Question

A process is in statistical control with ?̿ = 39.7 and ? = 2.5. The control chart uses a sample size of ? = 2. Specifications for the process are at 40±5. The quality characteristic is normally distributed. What is the process capability ratio?

Answer 1

Given,

= 39.7

= 2.5

n = 2

d_{​​​​​​2}​​​​​ = 1.128 (from control chart factor)

Specification for the process = 40 5

Upper Specification U = 40+5 = 45

Lower Specification L = 40-5 = 35

Process Standard Deviation

= / d^{​​​​​​}_{​​​​​​2}​  

= 2.5/1.128

= 2.2163

Therefore, the capability ratio C_{​​​​​​p} ,

C_{​​​​​​p}  = (Upper Specification−Lower Specification)/6

= (45 - 35)/6*2.2163

= 10/13.2978

= 0.752

Therefore, the process capability ratio is C_{​​​​​​p} = 0.75 .

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