Exercises Quality 1. Process Capability Ratio We want to produce a new item whic

Question

Exercises Quality 1. Process Capability Ratio We want to produce a new item which has a diameter of 3mm and a tolerance of 0.5 mm One of our machines produces with a precision of 0.1 mm (= our standard deviation of the production) Can we use this machine for this process? 2. Sigma level of the production We are producing the previous defined product with the same tolerances and we want to know what the sigma level of the production is. Also comment this result. Average production output is 3.2 mm Standard deviation of the production is 0.15 mm

Explanation / Answer

We have, Mean µ = 3 mm

Standard deviation = 0.1 mm

Upper specification USL = 3 mm + 0.5 mm = 3.5 mm

Lower specification LSL = 3 mm - 0.5 mm = 2.5 mm

The process capability index,

Cp = (USL –LSL)/6 = (3.5 -2.5) /6*0.1 = 1.67

Cpk= Min [(Mean – LSL)/3 *, (USL – Mean)/3* ]

= min [(3 – 2.5)/ 3* 0.1, (3.5 – 3)/ 3 * 0.1]

= min [(1.67, 1.67] = 1.67

Cpk =1.67 (more than 1)

The process is under control therefore we can use machine for this process.

Sigma level of production is denoted by sigma level of production, Z or Z-score

Z = (x – ) /

Where,

Average production output x = 3.2 mm

And standard deviation of the production =0.15 mm

Mean µ = 3 mm (given in above part)

Therefore,

Z = (3.2 - 3) / 0.15 = 1.33

Therefore the process is at a 1.33 sigma quality level.

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