Practical Operations Management
Practical Operations Management
2nd Edition
ISBN: 9781939297136
Author: Simpson
Publisher: HERCHER PUBLISHING,INCORPORATED
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Question
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Chapter 13, Problem 29P

(a)

Summary Introduction

Interpretation:

The place of indicating control limits on a mean chart by using the sampling procedure that produced the data.

Concept Introduction:

Control limits are the lines which define whether a process is out of control or not. These are the horizontal line which comes above and below the central line.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

The data is given as below.

    Sample Sample mean Sample range
    1350.85ml0.6ml
    2350.80ml0.8 ml
    3351.20ml0.5 ml
    4351.00 ml1.0 ml
    5350.62 ml0.8 ml
    6351.12 ml0.7 ml
    7351.50 ml0.8 ml

First, calculate the average of the sample mean.

  x=350.85+350.80+351.20+351.00+350.62+351.12+351.507x=351.013ml

Then calculate the average of the range.

  R=0.6+0.8+0.5+1.0+0.8+0.7+0.87R=0.743ml

Find the value of A2 from the mean chart table =0.48

Then,

Calculate the upper control limit by using below formula.

  UCL=x+A2*RUCL=351.013+0.48*0.743UCL=351.37

Next, calculate the lower control limit by using below formula.

  LCL=xA2*RLCL=351.0130.48*0.743LCL=350.65

(b)

Summary Introduction

Interpretation:

The position to indicate control limits on range chart by using the same sampling procedure that produced the data.

Concept Introduction:

Control limits are the lines which define whether a process is out of control or not. These are the horizontal line which comes above and below the central line.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

The data is given as below.

    Sample Sample mean Sample range
    1350.85ml0.6ml
    2350.80ml0.8 ml
    3351.20ml0.5 ml
    4351.00 ml1.0 ml
    5350.62 ml0.8 ml
    6351.12 ml0.7 ml
    7351.50 ml0.8 ml

Find the values of D3 and D4 from the range chart for a sample of 6.

  D3=2.00

  D4=0

Then calculate the average of the range.

  R=0.6+0.8+0.5+1.0+0.8+0.7+0.87R=0.743ml

Now, derive the upper control limit and lower control limit for the rage charts as shown below.

  UCL=D3*RUCL=2.00*0.743UCL=1.486mlAndLCL=D4*RLCL=0*0.743LCL=0

(c)

Summary Introduction

Interpretation:

Using the control limits in part a and part b, the sample is in control or not.

Concept Introduction:

Control limits are the lines which define whether a process is out of control or not. These are the horizontal line which comes above and below the central line.

(c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

The data is given as below.

New sample data are 350.82ml, 350.07 ml, 350.10 ml, 350.50 ml, 349.75 ml and 349.90 ml.

First, calculate the average of sample mean by using below formula.

  x=350.82+350.07+350.10+350.50+349.75+349.906x=350.19ml

Then, calculate the range by using below formula.

  R=uppersamplemeanlowersamplemeanR=350.82349.75R=1.07ml

In this, the upper control limit =351.37ml and lower control limit =350.65 ml . It is clear that the sample mean of new sample at 350.19 ml , which is outside the mean control limits.

Hence, the process is out of control.

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