Process Performance Determination in C#

• Download source code - 19.3 KB

Introduction

Process performance metrics are important to determine the performance capability (of a process) in terms of customer requirement. Process performance can be determined via the following ways:

• DPMO (Defect per Million Opportunity)
• PPM (Part per Million)
• Yield
• Z-transformation

This is the first of a four part series that determines Process Performance.

Background

This article describes how to determine the process performance from DPMO.  

The DPMO metric is a measure of capability for discrete (attribute) data found by:

DPMO=DPO x 1,000,000

where:

DPO (Defect per Opportunity) = number of defects / (number of units ×number of opportunities per unit)

The DPMO metric is important because it allows you to compare different types of products.

For example, a process produces 40,000 pencils. Three types of defects can occur. The number of occurrences of each defect type is:

• Blurred printing: 36
• Too long: 118
• Rolled ends: 11

Total number of defects: 165

First, determine the number of ways each defect can occur on each item. For this product, blurred printing occurs in only one way (the pencil slips in the fixture). And there are three independent places where dimensions are checked. Rolled ends can occur at the top and the bottom of the pencil, so there are two. The total number of opportunities per unit is: 1 + 3 + 2 = 6.

Applying the DPMO formula, you can readily determine the DPMO metric:

DPO = = 165 / (6×40000) = 0.0006875, and DPMO = 0.0006875 x 1000000 = 687.5

Requirement

To run the code, you need to have the following:

• .NET Framework 2.0 and above
• Microsoft Visual Studio 2005 if you want to open the project files included in the download project
• Nunit 2.4 if you want to run the unit tests included in the download project

Using the code

We envisage that the user will perform the following code to get the desired results. This involves a simple four-step process:

1. Instantiate a ProcessPerformanceFrDPMO object
2. Input NumOfUnitProcessed, NumOfDefects, and NumOfDefectOpportunities
3. Invoke its .Analyze() method
4. Retrieve results from its .Result object.

Here is a typical user’s code:

ProcessPerformanceFrDPMO dpmo = new ProcessPerformanceFrDPMO();
dpmo.NumOfUnitProcessed = 40000;
dpmo.NumOfDefects = 165;
dpmo.NumOfDefectOpportunities = 6;
dpmo.Analyze();
Console.WriteLine("DPO is: " + dpmo.Result.DPO);
Console.WriteLine("DPMO is: " + dpmo.Result.DPMO);
Console.WriteLine("Yield in % is: " + dpmo.Result.YieldInPercent);

Two classes are implemented:

1. ProcessPerformanceFrDPMOResult
2. ProcessPerformanceFrDPMO

ProcessPerformanceFrDPMOResult is a class from which a result object derives, which holds the analysis results. In our implementation, the .Result member variable is defined as follows:

/// <summary>
/// Process Performance from DPMO Result class
/// </summary>
public class ProcessPerformanceFrDPMOResult
{
    /// <summary>
    /// Default constructor
    /// </summary>
    public ProcessPerformanceFrDPMOResult() { }
    /// <summary>
    /// Defects Per Opportunity
    /// </summary>
    public double DPO;
    /// <summary>
    /// Defects Per Million Opportunity
    /// </summary>
    public double DPMO;
    /// <summary>
    /// Yield in Percent
    /// </summary>
    public double YieldInPercent;   
}

The following table lists the available results (assuming that the ProcessPerformanceFrDPMO object name you use is dpmo):

Result	Result stored in variable
Defect per Opportunity	dpmo.Result.DPO
Defect per Million Opportunity	dpmo.Result.DPMO
Yield in %	dpmo.Result.YieldInPercent

ProcessPerformanceFrDPMO Class

The ProcessPerformanceFrDPMO class does the analysis (calculation), and it is implemented as follows:

/// <summary>
/// Determine Process Performance from DPMO
/// </summary>
public class ProcessPerformanceFrDPMO
{
    private int N = 0;
    private int D = 0;
    private int O = 0;
    private double DPO = 0;
    private double DPMO = 0;
    private double yieldInPercent = 0;
    
    /// <summary>
    /// ProcessPerformanceFrDPMO Result
    /// </summary>
    public ProcessPerformanceFrDPMOResult Result = new ProcessPerformanceFrDPMOResult();

    #region Constructors
    /// <summary>
    /// Process performace  from DPMO constructor
    /// </summary>
    public ProcessPerformanceFrDPMO() { } //default empty constructor

#endregion //Constructors

    /// <summary>
    /// Write only property: number of unit processed
    /// </summary>
    public int NumOfUnitProcessed
    {
        set { N = value; }
    }

    /// <summary>
    /// Write only property: total number of defects
    /// </summary>
    public int NumOfDefects
    {
        set { D = value; }
    }

    /// <summary>
    /// Write only property: number of defect opportunities
    /// </summary>
    public int NumOfDefectOpportunities
    {
        set { O = value; }
    }

Once the ProcessPerformanceFrDPMO object is instantiated, the user needs to set the input values for the number of units processed, number of defects, and the number of defect opportunities, as follows:

ProcessPerformanceFrDPMO dpmo = new ProcessPerformanceFrDPMO();
dpmo.NumOfUnitProcessed = 40000;
dpmo.NumOfDefects = 165;
dpmo.NumOfDefectOpportunities = 6;

Then the .Analyze() method is called to perform the analysis. Subsequently, the user can retrieve the analysis results from the .Result object in the ProcessPerformanceFrDPMO object.  

The Analyze() method is implemented as follows:

/// <summary>
/// Calculate the process performance from DPMO
/// </summary>
public void Analyze()
{
    DPO = (double)D / N / O;
    DPMO = DPO * 1000000;
    yieldInPercent = 100 * (1 - DPO);
    //Result
    Result.DPO = DPO;
    Result.DPMO = DPMO;
    Result.YieldInPercent = yieldInPercent;
 }

Conclusion

The program presented here provides a simple way to obtain process performance through DPMO.

History

• 8 June 2012: Initial post.