Need help with your Discussion

Get a timely done, PLAGIARISM-FREE paper
from our highly-qualified writers!


Quality Control

Quality Control

Sample Answer 

Quality Control

Problem 2

Control limits are horizontal lines placed above (UCL) and below (LCL) the centre line; they are used to determine if a process is out of control.

To determine the control limits, first, compute the mean () of the provided samples and apply the UCL and LCL formulas.

x ̅=(∑_(i=1)^n▒x_i )/n
σ=√((∑_(i=1)^n▒〖(x_i-x ̅)〗^2 )/(n-1))
UCL=x ̿+zσ_x ̅
LCL=x ̿-zσ_x ̅
σ_x ̅ =σ/√n

Finding the mean for each sample.

Samples of shampoo bottle volume in Ounces
Sample 1 2 3 4 Mean
1 19.7 20.6 18.9 20.8 20
2 19.7 20.2 18.9 20.7 19.875
3 19.7 18.7 21.6 20 20
Total 59.875

Finding the center line, which is the average of the samples.

x ̿=59.875/3=19.958

Finding the upper and lower control limits.

UCL=x ̿+zσ_x ̅ =19.958+3(0.2/√4)=20.258

The upper control limit is 20.258

UCL=x ̿+zσ_x ̅ =19.96-3(0.2/√4)=19.658

The lower control limit is 19.658.

The center line is always between the UCL and the LCL, and is equal to 19.958

Problem 4

X-bar/mean charts are used to evaluate deviations in a certain process. They evaluate the dispersion of a process results; the mean is considered the central tendency, and the upper and lower control limits are considered the extreme limits in relation to the dispersion.

The UCL and LCL are calculated using the formulas below:

UCL=x ̿+A_2 R ̅
LCL=x ̿-A_2 R ̅

R-charts identify the variability in a process by evaluating the process ranges.

The UCL and LCL are calculated as follows:

UCL=D_4 R ̅
LCL=D_3 R ̅


x ̿=mean of sample
R ̅=mean of sample range
A_2=x bar charts sigma control limit
D_n=R charts sigma control limits

Sample 1 2 3 4 Average Range
1 16.4 16.11 15.9 15.78 16.0475 0.62
2 15.97 16.1 16.2 15.81 16.02 0.39
3 15.91 16 16.04 15.92 15.9675 0.13
4 16.2 16.21 15.93 15.95 16.0725 0.28
5 15.87 16.21 16.34 16.43 16.2125 0.56
6 15.43 15.49 15.55 15.92 15.5975 0.49
7 16.43 16.21 15.99 16 16.1575 0.44
8 15.5 15.92 16.12 16.02 15.89 0.62
9 16.13 16.21 16.05 16.01 16.1 0.2
10 15.68 16.43 16.2 15.97 16.07 0.75
  Total       160.135 4.48

Range = Maximum Observation – Minimum Observation

Finding the center line for both x-bar charts and R-charts.

x ̿=160.135/10=16.01
R ̅=(Total Range)/(Number of Samples)=4.48/10=4.45

Calculating the UCL and LCL for x-bar charts:


The x bar chart is shown below.

X Bar Chart

X Bar Chart

The 6th sample is outside the control limit meaning the process is out of control.

Finding UCL and LCL for R-chart.


Plotting the R-chart.

R Chart

R Chart

Since the samples are within the control limits, the variability of the process is within control.

To determine if the process is capable of meeting the design standards, calculate the  Measure.

C_pk=min((16.34-16.01)/3(0.45/√4) ,(16.01-15.68)/3(0.45/√4) )

Since C_pk Is less than 1, the process cannot meet the design standard.


Reid, R. D., & Sanders, N. R. (2016). Operations Management, Binder Ready Version: An Integrated Approach. John Wiley & Sons.


We’ll write everything from scratch


[u04a1] Unit 4 Assignment 1 Quality Control

Complete problems 2 and 4 on pages 227–228 of your textbook. For help on how to complete these problems, see the Solved Problems on pages 222–227.

Quality Control

Quality Control

When completed, submit your answers as an attachment to this assignment. Be sure to include your work with your answers.


Quality Control Scoring Guide

Due Date: Unit 4
Percentage of Course Grade: 2%.

Accurately solves all computation aspects of the quality control problem.
Accurately solves all computation aspects of the problem and shows work.
Provides summary, and/or rationale useful in interpreting the quality control results.
Accurately summarizes salient points with supporting rationale for interpreting results.


Have a similar assignment? "Place an order for your assignment and have exceptional work written by our team of experts, guaranteeing you A results."

Order Solution Now


Our Service Charter

1. Professional & Expert Writers: Eminence Papers only hires the best. Our writers are specially selected and recruited, after which they undergo further training to perfect their skills for specialization purposes. Moreover, our writers are holders of masters and Ph.D. degrees. They have impressive academic records, besides being native English speakers.

2. Top Quality Papers: Our customers are always guaranteed of papers that exceed their expectations. All our writers have +5 years of experience. This implies that all papers are written by individuals who are experts in their fields. In addition, the quality team reviews all the papers before sending them to the customers.

3. Plagiarism-Free Papers: All papers provided by Eminence Papers are written from scratch. Appropriate referencing and citation of key information are followed. Plagiarism checkers are used by the Quality assurance team and our editors just to double-check that there are no instances of plagiarism.

4. Timely Delivery: Time wasted is equivalent to a failed dedication and commitment. Eminence Papers are known for the timely delivery of any pending customer orders. Customers are well informed of the progress of their papers to ensure they keep track of what the writer is providing before the final draft is sent for grading.

5. Affordable Prices: Our prices are fairly structured to fit in all groups. Any customer willing to place their assignments with us can do so at very affordable prices. In addition, our customers enjoy regular discounts and bonuses.

6. 24/7 Customer Support: At Eminence Papers, we have put in place a team of experts who answer all customer inquiries promptly. The best part is the ever-availability of the team. Customers can make inquiries anytime.

We Can Write It for You! Enjoy 20% OFF on This Order. Use Code SAVE20

Stuck with your Assignment?

Enjoy 20% OFF Today
Use code SAVE20