk} to reach levels of greater than 1 and preferably over 1.67.

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]]>The post Attribute MSA with SigmaXL appeared first on Deploy OpEx.

]]>Data File: “Attribute MSA” tab in “Sample Data.xlsx” (an example in the AIAG MSA Reference Manual, 3rd Edition).

Step 1: Reorganize the original data into four new columns (i.e., Appraiser, Assessed Result, Part, and Reference).

- Select the entire range of the original data (“Part”, “Reference”, “Appraiser A”, “Appraiser B” and “Appraiser C” columns)
- Click SigmaXL -> Data Manipulation -> Stack Subgroups Across Rows
- A new window named “Stack Subgroups” pops with the selected data range appearing in the box under “Please select your data”

- Click “Next>>”
- A new window named “Stack Subgroups Across Rows” appears
- Select “Appraiser A”, “Appraiser B” and “Appraiser C” as “Numeric Data Variables”

Select “Part” and “Reference” as the “Additional Category Columns”

Enter “Assessed Result” as the “Stacked Data (Y) Column Heading (Optional)

Enter “Appraiser” as the “Category (X) Column Heading (Optional)”

- Click “OK>>”
- The stacked data are created in a new worksheet.

Step 2: Run a MSA using SigmaXL

- Select the entire range of the data (“Part”, “Reference”, “Appraiser” and “Assessment Result” columns)
- Click SigmaXL -> Measurement Systems Analysis -> Attribute MSA (Binary)
- A new window named “Attribute MSA (Binary)” pops with the selected data range appearing in the box under “Please select your data”

- Click “Next>>”
- A new window named “Attribute MSA (Binary)” appears
- Select “Part” as “Part/Sample”

Select “Appraiser” as “Appraiser”

Select “Assessed Result” as “Assessed Result”

Select “Reference” as “True Standard (Optional)”

Select “1” as “Good Level”

- Click “OK”

The MSA results appear in the newly generated tab “Att_MSA_Binary”.

The rater scores represent how the raters agree with themselves. Appraiser A, for instance, agreed with himself on 84% of the measurements made.

The important numbers are called out here. Of the 50 total measurements performed, for 78% of those (39) the appraisers agreed with both themselves and the other appraisers.

*Kappa statistic* is a coefficient indicating the agreement percentage above the expected agreement by chance. Kappa ranges from −1 (perfect disagreement) to 1 (perfect agreement). When the observed agreement is less than the chance agreement, Kappa is negative. When the observed agreement is greater than the chance agreement, Kappa is positive. Rule of thumb: If Kappa is greater than 0.7, the measurement system is acceptable. If Kappa is greater than 0.9, the measurement system is excellent.

Model summary: In all cases the Kappa indicates that the measurement system is acceptable.

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]]>The post Variable Gage R&R with SigmaXL appeared first on Deploy OpEx.

]]>Variable Gage Repeatability & Reproducibility (Gage R&R) is a method used to analyze the variability of a measurement system by partitioning the variation of the measurements using ANOVA (Analysis of Variance). Whenever something is measured repeatedly or by different people or processes, the results of the measurements will vary. Variation comes from two primary sources:

- Differences between the parts being measured
- The measurement system

We can use a Gage R&R to conduct a measurement system analysis to determine what portion of the variability comes from the parts and what portion comes from the measurement system. There are key study results that help us determine the components of variation within our measurement system.

Variable Gage R&R primarily addresses the precision aspect of a measurement system. It is a tool used to understand if a measurement system can repeat and reproduce and if not, help us determine what aspect of the measurement system is broken so that we can fix it.

Gage R&R requires a deliberate study with parts, appraisers and measurements. Measurement data must be collected and analyzed to determine if the measurement system is acceptable. Typically Variable Gage R&Rs are conducted by 3 appraisers measuring 10 samples 3 times each. Then, the results can be compared to determine where the variability is concentrated. The optimal result is for the measurement variability to be due to the parts.

Measurement System Analysis (MSA) is a systematic method to identify and analyze the variation components of a measurement system. It is a mandatory step in any Six Sigma project to ensure the data are reliable before making any data-based decisions. A MSA is the check point of data quality before we start any further analysis and draw any conclusions from the data. Some good examples of data-based analysis where MSA should be a prerequisite:

- Correlation analysis
- Regression analysis
- Hypothesis testing
- Analysis of variance
- Design of experiments
- Statistical process control

You will see where and how the analysis techniques listed above are used. It is critical to know that any variation, anomalies, or trends found in your analysis are actually due to the data and not due to the inaccuracies or inadequacies of a measurement system. Therefore the need for a MSA is vital.

A measurement system is a process used to obtain data and quantify a part, product or process. Data obtained with a measurement device or measurement system are the observed values. Observed values are comprised of two elements

- True Value = Actual value of the measured part
- Measurement Error = Error introduced by the measurement system.

The true value is what we are ultimately trying to determine through the measurement system. It reflects the true measurement of the part or performance of the process.

Measurement error is the variation introduced by the measurement system. It is the bias or inaccuracy of the measurement device or measurement process.

The observed value is what the measurement system is telling us. It is the measured value obtained by the measurement system. Observed values are represented in various types of measures which can categorized into two primary types discrete and continuous. Continuous measurements are represented by measures of weight, height, money and other types of measures such as ratio measures. Discrete measures on the other hand are categorical such as Red/Yellow/Green, Yes/No or Ratings of 1–10 for example.

The guidelines for acceptable or unacceptable measurement systems can vary depending on an organizations tolerance or appetite for risk. The common guidelines used for interpretation are published by the Automotive Industry Action Group (AIAG). These guidelines are considered standard for interpreting the results of a measurement system analysis using Variable Gage R&R. Table 1.0 summarizes the AIAG standards.

Data File: “Variable MSA” tab in “Sample Data.xlsx”

Let’s take a look at an example of a Variable MSA using the data in the Variable MSA tab in your “Sample Data.xlsx” file. In this exercise we will first walk through how to set up your study using SigmaXL and then we will perform a Variable MSA using 3 operators who all measured 10 parts three times each. The part numbers and operators and measurement trials are all generic so that you can apply the concept to your given industry. First we need to set up the study:

Step 1: Set up your data collection worksheet

- Click on SigmaXL -> Measurement Systems Analysis ->

Create Gauge R&R (Crossed) Worksheet - A new window named “Create Gauge R&R (Crossed) Worksheet” appears
- Enter 10 as the “Number of Parts/Samples”
- Enter 3 as the “Number of Operators/Appraisers”
- Enter 3 as the “Number of Replicates/Trials”
- Uncheck the checkboxes for both “Randomize Parts/Sample” and “Randomize Operators/Appraisers”

- Click “OK>>”
- A new tab named “Gage R&R (Crossed) WKS” is generated

Step 2: Data collection

In the newly generated data table, SigmaXL has provided the template where we can organize the data. We will need to enter test results into the measurement column. In the “Sample Data.xlsx” file under the “Variable MSA” tab there are already “Measurement” values collected by the three operators (i.e., operator A, B, and C). The data are listed in Run order.

Step 3: Enter the data into the MSA template generated in SigmaXL

Transfer the data from the “Measurement” column in “Variable MSA” tab of “Sample Data.xlsx” file to the last column in the MSA template that SigmaXL generated from the steps above.

- Click SigmaXL -> Measurement Systems Analysis -> Analyze Gage R&R (Crossed)
- A new window named “Analyze Gage R&R (Crossed)” appears with the data range automatically selected in the box right below “Please select your data”

- Click “Next>>”
- A new window also named “Analyze Gauge R&R (Crossed)” pops up.
- Select “Part” as “Part”

Select “Operator” as “Operator”

Select “Measurement” as “Measurement” - Enter 5.15 as the “Standard Deviation Multiplier” and enter 95% as the “Confidence Level”.

- Click “OK”

Step 5: Interpret the MSA results

Model summary: The result of this Gage R&R study leaves room for consideration on one key measure. As noted in previous pages, the targeted percent contribution R&R should be less than 10% and study variation less than 30%. With % contribution at 7.76% it is below our 10% unacceptable threshold and similarly, Study variation at 26.86% is also below the threshold of 30% but this result is at best marginal and should be heavily scrutinized by the business before concluding that the measurement system does not warrant further improvement.

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]]>The post Run Chart with SigmaXL appeared first on Deploy OpEx.

]]>A run chart is a chart used to present data in time order. These charts capture process performance over time. The X axis indicates time and the Y axis shows the observed values. A run chart is similar to a scatter plot in that it shows the relationship between X and Y. Run charts differ however, because they show how the Y variable changes with an X variable of time.

Run charts look similar to control charts except that run charts do not have control limits and they are much easier to produce than a control chart. A run chart is often used to identify anomalies in the data and discover pattern over time. They help to identify trends, cycles, seasonality and other anomalies.

Data File: “Run Chart” tab in “Sample Data.xlsx”

- Select the entire range of the data (“Measurement”, “Cycle” and “Trend”).
- Click SigmaXL -> Graphical Tools -> Run Chart

A new window named “Run Chart” pops up with the selected range of data appearing in the box under “Please select your data”

- Click “Next>>”
- A new window also named “Run Chart” appears
- Select “Measurement” as the “Numeric Data Variable (Y)”

- Click “OK”
- The run chart appears automatically in the tab “Run Chart (1)”

The figure above is a run chart created with SigmaXL. The time series displayed by this chart appears stable. There are no extreme outliers, no visible trending or seasonal patterns. The data points seem to vary randomly over time.

Now, let us look at another example which may give us a different perspective. We will create another run chart using the data listed in the column labeled “Cycle”. This column is in the same file used to generate the figure above. Follow the steps used for the first run chart and instead of using “Measurement” use “Cycle” in the Run Chart dialog box pictured in the figure below.

In the figure above, the data points are clearly exhibiting a pattern. It could be seasonal or it could be something cyclical. Imagine that the data points are taken monthly and this is a process performing over a period of 2.5 years. Perhaps the data points represent the number of customers buying new homes. The home buying market tends to peak in the summer months and dies down in the winter.

Using the same data tab lets create a final run chart. This time use the “Trend” data. Again, follow the steps outlined previously to generate a run chart.

In this example, the process starts out randomly, but after the seventh data point almost every data point has a lower value than the one before it. This clearly illustrates a downward trend. What might this represent? Perhaps a process winding down? Product sales at the end of a product’s life cycle? Defects decreasing after introducing a process improvement?

Model summary: It should be clearly evident through our review of Histograms, Scatterplots and Run Charts, that there is great value in “visualizing” the data. Graphical displays of data can be very telling and offer excellent information.

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]]>The post Scatter Plot with SigmaXL appeared first on Deploy OpEx.

]]>A scatter plot is a diagram to present the relationship between two variables of a data set. It consists of a set of data points set on two axis. On the scatter plot, a single observation is presented by a data point with its horizontal position equal to the value of one variable and its vertical position equal to the value of the other variable. A scatter plot helps us to understand:

- Whether the two variables are related to each other or not
- What is the strength of their relationship
- The shape of their relationship
- The direction of their relationship
- Whether outliers are present

Data File: “Scatter Plot” tab in “Sample Data.xlsx”

Steps to render a Scatterplot in SigmaXL:

- Select the entire range of data (both “MPG” and “weight”)
- Click SigmaXL -> Graphical Tools -> Scatter Plots
- A new window named “Scatter Plots” pops up with the selected range of data appearing in the box under “Please select your data”

- Click “Next>>”
- A new window also named “Scatter Plots” appears
- Select “MPG” as the “Numeric Response (Y)”
- Select “weight” as the “Numeric Predictor (X1)”

- Click “OK>>”
- The scatterplot appears in the new tab “Scatterplot (1)”

Model summary: The figure above is SigmaXL’s output of the scatterplot data. You can immediately see the value of graphical displays of data. This information obtainable by viewing this output shows a relationship between weight and MPG. This scatterplot shows that the heavier the weight the lower the MPG value and vice versa.

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]]>The post Histogram Rendering with SigmaXL appeared first on Deploy OpEx.

]]>A histogram is a graphical tool to present the distribution of the data. These plots are used to better understand how values occur in a given set of data. The X axis represents the possible values of the variable and the Y axis represents the frequency of the value occurring. This graphical tool consists of adjacent rectangles erected over intervals with heights equal to the frequency density of the interval. The total area of all the rectangles in a histogram is the number of data values.

A histogram can also be normalized. In the case of normalization, the X axis still represents the possible values of the variable, but the Y axis represents the percentage of observations that fall into each interval on the X axis. The total area of all the rectangles in a normalized histogram is 1. When using this type of graph, we have a better understanding of the shape, location, and spread of the data.

Data File: “Histogram” tab in “Sample Data.xlsx”

Steps to render a histogram in SigmaXL:

- Select the entire range of data
- Click SigmaXL -> Graphical Tools -> Histograms & Descriptive Statistics
- A new window named “Histograms & Descriptive” pops up with the selected range appearing in the box under “Please select your data”

- Click “Next>>”
- A new window named “Histograms & Descriptive Statistics” appears
- Select “HtBk” as the “Numeric Data Variables (Y)”

- Click “OK”
- The normality test results appear in the newly generated tab “Hist Descript (1)”

Model summary: The output from the previous steps has generated a graphical summary report of the data set HtBk. Among the information provided is a histogram. The image shows the frequency of the data for the numerical categories ranging from 5.7 to 7. You can see the shape of the data roughly follows the bell curve.

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]]>The post Box Plot with SigmaXL appeared first on Deploy OpEx.

]]>In statistics, graphical analysis is a method to visualize the quantitative data. Graphical analysis is used to discover structure and patterns in the data. The presence of which may explain or suggest reasons for additional analysis or consideration. A complete statistical analysis includes both quantitative analysis and graphical analysis.

When we think of statistics, we often think of numbers. However, graphical analysis is complementary to purely quantitative statistics because it allows us to visualize structure and patterns in the data. Often, the graphical presentation of data can tell a story on its own, but the total statistical analysis is important to complete the picture. Sometimes our eyes can deceive us. There are various graphical analysis tools available, one most commonly used is a Box Plot.

A box plot is a graphical method to summarize a data set by visualizing the minimum value, 25th percentile, median, 75th percentile, the maximum value, and potential outliers. A percentile is the value below which a certain percentage of data fall. For example, if 75% of the observations have values lower than 685 in a data set, then 685 is the 75th percentile of the data. At the 50th percentile, or median, 50% of the values are lower and 50% are higher than that value.

The figure above describes how to read a box plot. Here are a few explanations that may help. The middle part of the plot, or the “interquartile range,” represents the middle quartiles (or the 75th minus the 25th percentile). The line near the middle of the box represents the median (or middle value of the data set). The whiskers on either side of the IQR represent the lowest and highest quartiles of the data. The ends of the whiskers represent the maximum and minimum of the data, and the individual dots beyond the whiskers represent outliers in the data set.

Data File: “Box Plot” tab in “Sample Data.xlsx”

Steps to render a box plot in SigmaXL:

- Select the entire range of the data.
- Click SigmaXL -> Graphical Tools -> Boxplots
- A new window named “Boxplots” pops up with the selected range appearing in the box under “Please select your data”

- Click “Next>>”
- A new window also named “Boxplots” appears
- Select “HtBk” as the “Numeric Data Variables (Y)”

- Check the check box “Show Legend”
- Click “OK>>”
- The Boxplot appears automatically in the new tab “Boxplot (1)”

Model summary: The figure above demonstrates the result of the boxplot after navigating through the SigmaXL menus to yield this output. Notice the interquartile range between the 25^{th} and 75^{th} quartiles, the median line, the mean, and the whiskers.

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]]>The post One Sample t Test with SigmaXL appeared first on Deploy OpEx.

]]>A One sample t test is a hypothesis test to study whether there is a statistically significant difference between a population mean and a specified value.

- Null Hypothesis (H0): μ = μ0
- Alternative Hypothesis (Ha): μ ≠ μ0

Where:

- μ is the mean of a population of our interest
- μ0 is the specific value we want to compare against.

In statistics, a t-test is a hypothesis test in which the test statistic follows a Student’s t distribution if the null hypothesis is true. We apply a t-test when the population variance (σ) is unknown and we use the sample standard deviation (s) instead. A hypothesis test is a statistical method in which a specific hypothesis is formulated about a population, and the decision of whether to reject the hypothesis is made based on sample data. Hypothesis tests help to determine whether a hypothesis about a population or multiple populations is true with certain confidence level based on sample data. Hypothesis testing is a critical tool in the Six Sigma tool belt. It helps us separate fact from fiction, and special cause from noise, when we are looking to make decisions based on data.

- The sample data of the population of interest are unbiased and representative.
- The data of the population are continuous.
- The data of the population are normally distributed.
- The variance of the population of our interest is unknown.
- One sample t-test is more robust than the z-test when the sample size is small (< 30).

To check whether the population of our interest is normally distributed, we need to run normality test. While there are many normality tests available, such as Anderson–Darling, Sharpiro–Wilk, and Jarque–Bera, our examples will default to using the Anderson-Darling test for normality.

- Null Hypothesis (H0): The data are normally distributed.
- Alternative Hypothesis (Ha): The data are not normally distributed.

To understand what is happening when you run a t-test with your software, the formulas here will walk you through the key calculations and how to determine if the null hypothesis should be accepted or rejected. To determine significance, you must calculate the t-statistic and compare it to the critical value, which is a reference value based on the alpha value and degrees of freedom (n – 1). The t-statistic is calculated based on the sample mean, the sample standard deviation, and the sample size.

(Y ) ̅is the sample mean, n is the sample size, and s is the sample standard deviation

*tcrit*is the t-value in a Student’s t distribution with the predetermined significance level α and degrees of freedom (n –1).*tcrit*values for a two-sided and a one-sided hypothesis test with the same significance level α and degrees of freedom (n – 1) are different.

Based on the sample data, we calculated the test statistic tcalc, which is compared against tcrit to make a decision of whether to reject the null.

- Null Hypothesis (H0):
*μ = μ0* - Alternative Hypothesis (Ha):
*μ ≠ μ0*

If |tcalc| > tcrit, we reject the null and claim there is a statistically significant difference between the population mean μ and the specified value μ0.

If |tcalc| < tcrit, we fail to reject the null and claim there is not any statistically significant difference between the population mean μ and the specified value μ0.

Case study: We want to compare the average height of basketball players against 7 feet.

Data File: “One Sample T-Test” tab in “Sample Data.xlsx”

- Hypothesis (H0):
*μ = 7* - Alternative Hypothesis (Ha):
*μ ≠ 7*

Step 1: Test whether the data are normally distributed

- Select the entire range of data
- Click SigmaXL -> Graphical Tools -> Histograms & Descriptive Statistics
- A new window named “Histograms & Descriptive” pops up with the selected range appearing in the box under “Please select your data”

- Click “Next>>”
- A new window named “Histograms & Descriptive Statistics” appears
- Select “HtBk” as the “Numeric Data Variables (Y)”

- Click “OK”
- The normality test results appear in the newly generated tab “Hist Descript (1)”

- Null Hypothesis(H
_{0}): The data are normally distributed. - Alternative Hypothesis(H
_{a}): The data are not normally distributed.

Since the p-value of the normality is 0.275, which is greater than alpha level (0.05), we fail to reject the null and claim that the data are normally distributed. If the data are not normally distributed, you need to use hypothesis tests other than the one sample t-test.

Now we can run the one-sample t-test, knowing the data are normally distributed.

Step 2: Run the one-sample t-test

- Select the entire range of “HtBk”
- Click SigmaXL -> Statistical Tools -> 1 Sample t-Test & Confidence Intervals
- A new window named “1 Sample t-Test” pops up with the selected range pre-populated in the box under “Please select your data”

- Click “Next>>”
- Another window also named “1 Sample t-Test” appears
- Select the radio button for “Unstacked Column Format”
- Select “HtBk” as the “Numerical Data Variable (Y)”
- Enter the hypothesized value “7” into the box next to “H0: Mean =”
- Select “Not Equal To” in the box next to “Ha:”

- Click “OK>>”
- The one-sample t-test result appears automatically in the tab “1 Sample t-Test (1)”.

Model summary: Since the p-value is smaller than alpha level (0.05), we reject the null hypothesis and claim that average of basketball players is statistically different from 7 feet.

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]]>The post Central Limit Theorem with SigmaXL appeared first on Deploy OpEx.

]]>The Central Limit Theorem is one of the fundamental theorems of probability theory. It states a condition under which the mean of a large number of independent and identically-distributed random variables, each of which has a finite mean and variance, would be approximately normally distributed. Let us assume Y1, Y2 . . . Yn is a sequence of n i.i.d. random variables, each of which has finite mean μ and variance σ2, where σ2 > 0. When n increases, the sample average of the n random variables is approximately normally distributed, with the mean equal to μ and variance equal to σ2/n, regardless of the common distribution Yi follows where i = 1, 2 . . . n.

A sequence of random variables is independent and identically distributed (i.i.d.) if each random variable is independent of others and has the same probability distribution as others. It is one of the basic assumptions in Central Limit Theorem. Consider the law of large numbers (LLN)—It is a theorem that describes the result of performing the same experiment a large number of times. According to the LLN, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed. The following example will explain this further.

Let us assume we have 10 fair die at hand. Each time we roll all 10 die together we record the average of the 10 die. We repeat rolling the die 50 times until we will have 50 data points. Upon doing so, we will discover that the probability distribution of the sample average approximates the normal distribution even though a single roll of a fair die follows a discrete uniform distribution. Knowing that each die has six possible values (1, 2, 3, 4, 5, 6), when we record the average of the 10 dice over time, we would expect the number to start approximating 3.5 (the average of all possible values). The more rolls we perform, the closer the distribution would be to a normal distribution centered on a mean of 3.5.

The confidence interval is an interval where the true population parameter would fall within a certain confidence level. A 95% confidence interval, the most commonly used confidence level, indicates that the population parameter would fall in that region 95% of the time or we are 95% confident that the population parameter would fall in that region. The confidence interval is used to describe the reliability of a statistical estimate of a population parameter.

The width of a confidence interval depends on the:

- Confidence level—The higher the confidence level, the wider the confidence interval
- Sample size—The smaller the sample size, the wider the confidence interval
- Variability in the data—The more variability, the wider the confidence interval

Data File: “Central Limit Theorem” tab in “Sample Data.xlsx”

- Select the entire range of “Cycle Time (Minutes)”
- Click SigmaXL -> Graphical Tools -> Histogram & Descriptive Statistics
- A new window named “Histogram & Descriptive” pops up with the selected range automatically appearing in the box under “Please select your data”

- Click “Next”
- Another window named “Histogram & Descriptive Statistics” pops up.
- Select “Cycle Time (Minutes)” as the “Numeric Data Variable (Y)”

- Click “OK>>”
- The 95% confidence interval of the mean is shown in the newly generated ta “Hist Descript (1)”

The 95% confidence interval of the mean is shown in the newly-generated “Summary for Cycle Time (Minutes).” The confidence level is 95% by default. In order to see the confidence interval of “Cycle Time (Minutes)” at other confidence level, we need to enter the confidence level of our interest in the window “Graphical Summary” and click “OK.”

The following example shows how to generate 90% confidence interval of the mean.

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]]>The post Multi Vari Analysis with SigmaXL appeared first on Deploy OpEx.

]]>Multi Vari Analysis is a graphic-driven method to analyze the effects of categorical inputs on a continuous output. It studies how the variation in the output changes across different inputs and helps us quantitatively determine the major source of variability in the output. Multi Vari charts are used to visualize the source of variation. They work for both crossed and nested hierarchies.

- Y: continuous variable
- X’s: discrete categorical variables. One X may have multiple levels

Hierarchy is a structure of objects in which the relationship of objects can be expressed similar to an organization tree. Each object in the hierarchy is described as above, below, or at the same level as another one. If object A is above object B and they are directly connected to each other in the hierarchy tree, A is B’s parent and B is A’s child. In Multi-Vari analysis, we use the hierarchy to present the relationship between categorical factors (inputs). Each object in the hierarchy tree indicates a specific level of a factor (input). There are generally two types of hierarchies: crossed and nested.

**Crossed Hierarchy**

In the hierarchy tree, if one child item has more than one parent item at the higher level, it is a crossed relationship.**Nested Hierarchy**

In the hierarchy tree, if one child item only has one parent item at the higher level, it is a nested relationship.

Data File: “Multi-Vari” tab in “Sample Data.xlsx.”

Case study: ABC Company produces 10 kinds of units with different weights. Operators measure the weights of the units before sending them out to customers. Multiple factors could have an impact on the weight measurements. The ABC Company wants to have a better understanding of the main source of variability existing in the weight measurement. The ABC Company randomly selects three operators (Joe, John, and Jack) each of whom measures the weights of 10 different units. For each unit, there are three items sampled.

Steps in SigmaXL to perform a Multi-Vari Analysis:

- Open the “Multi-Vari’ tab in “Sample Data.xlsx”
- Select the range of data that we are interested in analyzing.
- Click SigmaXL -> Graphical Tools -> Multi-Vari Charts
- A new window also named “Multi-Vari Charts” pops up

- Click on “Next >>”
- A new window also named “Multi-Vari Charts” pops up.
- Select “Measurement” as “Numeric Response (Y)”

Select “Unit” as “Group Category (X1)”

Select “Operator” as “Group Category (X2)”

- Click “OK >>”

Model summary: Based on the Multi-Vari chart output, the measurement of units ranges from 0.4 to 1.1. Joe’s and John’s mean measurements stay between 0.8 and 0.9. Jack’s mean is slightly lower than both Joe’s and John’s. John has the worst variation when measuring the same kind of unit because John has the highest difference between the maximum and minimum bars for any kind of unit. By observing the black lines of three operators, it seems like all three operators’ measurements follow the same pattern. The operator-to-operator variability is not large. The unit-to-unit variability is large and it could be the main source of variation in measurements.

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