Total Quality Management Control Charts Excel Add-In Software

mytest > help > Part 2. MM4XL Tools > 1. Strategic Tools > Quality Manager > 3. Process Capability > Process Capability

Quality Manager

Process Capability

Capability is the ability of a process to perform a task. A process capability (PC) study assesses whether the process is working correctly. That is: (1) the process is stable, and (2) the input data is normally distributed. Unstable processes are influenced by external nonrandom forces, and they have to be stabilized in order to perform meaningful PC analyses. Stabilizing a process may require collecting new data and/or enlarging the sample size.

The picture below shows the PC analysis drawn with MM4XL's Quality Manager tool. After the desired Chart type is selected the charts are displayed in the right side of the window as shown below. The result can, of course, be printed in a worksheet.

Total Quality Management Control Charts Excel Add-In Software

The objective of a capability study is to evaluate the relationship between the output produced by a process and the limits set by the analyst. Output falling outside the limits is nonconforming to the planned functioning of the process. There are two kinds of limits:

Specification limits (LSL and USL) are typically set by users such as engineers, managers, etc. For instance, one could set the limits for the number of visits one sales representative is supposed to make in a given period of time to 75 and 200.
Natural tolerance limits (LNTL and UNTL) are based on the process capability and are computed using mean and standard deviation.

Input data

The input data for Process Capability analysis requires one or more columns of either counts or continuous values, as shown for the SQC charts (C, U, P and nP). Both tables below, for instance, are suited for PC analysis.

Output results

Output from the Process Capability analysis is made up of two charts and two tables in accordance with the user selection in the third window (see section Introduction to Quality Manager). The first table, in the picture below, shows indexes describing the process capability.

Process capability is measured with indexes. An index is a relative relationship. When it falls outside limits the process requires the attention of the analyst. Three common kinds of indexes are used to measure process capability:

Cp measures the relative distance of the sample mean from the target mean. CpL and CpU measure the distance of the sample mean from the lower and upper specification limits. A CpL and CpU greater than one means that natural tolerance limits are greater than specification limits, which means that the specification limits are requiring a precision beyond the capability of the process. On the other hand, when they do not exceed specification limits the chance of producing nonconformities is low.
Two more process capability indexes are called Cr and Cpk. The first is the inverse of Cp, measuring the percentage of the specification band used up by the process, and it should be as close to zero as possible in order to improve the processes. Cpk is a more accurate measure than Cp when the process is not centered because it compares both halves before and after the mean to the lower and upper specification limit, respectively.

The formulae of the process capability indices are as follows.

Index	Formula	Description
CpU		Upper capability index
Cp		Potential capability
CpL		Lower capability index
Cr		Capability ratio
Cpk		Demonstrated excellence

For the sake of brevity, the second table is not shown here. In 9 columns it shows the details of the chart limits by item. The Cumulative Frequency and Cumulative Normal are the columns used to draw the Cumulative chart, shown below. Interval (equal to the process average +/- z standard deviations), Frequency and Count Expected are used to draw the histogram chart.

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 bell-shaped 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.

Kolmogorov-Smirnov test

The Kolmogorov-Smirnov is a popular test for goodness-of-fit of normally distributed variables. It returns a value (D) that, compared to critical values of D for the K-S one-sample test, tells us whether the analyzed data follow a normal process or not. Quality Manager performs the whole job and returns one of 5 self-explaining labels. In the table above we read Little doubt, which means, as the label suggests, that there is little doubt that the data analyzed are normally distributed. The same conclusion can be also reached with a visual inspection of the Cumulative chart where it is clear that the shape of the input data of Cumulative Frequencies (blue line) follows a normal pattern as the Cumulative Normal curve (pink one) suggests. The other labels that Quality Manager returns in answer to the K-S test are N/A when the test cannot be successfully run, Very unlikely, Low chances, Concern and Reasonable to believe.

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