EBK PRINCIPLES OF OPERATIONS MANAGEMENT
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
11th Edition
ISBN: 9780135175644
Author: Munson
Publisher: VST
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Chapter 6.S, Problem 10P

a)

Summary Introduction

To determine: The value of σx .

Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.

a)

Expert Solution
Check Mark

Answer to Problem 10P

The value of σx is 0.61.

Explanation of Solution

Given information:

The following information is given:

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  1

Sample size is given as 5 and process standard deviation is given as 1.36.

Determine σx :

The standard deviation of the sample means denoted by σx¯ is calculated by the following formula

σx¯=σn

Here,

σ refers to process standard deviation

n refers to the sample size.

The given values are σ=1.36 and sample size n=5 , substitute the values in the above formula:

σx¯=σn=1.365=1.362.23=0.61

The standard deviation of the sample means σx¯=0.61

b)

Summary Introduction

To determine: The control limits for the mean chart if the value of z is 3.

Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.

b)

Expert Solution
Check Mark

Answer to Problem 10P

The UCL value of x¯ is 11.83 and the LCL value is 8.17.

Explanation of Solution

Given information:

The following information is given:

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  2

Sample size is given as 5 and process standard deviation is given as 1.36.

Determine the control limits for the mean chart if the value of z is 3:

Formulae to calculate control limits:

UCL=x¯¯+z×σx¯ (1)

LCL=x¯¯z×σx¯ (2)

Here,

The value of z=3

x¯¯ is the mean of the sample means

the standard deviation of the mean σx¯=0.61

Calculate the average for each sample:

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  3

Working note:

Average for sample #1:

It is calculated by dividing the total of sample #1 and sample size.

Average=Total of Sample #1Sample size=515=10

Note: The same continues for all the samples.

Calculate the value of x¯¯ :

It is calculated by dividing the sum of average of all the samples and the number of samples. Hence, the value of x¯¯ is 10.

x¯¯=Average of all samplesNumber of samples=10+10+10.2+10.2+10.4+9.8+9.6+9.8+9.8+1010=10

Substitute the values in equation (1)to determine the value of UCL as follows:

UCL=x¯¯+z×σx¯=10+3×(0.61)=10+1.83=11.83

Hence, the UCL value is 11.83.

Substitute the values in equation (2) to determine the value of LCL as follows:

LCL=x¯¯z×σx¯=103×(0.61)=101.83=8.17

Hence, the LCL value is 8.17.

c)

Summary Introduction

To determine: The control limits for the range chart.

Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.

c)

Expert Solution
Check Mark

Answer to Problem 10P

The UCL value of R-chart is 6.9795 and the LCL value is 0.

Explanation of Solution

Given information:

The following information is given:

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  4

Sample size is given as 5 and process standard deviation is given as 1.36.

Determine the control limits for the mean chart if the value of z is 3:

Formulae to calculate control limits:

UCLR=D4×R¯ (3)

LCLR=D3×R¯ (4)

Here,

D3 refers to the lower range factor

D4 refers to the upper range factor

R¯ refers to the average range

Substitute the values in equation (3) to determine the value of UCL as follows:

UCLR=D4×R¯=2.115×3.3=6.9795

Hence, the UCL value is 6.9795.

Substitute the values in equation (4) to determine the value of LCL as follows:

LCLR=D3×R¯=0

Hence, the LCL value is 0.

d)

Summary Introduction

To determine: Whether the process is in control.

Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.

d)

Expert Solution
Check Mark

Answer to Problem 10P

The process is in statistical control.

Explanation of Solution

Given information:

The following information is given:

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  5

Sample size is given as 5 and process standard deviation is given as 1.36.

Plot the sample mean values in the x¯ control chart where UCLx¯=11.83 and LCLx¯=8.17

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  6

Plot the sample mean values in theR-control chart where UCLR=6.9795oz and LCLR=0

EBK PRINCIPLES OF OPERATIONS MANAGEMENT, Chapter 6.S, Problem 10P , additional homework tip  7

The sample range values lie well within the upper control limit and lower control limits.

The process is in statistical control.

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EBK PRINCIPLES OF OPERATIONS MANAGEMENT

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