Q 575. Laney P' Chart - Laney P' Chart is an advanced variation of the traditional NP and P charts. Compare the three different control charts with their advantages and disadvantages. What are the specific conditions under which you will prefer to use a Laney P' chart. Provide an example to support your answer.

 

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The Laney’s P chart is based on the working principle of a p chart used for attribute data– the difference being that it adjusts for very large sample sizes(usually > 5000), to provide an accurate assessment of control points than in a p chart.

 

It is difficult to assess the statistical control of the proportion due to the over dispersion of results, with a normal p chart. Points on a p chart are shown out of control due to over dispersion. Laney’s sigma Z is a measure of over dispersion. While attribute p chart shows points out of control ,applying same data to plot Laney’s p chart shows points in control.

 

The advantage of the p chart is that it gives us the proportion defective in y axis & np chart gives us the whole number of defective in y axis.

while Laney's p chart has the advantage of using varying control limits - it avoids the variation due to over dispersion, in case of higher sample size ( of more than 5000).

 

The disadvantage of p chart is that its predictions may not be accurate if the population has varying sub groups. Hence under such specific conditions of sample size more than 5000 with varying sub groups Laney's P chart is used.

 

Let us take example of our central Govt planning to set up Temporary health care bedded hospitals in Tier 1 towns to tackle the pandemic. And let us say the each Tier 1 city has population varying between 5000 ~ 35000 , out of which % proportion of the people who are attacked by the COVID need hospitalization in let us say 10 such cities is the vital input to the govt to plan the priority. In this case use of p chart would give us over dispersion of results.so the statistical dept shall use Laney's p chart to calculate the proportion using varying control limits and also addressing the variation of the large sample using the Laney's sigma which is not expressed as binomial as in a normal p chart. In this way the govt can really find the tier 1 cities for which the number of persons to be treated exceeds the broader control limits set by Laney's p chart. This is very useful to disregard the variation due to over dispersion or under dispersion .

 

 

A control chart is a visual tool for monitoring process efficiency with time. These graphs help with determining whether or not the process is stable. The process will only have inherent variation (common cause variation) if it is stable. The range of common cause variation is determined by control limits (Upper and Lower control limits). Outside of these parameters, any process variation is referred to as a special cause variation.
 

	Laney’s P Chart	NP Chart	P Chart
·	The Laney P' chart is used to track the percentage of defective products produced by the process and to correct for data over- or under dispersion. It is used when the subgroup/sample size is very large and assumptions are not met.	NP chart control chart for defectives. It helps in identifying the presence of Special causes when the data is defective and has a Fixed sample size and follows binomial distribution	P Chart is a control chart for defectives. It helps in identifying the presence of Special causes when the data is defective and has a Variable Sample size and follows binomial distribution
Pros	A Laney P' chart can more easily and accurately distinguish between common-cause variation and special-cause variation if your data show over- or under dispersion.	Np-charts are used to check for predictability and stability in the process as well as to track the outcome of process improvement theories. The number of nonconforming units in subgroups of set sizes is represented by the Np-chart.	P charts helps in identifying sudden system changes that have an identifiable cause. It show whether the system is in control and stable and compares two systems before and after a significant change.
Cons	It requires more data and is more complicated than a Standard P chart. When the process is unstable or the probability of non-conformance varies over time, Laney's P chart may be sensitive to small sample sets and have limited applicability.	Np chart requires various complex calculations which make them more challenging to use.Setting proper control limits can be more difficult because the control limits for an NP-chart rely on how many units were inspected. It becomes more sensitive to changes made during the inspection process, which needs gathering of more data.	P chart can only be used when the sample is fixed. They are based on small sample sizes which results in wider control limits making it difficult to identify changes in the process. They may not offer information about the fundamental reasons of non-conformance.

·       Laney’s P chart follows moving range factor which helps to adjust the variation in sample sizes making it more sensitive to the changes in the process. This helps to identify if the process is in control or going out of control and what is the source of problem.

·       It is used when the data being tracked contains a broad range of variance in sample sizes. This is because the shifting range factor accounts for sample size change, which can aid in stabilising the control limits and lowering false alarm rates.

·       It should be sued when the process is stable or else the control limits will results in inaccuracy and the chart may not be useful to detect changes in the process.

There were many answers to this question, however only 2 are visible as the others were not published. The others either failed the plagiarism or the AI generated content test or both. I request all participants to write the answers in their own words.

 

Best answer has been provided by Venkateswaran Kazhagamani.