Concept explainers
To develop: Appropriate control chart and determine whether there is any cause for concern in the cutting process.
Introduction: Control charts used to determine whether the process is under control or not. Attributes and variables are the factors under the control charts.
Explanation of Solution
Given information:
The following information is given:
Develop appropriate control chart:
To check whether the process is in control, create the appropriate control charts for the mean
Determine mean of the averages:
It can be calculated by taking the average of all given values for
Hence, the mean of averages
Determine mean of the ranges:
It can be calculated by taking the average of all given values for R.
Hence, the mean of ranges is
Determine the upper control limit and lower control limit of
Determine the upper control limit (UCL) and the lower control limit (LCL) of the
Here, the overall mean
Given the
Substitute into the equation (1),
Substitute into the equation (2),
Hence, the upper control limit is
Determine the upper control limit and lower control limit of
Determine the upper control limit (UCLR) and lower control limit (LCLR) of the
Here,
Given the sample size of 4 for
Substitute into the equation (3),
Similarly, substitute in equation (4),
Hence, the upper control limit is
Draw the control chart for the sample means:
The process mean is
Observe that all the sample means are well within the control limits. The first five observations are above the mean of the averages.
Draw the control chart for the sample range:
The average range is
Observe that all the sample ranges are well within the control limits
Hence, the process seems to be in “statistical control”. (However, a process for making precision wires obviously should not have so much of variation in the mean or in the range.)
Want to see more full solutions like this?
Chapter 6 Solutions
EBK PRINCIPLES OF OPERATIONS MANAGEMENT
- Explain how to contruct process control chart and use them to determine whether a process is out of statistical control.arrow_forwardDescribe how to construct process control charts and use them to determine whether a process is out of statistical control.arrow_forwardConstruct a 3-sigma X-bar chart for the length in centimeters of a part from the following tabble . What is the upper controt limit? sample observation 1 observation 2 observation 3 observation 4 1 0.486 0.499 0.493 0.511 2 0.499 0.506 0.516 0.494 3 0.496 0.5 0.515 0.488 4 0.495 0.506 0.483 0.487 5 0.472 0.502 0.526 0.469 6 0.473 0.495 0.507 0.493 7 0.495 0.512 0.49 0.471 8 0.525 0.501…arrow_forward
- A manufacturer uses statistical process control to control the quality of the firm's products. Samples of 50 of Product A are taken, and a defective/acceptable decision is made on each unit sampled. For Product B, the number of flaws per unit is counted. What type(s) of control charts should be used? Select one: a. c-chart for A, mean and range charts for B b. p-chart for A , mean and range charts for B c. c-chart for both A and B d. p-chart for A, c-chart for B e. p-charts for both A and Barrow_forwardHermitage DNA Labs, LLC collected temperature readings in an analysis process. The data can be found in the Problems Data Compute the mean and range of each sample and calculate control limits for x-bar and R charts using the appropriate From the charts constructed, does the process appear to be in statistical control?arrow_forwardIn a fabric manufacturing factory, the quality control process using control charts from SPC. In an hour there are a total of 5 samples are taken each having 5 observations regarding the thickness of fabric in measured in millimeters In a particular hour, the sample means (X-bar) are noted to be: 172.11, 219.58, 208.24, 112.44, and 123.30 respectively. In the same sample, the corresponding ranges are: 13.17, 3.38, 15.34, 13.0 , and 13.02 respectively What are the lower and upper control limits for the X-bar chart? a . 157.21 , 177.05 b. 146.01, 157.87 c. 159.25, 175.02 d. 142.92, 160.66 e. 143.55, 165.47 f. None is correctarrow_forward
- A local steel pipe manufacturing company makes pipes. In a quality control assessment, a total of five (05) samples are collected with four (04) observations within each sample. The sample means (X-bar) are; 14.09, 13.94, 16.86, 18.77, and 16.64 respectively. Next, the corresponding ranges are; 9.90, 7.73, 7.89, 7.56, and 5.50 respectively. The lower and upper control limits of the R-chart are_ respectively Oa. None is correct O b. 0,16.68 O c. 0, 17.59 O d. 0,17.32 O e. 1, 10.5arrow_forwardExplain how can a Pareto chart used to improve quality?arrow_forwardCheckout time at a supermarket is monitored using a mean and a range chart. Six samples of n = 20 observations have been obtained and the sample means and ranges computed:arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,Operations ManagementOperations ManagementISBN:9781259667473Author:William J StevensonPublisher:McGraw-Hill EducationOperations and Supply Chain Management (Mcgraw-hi...Operations ManagementISBN:9781259666100Author:F. Robert Jacobs, Richard B ChasePublisher:McGraw-Hill Education
- Purchasing and Supply Chain ManagementOperations ManagementISBN:9781285869681Author:Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. PattersonPublisher:Cengage LearningProduction and Operations Analysis, Seventh Editi...Operations ManagementISBN:9781478623069Author:Steven Nahmias, Tava Lennon OlsenPublisher:Waveland Press, Inc.