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 45CE

In painting an automobile, the thickness of the color coat has a lower specification limit of 0.80 mil and an upper specification limit of 1.20 mils. Find the Cp and Cpk capability indexes if (a) the process mean is 1.00 mil and the process standard deviation is 0.05 mil; (b) the process mean is .90 mil and the process standard deviation is 0.05 mil.

(a)

Expert Solution
Check Mark
To determine

Find the Cp and Cpk indexes for a process with lower specification limit of 0.80 mil and an upper specification limit of 1.20 mils, process mean is 1.00 mil and the process standard deviation is 0.05.

Answer to Problem 45CE

The value of Cp is 1.33.

The value of Cpk is 1.33.

Explanation of Solution

Calculation:

The given information is that, lower specification limit is 0.80 mil and an upper specification limit is 1.20 mils, process mean is 1.00 mil and the process standard deviation is 0.05.

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=0.80,USL=1.20,σ=0.05,μ=1.00 is the formula of Cp.

Cp=1.200.806(0.05)=0.40.3=1.33

Hence, the value of Cp is 1.33.

Cpk:

Substitute, LSL=0.80,USL=1.20,σ=0.05,μ=1.00 is the formula of Cpk.

Cpk=min(1.000.80,1.201.00)3(0.05)=min(0.20,0.20)0.15=0.200.15=1.33

Hence, the value of Cpk is 1.33.

(b)

Expert Solution
Check Mark
To determine

Find the Cp and Cpk indexes for a process with lower specification limit of 0.80 mil and an upper specification limit of 1.20 mils, process mean is 0.90 mil and the process standard deviation is 0.05.

Answer to Problem 45CE

The value of Cp is 1.33.

The value of Cpk is 0.67.

Explanation of Solution

Calculation:

The given information is that, lower specification limit is 0.80 mil and an upper specification limit is 1.20 mils, process mean is 0.90 mil and the process standard deviation is 0.05.

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=0.80,USL=1.20,σ=0.05,μ=0.90 is the formula of Cp.

Cp=1.200.806(0.05)=0.40.3=1.33

Hence, the value of Cp is 1.33.

Cpk:

Substitute, LSL=0.80,USL=1.20,σ=0.05,μ=0.90 is the formula of Cpk.

Cpk=min(0.900.80,1.200.90)3(0.05)=min(0.10,0.30)0.15=0.100.15=0.67

Hence, the value of Cpk is 0.67.

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Chapter 17 Solutions

Loose-leaf For Applied Statistics In Business And Economics

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