In a double-sampling plan, a small sample is taken first; if the quality is very good, the lot is accepted, and if the sample is very poor, the lot is rejected. However, if the initial sample is incon- clusive, a second sample is taken and the lot is either accepted or rejected based on the combined results of the two samples. The objective of such a sampling procedure is to save costs relative to a single-sampling plan. For very good or very bad lots, the smaller, less expensive sample will suffice and a larger, more expensive sample is avoided.
A multiple-sampling plan, also referred to as a sequential-sampling plan, generally employs the smallest sample size of any of the sampling plans we have discussed. In its most extreme form, in- dividual items are inspected sequentially, and the decision to accept or reject a lot is based on the cumulative number of defective items. A multiple-sampling plan can result in small samples and, consequently, can be the least expensive of the sampling plans.
The steps of a multiple-sampling plan are similar to those for a double-sampling plan. An ini- tial sample (which can be as small as one unit) is taken. If the number of defective items is less than or equal to a lower limit, the lot is accepted, whereas if it exceeds a specified upper limit, the lot is rejected. If the number of defective items falls between the two limits, a second sample is obtained. The cumulative number of defects is then compared with an increased set of upper and lower limits, and the decision rule used in the first sample is applied. If the lot is neither accepted nor rejected with the second sample, a third sample is taken, with the acceptance/rejection limits revised upward. These steps are repeated for subsequent samples until the lot is either accepted or rejected.
Choosing among single-, double-, or multiple-sampling plans is an economic decision. When the cost of obtaining a sample is very high compared with the inspection cost, a single-sampling plan is preferred. For example, if a petroleum company is analyzing soil samples from various locales around the globe, it is probably more economical to take a single, large sample in Brazil than to return for additional samples if the initial sample is inconclusive. Alternatively, if the cost of sampling is low relative to inspection costs, a double- or multiple-sampling plan may be preferred. For example, if a winery is sampling bottles of wine, it may be more economical to use a sequential sampling plan, tasting individual bottles, than to test a large single sample con- taining a number of bottles, since each bottle sampled is, in effect, destroyed. In most cases in which quality control requires destructive testing, the inspection costs are high compared with sampling costs.
as the quality of the lots becomes poorer, it is more likely that bad lots will be identified and re- jected, and any defective items in these lots will be replaced with good ones.
S U M M A R Y
Four decades ago acceptance sampling constituted the primary means of quality control in many U.S. companies. However, it is the exception now, as most quality-conscious firms in the United States and abroad have either adopted or moved to- ward a quality-management program such as a OMS or Six
Sigma. The cost of inspection, the cost of sending lots back, and the cost of scrap and waste are costs that most companies cannot tolerate and remain competitive in today’s global mar- ket. Still, acceptance sampling is used by some companies and government agencies, and thus it is a relevant topic for study.
S U M M A R Y O F K E Y T E R M S
acceptable quality level (AQL) the fraction of defective items deemed acceptable in a lot.
acceptance samplinga statistical procedure for taking a random sample in order to determine whether or not a lot should be accepted or rejected.
average outgoing quality (AOQ)the expected number of defective items that will pass on to the customer with a sampling plan.
consumer’s risk() the profitability of accepting a lot in which the fraction of defective items exceeds the most (LTPD) the consumer is willing to accept.
lot tolerance percent defective (LTPD) the maximum percentage defective items in a lot that the consumer will knowingly accept.
operating characteristic (OC) curve a graph that measures the probability of accepting a lot for different proportions of defective items.
producer’s risk(␣) the probability of rejecting a lot that has an acceptable quality level (AQL).
sampling plana plan that provides guidelines for accepting a lot.
S O LV E D P R O B L E M
SINGLE-SAMPLE, ATTRIBUTE PLAN
PROBLEM STATEMENT
A product lot of 2000 items is inspected at a station at the end of the production process. Management and the product’s cus- tomer have agreed to a quality-control program whereby lots that contain no more than 2% defectives are deemed acceptable, whereas lots with 6% or more defectives are not acceptable. Furthermore, management desires to limit the
probability that a good lot will be rejected to 5%, and the cus- tomer wants to limit the probability that a bad lot will be ac- cepted to 10%. Using OM Tools, develop a sampling plan that will achieve the quality-performance criteria.
SOLUTION
The OM Tools solution is shown
as follows:
• Excel File
• Practice
Quizzes
QUESTIONS
S3-1. What is the difference between acceptance sampling and process control?
S3-2. Why are sample sizes for attributes necessarily larger than sample sizes for variables?
S3-3. How is the sample size determined in a single-sample attribute plan?
S3-4. How does the AQL relate to producer’s risk (␣) and the LTPD relate to consumer’s risk ()?
S3-5. Explain the difference between single-, double-, and multiple-sampling plans.
S3-6. Why is the traditional view of quality control reflected in the use of acceptance sampling unacceptable to adherents of quality management and continuous improvement.
S3-7. Under what circumstances is the total inspection of final products necessary?
S3-1. The Great Lakes Company, a grocery store chain, pur- chases apples from a produce distributor in Virginia. The grocery company has an agreement with the distributor that it desires shipments of 10,000 apples with no more than 2% defectives (i.e., severely blemished apples), although it will accept shipments with up to a maximum of 8% defective. The probability of rejecting a good lot is set at 0.05, whereas the probability of accepting a bad-quality lot is 0.10. Determine a sampling plan that will approximately achieve these quality performance criteria, and the operat- ing characteristic curve.
S3-2. The Academic House Publishing Company sends out the textbooks it publishes to an independent book binder.
When the bound books come back, they are inspected for defective bindings (e.g., warped boards, ripples, cuts, poor adhesion). The publishing company has an acceptable quality level of 4% defectives but will tolerate lots of up to 10% defective. What (approximate) sample size and accep- tance level would result in a probability of 0.05 that a good lot will be rejected and a probability of 0.10 that a bad lot will be accepted?
S3-3. The Metro Packaging Company in Richmond produces clear plastic bottles for the Kooler Cola Company, a soft- drink manufacturer. Metro inspects each lot of 5000 bottles before they are shipped to the Kooler Company. The soft- drink company has specified an acceptable quality level of 0.06 and a lot tolerance percent defective of 0.12. Metro currently has a sampling plan with n150 and c4. The two companies have recently agreed that the sampling plan
should have a producer’s risk of 0.05 and a consumer’s risk of 0.10. Will the current sampling plan used by Metro achieve these levels of αand β?
S3-4. The Fast Break Computer Company assembles personal computers and sells them to retail outlets. It purchases key- boards for its PCs from a manufacturer in the Orient. The keyboards are shipped in lots of 1000 units, and when they arrive at the Fast Break Company samples are inspected.
Fast Break’s contract with the overseas manufacturer specifies that the quality level that they will accept is 4%
defective. The personal computer company wants to avoid sending a shipment back because the distance involved would delay and disrupt the assembly process; thus, they want only a 1% probability of sending a good lot back. The worst level of quality the Fast Break Company will accept is 10% defective items. Using OM Tools develop a sampling plan that will achieve these quality-performance criteria.
S3-5. A department store in Beijing, China, has arranged to pur- chase specially designed sweatshirts with the Olympic logo from a clothing manufacturer in Hong Kong. When the sweatshirts arrive in Beijing in lots of 2000 units, they are inspected. The store’s management and manufacturer have agreed on quality criteria of AQL 2% defective and LTPD 8% defective. Because sending poor-quality ship- ments back to Hong Kong would disrupt sales at the stores, management has specified a low producer’s risk of 0.01 and will accept a relatively high consumer’s risk of 0.10.
Using OM Tools, develop a sampling plan that will achieve these quality-performance criteria.
PROBLEMS
• GO Tutorial
M
ars takes a cross-functional approach toproduct development in which people from R&D, plant operations, packaging, marketing, and other departments all play key andformalized roles. One difference in recent years is the inclusion of the extended supply chain. Supply chain partners make a good "bridge"
between functional units because they encompass external as well as internal suppliers of ingredients, equipment, packaging, and other components of a product launch, as well as the logistics involved in bringing them all together.
To begin with, Mars has a network of global R&D centers from the United States to the Netherlands, Poland, Russia, Australia, and the United Kingdom.
The R&D heads meet in person for a week-long planning session each year and follow up with quarterly updates and monthly conference calls. A global Wiki maintains an online dialog with Mars employees, and a vendors
assurance group gathers information and suggestions from suppliers.
Samples and prototypes of new products are sent out for others to comment on, and sometimes process engineers will switch places for awhile, say from Australia to the Netherlands, to share ideas. In the United States, Mars has three R&D centers. Hackettstown, New Jersey, is the corporate headquarters, the home of M&M’s and the place where flavanols were discovered.
Product Design 4
In this chapter, you will learn about . . .
The Design Process
Rapid Prototyping and Concurrent Design Technology in Design
Design Quality Reviews Design for Environment Quality Function Deployment Design for Robustness Web resources for
this chapter include OM Tools Software Internet Exercises Online Practice Quizzes Lecture Slides in
PowerPoint Virtual Tours Excel Worksheets Company and Resource Weblinks
Product Design AT MARS
www.wiley.com/college/russell
Elizabethtown, Pennsylvania, is the center for chocolate and cocoa development, and where cacao beans are roasted. Cleveland, Tennessee, focuses on baked products—such as the cookie centers of Twix and the Combos salty snacks—and also makes M&M’s.
Mars seeks ideas from three general sources: (1) the place of making things—
manufacturing plants, product development labs, workers, and managers;
(2) the place of acquisition—retail stores, grocery stores, convenience stores, restaurants, the Internet; and (3) the place of consumption—ethnographic studies that observe whether consumers eat the product on the run, in the car, at home or at work, together or alone, sharing or hoarding, in formal or informal settings, and planned or on impulse.
R&D, marketing, manufacturing, and the supply chain all share credit for keeping the pipeline of new ideas full. To narrow down what ideas to pursue, an Activity Management Project(AMP) is chartered for the most promising ideas.
Those that pass the AMP are qualified in terms of marketability and resource availability for a Development Quality Plan(DQP). For the DQP, representatives of all job functions formally get together to discuss the product under study. At this point, packaging and quality also are brought into the process. If the process continues successfully, prototypes are produced in the pilot lab and if approved, the product is launched to a test market.
This cross-functional development process has produced fun snack foods such as Skittles and Twix, healthy chocolate such as CocoaVia, and premium brands such as Dove chocolates, as well as innovations in liquid chocolate, dark chocolate, flavored chocolate, spicy chocolate, and more.
In this chapter we'll learn about the product development process and talk about techniques for improving both the quality and speed of design.
Source: David Fusaro, “Product Development at Mars,” Food Processing, February 2008, retrieved from http://www.foodprocessing.com/articles/2008/016.html.
N
ew products and services are the lifeblood of an organization. Designs can provide a competitive edge by bringing new ideas to the market quickly, doing a better job of satis- fying customer needs, or being easier to manufacture, use, and repair.Design is a critical process for a firm. Strategically, it defines a firm’s customers, as well as its competitors. It capitalizes on a firm’s core competencies and determines what new competencies need to be developed. It is also the most obvious driver of change—new products and services can rejuvenate an organization, define new markets, and inspire new technologies.