ADDITIONAL SAMPLING PROCEDURES Chapter 16

Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 2 ADVANTAGES Same operating-characteristic curve can be obtained with a smaller sample size than would be required by an attributes sampling plan Measurement data usually provide more information than attributes data Finally, when acceptable quality level as are very small, sample sizes required by attributes sampling plans are very large Acceptance Sampling by Variables

DISADVANTAGES Distribution of OC curve must be known. Most standard plans assume distribution of quality characteristic is normal. If not then it is assumed that it is, which leads to serious problems regarding accepting or rejecting of lots. A separate sampling plan must be employed for each quality characteristic that is being inspected i.e f there are 4 quality characteristics, then 4 sampling plans. Possible to reject a lot even though the actual sample inspected does not contain any defective items

Types of Sampling Plans available Two types of variable sampling plans –Plans that control lot or process fraction defective, and –Plans that control the process parameter (usually mean)

Consider the first type of plan,either the LSL or USL will be defined or both. In Fig 16.1 LSL is mentioned, x is normally distributed, mean is u and SD is

SD is known We may want to know that the sample from the lot to determine whether or not the value of the mean is such that the fraction defective p is acceptable.

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 7

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 8

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 9

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 10 Cautions in the use of variables sampling: Usual assumption is that the parameter of interest follows the normal distribution If parameter of interest is not normally distributed, estimates of the fraction defective will not be the same as if normally distributed Difference between estimated fraction defectives may be large when dealing with very small fractions defective

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc MIL STD 414 (ANSI/ASQ Z1.9) MIL STD 414 is a lot-by-lot acceptance-sampling plan for variables Focal point is the AQL which ranges from 0.04% to 15% Five general inspection levels,where level IV is designated as normal. –Level V gives a steeper OC curve than level IV. –When reduced costs are required, or greater risks can be tolerated than lower levels can be used.

Sample sizes are a function of the lot size and the inspection level Provision is made for normal, tightened, and reduced inspection Quality characteristic of interest is assumed to be normally distributed

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 13

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 14 Refer to the textbook, page 678 for Table 16.2

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 15

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 16

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 17 Discussion It is not possible to move directly from an attributes sampling plan in the current MIL STD 105E to a corresponding variables plan in MIL STD 414 if the assurance of continued protection is desired for certain lot sizes and AQLs Civilian counterpart of MIL STD 414 restores the match to attributes plans—that is, ANSI/ASQC Z1.9 is directly compatible with MIL STD 105E – Makes it possible to start inspection by using an attributes scheme from MIL STD 105E, collect sufficient information to use variables inspection, then switch to variables scheme while maintaining the same AQL-code letter combination

Continuous Sampling All the sampling plans are based on lot by lot sampling. Explicit assumption is that the lots are formed and then the sample from them is tested to decide the acceptance or rejection. But there are many manufacturing processes when that is not the case.

Two procedures can be used. –Accumulation of production at a given point in assembly line. But this may lead to in-process inventory –Second procedure marks off the given segment of the production as lot. But if the lot is rejected, and 100% inspection is required, then it will lead to disassembly of semi fnished products.

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 20

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 21

Chapter 16Introduction to Statistical Quality Control, 6 th Edition by Douglas C. Montgomery. Copyright (c) 2009 John Wiley & Sons, Inc. 22