Question

Question: Prepare X -and R-charts using these data with the method described in the chapter

Short answer

Answer

Thebar X and R chartis a type of statistical process monitoring scheme, also known as a control chart.

Step-by-step solution

Determining the X-bar charts

As given,

A2 = 0.73

D3 = 0

D4 = 2.28

N = 4

Calculating the upper and lower limits of X-bar -

Where,

$\stackrel{=}{x}$= 30.40289

$A_2$= 0.73

$\stackrel{-}{R}$= 5.932155

Upper Control Limit = $\stackrel{=}{x}+A_2\stackrel{-}{R}$

= 30.40289 + (0.73 x 5.932155)

= 30.40289 + 4.33047

= 34.73

Lower Control Limit =$\stackrel{=}{x}-A_2\stackrel{-}{R}$

= 30.40289 - (0.73 x 5.932155)

= 30.40289 - 4.33047

= 26.07

The bar chart is represented below:

 Determining the R-chart

Given,

A2 = 0.73

D3 = 0

D4 = 2.28

Calculating the upper and lower limits of R-bar -

Upper Control Limit =${\text{D}}_4\stackrel{-}{R}$

= 2.28 X 5.932155

= 13.53

Lower Control Limit =${\text{D}}_3\stackrel{-}{R}$

= 0 X 5.932155

= 0

The R-chart is represented below:

The chart is shown below: