Question

A control chart for the number nonconforming is to be established, based on samples of size 400. To start the control chart, 30 samples were selected and the number nonconforming in each sample determined, yielding Σ'1D,-1.200 What are the parameters of the np chart?

Answer 1

The parameters of the np chart are
`\(n = 400\)` (sample size) and
`\(p\)`(probability of nonconformity) is calculated as
`\(p = (\Sigma' 1D)/(n * k)\), where \(\Sigma' 1D = -1.200\) and \(k = 30\)`

(number of samples).

Step-by-step explanation:

To establish the np chart parameters, we use the formula
`\(p = (\Sigma' 1D)/(n * k)\), where \(n\`

is the sample size and
`\(k\)` is the number of samples. In this case,
`\(n = 400\)` and \(k = 30\). The given data
`\(\Sigma' 1D = -1.200\)` represents the sum of the number of nonconforming units across the 30 samples.

Substituting these values into the formula:

`\[ p = (-1.200)/(400 * 30) \]`

This calculation yields the probability of nonconformity (\(p\)). The resulting \(p\) value is a key parameter for the np chart, representing the average proportion of nonconforming units in a sample.

The final parameters for the np chart are
`\(n = 400\)` and
`\(p\` as calculated above. These parameters are crucial for monitoring and maintaining the quality of a process, allowing for the detection of shifts in the proportion of nonconforming units. The np chart is a valuable tool in statistical process control, providing insights into the stability and performance of a process over time.