A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 mm and an upper specification limit of 23.2 mm. The standard deviation is 0.1 mm and the mean is 23 mm. The process capability index for the process is ___ (round up to two decimal places).

Explanation:

The CP value measures the ability of a production process to manufacture products that are within the tolerance required by a customer. The higher the cpk, the higher the ability of the product to meet expected requirements.

CPK=min (USL-μ/3σ, μ-LSL/3σ)

CPK=min(23.2-23/3*0.12/, 23-22.8/3*0.1)

CPK=min(0.2/0.3,0.2/0.3)

CPK=min/0.67,0.67)

A CPK of less than 1.0 means that the process is not capable of meeting its requirements.

Here at least 86.8% of the tires are good.

USL= Upper specification limit=23.2m

LSL= Lower specification limit=22.8m

μ=mean=23m

σ=standard deviation=0.1m

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