Histogram as a Component of Seven Basic Quality Tool

本文介绍了直方图作为一种质量工具的基本概念及其在预防和纠正措施中的应用。通过实例展示了如何从检查表中提取数据来构建直方图,并解释了其在计划质量和控制质量过程中的作用。

Histogram is a bar chart to show frequencies of causes of problems to understand preventive or corrective action.
PMBOK(r) Guide fifth Edition defines Histogram as:

“A special form of bar chart used to describe the central tendency, dispersion, and shape of a statistical distribution”

A histogram is a way to represent tabulated frequencies shown as adjacent rectangles.

Development of Histogram:

Check sheet is used as an input to develop histogram, Please refer to the Blog Check Sheet as a Component of Seven Basic Quality Tool 
To get more details about check sheet;
As a reference, I am using the same example as used in check sheet:
An IT test team member is evaluating work products to detect problems from the specifications. Team may choose to categorise data about quality problems in following categories:
Categories suggested by Roger S. Pressman:

  1. Incomplete or erroneous specification (IES)
  2. Misinterpretation of customer communication (MCC)
  3. Intentional deviation from specifications (IDS)
  4. Violations of programming standards. (VPS)
  5. Error in data representations (EDR)
  6. Inconsistent component interface (ICI)
  7. Error in design logic (EDL)
  8. Incomplete or erroneous testing (IET)
  9. Inaccurate or inconsistent documentation (IID)
  10. Error in programming language translation of design (PLT)
  11. Ambiguous or inconsistent human/computer interface (HCI)
  12. Miscellaneous (MIS)

While examination the work product, test team member assesses the defects and enter frequencies in their respective category of causes like:
Check Sheet suggested by roger s. pressman in software engineering a practitioner’s approach

Error Causes Total Serious Moderate Minor
Error Frequency % Frequency % Frequency % Frequency %
IES 205 22% 34 27% 68 18% 103 24%
MCC 156 17% 12 9% 68 18% 76 17%
IDS 48 5% 1 1% 24 6% 23 5%
VPS 25 3% 0 0% 15 4% 10 2%
EDR 130 14% 26 20% 68 18% 36 8%
ICI 58 6% 9 7% 18 5% 31 7%
EDL 45 5% 14 11% 12 3% 19 4%
IET 95 10% 12 9% 35 9% 48 11%
IID 36 4% 2 2% 20 5% 14 3%
PLT 60 6% 15 12% 19 5% 26 6%
HCI 28 3% 3 2% 17 4% 8 2%
MIS 56 6% 0 0% 15 4% 41 9%
Total 942 100% 128 100% 379 100% 435 100%

As a further explanation, first two columns are used to develop Pareto chart, as shown below:

Error  Causes Frequency
IES 205
MCC 156
IDS 48
VPS 25
EDR 130
ICI 58
EDL 45
IET 95
IID 36
PLT 60
HCI 28
MIS 56
Total 942

Now using excel we can develop Histogram, as mentioned below:
histogram
Histogram is showing using bar chart that most of the frequencies of causes are coming from IES. MCC and EDR and we need to take corrective action to solve the source of problems.

Usage of histogram:

I am describing usage of Histogram in context of “Plan Quality” and “Control Quality”
When Histogram is used in “Plan Quality”, serves as a preventive approach to improve processes where historical data is used to identify categories of causes effecting most. Processes are selected to improve, for example due to higher frequencies in IES, MCC and EDR we may select improvements in “Collect Requirement”, “Define Scope” processes.
Histogram is used in “Control Quality” to identify causes of poor performance in process and work products.
Difference between Pareto Chart and Histogram:

Histogram Pareto Chart
Histogram is a kind of bar chart showing a distribution of variables or causes of problems. A Pareto chart is a specific type of histogram that represents causes of problems by their overall influence. This is an effective tool to prioritise corrective action as errors with greatest impact are displayed in descending order of frequency.
A histogram represents cause of a problem as a column and the frequency of each cause of problem as the height of the column. In addition an arc representing the cumulative percentage of frequencies of causes is also included.

In short, A histogram is a bar chart that show the frequency of a cause of a problem occurring using the height of the bar as an indicator.
I hope this blog has sufficiently answered your all queries related to Histogram. Good Luck with your PMP® Certification Exam.
You can join the discussion on the same in our Forum. You may also want to check our other blogs PMP® Trainings.


### 回答1: 在ROOT中创建直方图的代码如下: ``` #include <TH1D.h> #include <TCanvas.h> #include <TRandom.h> void histogram() { TH1D *h = new TH1D("h", "Example Histogram", 100, -4, 4); TRandom r; for (int i = 0; i < 10000; i++) { h->Fill(r.Gaus(0, 1)); } TCanvas *c = new TCanvas("c", "Example Histogram", 800, 600); h->Draw(); c->SaveAs("histogram.pdf"); } ``` 这段代码创建了一个名为"h"的1维直方图,包含了100个柱子,数据范围在-4到4之间。然后使用TRandom生成了10000个高斯分布的随机数,并将它们填入直方图。最后,创建了一个TCanvas,将直方图绘制到画布上,并将画布保存为PDF文件。 ### 回答2: 在ROOT中创建直方图的代码可以通过以下步骤实现: 首先,我们需要在程序中导入必要的文件以使用ROOT的相关功能。代码如下所示: ```cpp #include <TH1.h> #include <TCanvas.h> #include <TROOT.h> #include <TRandom.h> ``` 接下来,我们需要创建一个TCanvas对象,它将用于显示直方图。代码如下所示: ```cpp TCanvas *c1 = new TCanvas("c1", "Histogram", 800, 600); c1->SetFillColor(kWhite); ``` 然后,我们可以定义并填充直方图。在本例中,我们将使用随机数生成器来填充一个100个数的直方图。代码如下所示: ```cpp TH1F *histogram = new TH1F("histogram", "Example Histogram", 100, 0, 100); TRandom random; for (int i = 0; i < 100; i++) { double value = random.Gaus(50, 10); // 使用高斯分布生成随机数 histogram->Fill(value); } ``` 接下来,我们可以设置直方图的各种属性,例如标题、坐标轴名称和线条颜色等。代码如下所示: ```cpp histogram->SetTitle("Example Histogram"); histogram->GetXaxis()->SetTitle("x"); histogram->GetYaxis()->SetTitle("Counts"); histogram->SetLineColor(kBlue); ``` 最后,我们可以使用c1对象来在屏幕上绘制直方图。代码如下所示: ```cpp histogram->Draw(); c1->Update(); ``` 以上就是在ROOT中创建直方图的代码示例。你可以根据需要进一步修改和扩展此代码,以满足你的具体需求。 ### 回答3: 在ROOT中创建直方图的代码如下: ```cpp #include <TH1F.h> #include <TCanvas.h> void createHistogram() { // 创建一个直方图对象 TH1F *histogram = new TH1F("histogram", "Histogram", 100, 0, 10); // 向直方图中添加数据点 histogram->Fill(2); histogram->Fill(4); histogram->Fill(5); histogram->Fill(7); // 创建一个画布对象 TCanvas *canvas = new TCanvas("canvas", "Histogram Canvas", 800, 600); // 将直方图绘制在画布上 histogram->Draw(); // 显示画布 canvas->Draw(); } ``` 首先,我们使用`TH1F`类创建了一个名为`histogram`的直方图对象,它有100个bin,范围从0到10。然后,通过`Fill()`函数向直方图添加了数据点,这里添加了4个数据点:2、4、5和7。 接下来,我们创建了一个名为`canvas`的画布对象,它的尺寸为800x600像素。我们使用`Draw()`函数将直方图绘制在画布上,然后使用`Draw()`函数将画布显示出来。 这段代码实现了在ROOT中创建直方图的基本操作,你可以根据实际需求调整直方图的参数和数据点。
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