Loose-leaf For Applied Statistics In Business And Economics
Loose-leaf For Applied Statistics In Business And Economics
5th Edition
ISBN: 9781259328527
Author: David Doane, Lori Seward Senior Instructor of Operations Management
Publisher: McGraw-Hill Education
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Chapter 17, Problem 44CE

(a)

To determine

Find the Cp and Cpk indexes for a process with LSL=540,USL=550,σ=1.25,μ=545.

(a)

Expert Solution
Check Mark

Answer to Problem 44CE

The value of Cp is 1.33.

The value of Cpk is 1.33.

Explanation of Solution

Calculation:

The given information is that, LSL=540,USL=550,σ=1.25,μ=545.

The formula for Cp is,

Cp=USLLSL6σ

In the formula, USL denotes the upper specification limit, LSL denotes the lower specification limit, σ denotes the magnitude of the process variation.

The formula for Cpk is,

Cpk=min(μLSL,USLμ)3σ

In the formula, USL denotes the upper specification limit, LSL denotes the lower specification limit, σ denotes the magnitude of the process variation, μ is the center line.

Cp:

Substitute, LSL=540,USL=550,σ=1.25,μ=545 is the formula of Cp.

Cp=5505406(1.25)=107.5=1.33

Hence, the value of Cp is 1.33.

Cpk:

Substitute, LSL=540,USL=550,σ=1.25,μ=545 is the formula of Cpk.

Cpk=min(545540,550545)3(1.25)=min(5,5)3.75=53.75=1.33

Hence, the value of Cpk is 1.33.

(b)

To determine

Find the Cp and Cpk indexes for a process with LSL=540,USL=550,σ=1.25,μ=543.

(b)

Expert Solution
Check Mark

Answer to Problem 44CE

The value of Cp is 1.33.

The value of Cpk is 0.80.

Explanation of Solution

Calculation:

The given information is that LSL=540,USL=550,σ=1.25,μ=543.

The formula for Cp is,

Cp=USLLSL6σ

In the formula, USL denotes the upper specification limit, LSL denotes the lower specification limit, σ denotes the magnitude of the process variation.

The formula for Cpk is,

Cpk=min(μLSL,USLμ)3σ

In the formula, USL denotes the upper specification limit, LSL denotes the lower specification limit, σ denotes the magnitude of the process variation, μ is the center line.

Cp:

Substitute LSL=540,USL=550,σ=1.25,μ=543 is the formula of Cp.

Cp=5505406(1.25)=107.5=1.33

Hence, the value of Cp is 1.33.

Cpk:

Substitute, LSL=540,USL=550,σ=1.25,μ=543 is the formula of Cpk.

Cpk=min(543540,550543)3(1.25)=min(3,7)3=33.75=0.80

Hence, the value of Cpk is 0.80.

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Chapter 17 Solutions

Loose-leaf For Applied Statistics In Business And Economics

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