PoissonPointProcess
RandomPointConfiguration
PointCountDistribution
NProbability
CDF
FindRoot

Engineering
System Modeling

Analyze Faulty Pixel Distributions in LCD Displays

Use a Poisson point process to model faulty pixels on an LCD display and compute manufacturing acceptance rates

Open in Cloud
Download Notebook

An LCD display can be modeled as a rectangular region in which faulty pixels occur independently at random. This example models faulty pixels with a spatial Poisson point process, computes the proportion of 1920×1080 displays that are accepted when at most 15 pixels are faulty, and then determines the largest pixel failure rate that still gives at least a 90% acceptance rate for a 4000×2000 display.

Define the faulty-pixel process and the display region:

In[1]:=

faultProcess=PoissonPointProcess[5

-6

,2];

In[2]:=

display=Rectangle[{0,0},{1920,1080}];

Generate sample faulty-pixel configurations to visualize possible defect patterns on the display:

In[3]:=

SeedRandom[1234];samples=RandomPointConfiguration[faultProcess,display,3]

Out[3]=

SpatialPointData

Data Type: Cartesian

Number of Points: {15,5,11}

Dimension: 2



Visualize a sample display, highlighting faulty pixels:

In[4]:=

ListPlot[samples,PlotRange{{0,1920},{0,1080}},AspectRatio1080/1920,AxesLabel{"x","y"}]

Out[4]=

Compute the acceptance rate by evaluating the probability that the number of faulty pixels does not exceed 15:

In[5]:=

NProbability[n≤15,nPointCountDistribution[faultProcess,display]]

Out[5]=

0.937281

Define a larger display and express its acceptance rate as a function of the pixel failure rate:

In[6]:=

display2=Rectangle[{0,0},{4000,2000}];

In[7]:=

prob=Probability[n≤15,nPointCountDistribution[PoissonPointProcess[λ,2],display2]]

Out[7]=

GammaRegularized[16,8000000λ]

Plot how the acceptance rate changes as the pixel failure rate varies:

In[8]:=

LogLogPlot[prob,{λ,

-7

-5

},GridLinesAll,FrameTrue,FrameLabel{"Pixel Failure Rate",None},PlotLabel"LCD Acceptance Rate"]

Out[8]=

Find the largest pixel failure rate that still gives at least a 90% acceptance rate:

In[9]:=

Maximize[{λ,prob≥0.90&&

-6

<λ<2*

-6

},λ,Reals]

Out[9]=

{1.39191×

-6

,{λ1.39191×

-6

}}

Check the result:

In[10]:=

CDF[PointCountDistribution[PoissonPointProcess[λ,2],display2],15]/.Last[%]

Out[10]=

0.9

Related Symbols

PoissonPointProcess
RandomPointConfiguration
PointCountDistribution
NProbability
CDF
FindRoot

Publisher Information

Contributed by: Wolfram staff

Wolfram Language Example Repository

Analyze Faulty Pixel Distributions in LCD Displays

See Also

Publisher Information