Chapter 15
-
Upload
tamekah-davenport -
Category
Documents
-
view
32 -
download
0
description
Transcript of Chapter 15
![Page 1: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/1.jpg)
Chapter 15Lot-by-Lot Acceptance Sampling
for Attributes
![Page 2: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/2.jpg)
The Acceptance-Sampling Problem
• Acceptance sampling is concerned with inspection and decision making regarding products.
![Page 3: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/3.jpg)
Three aspects of sampling
• The purpose of acceptance sampling is to sentence lots, not to estimate the lot quality– Although, some plans do this
• Acceptance sampling is not quality control– Reject or accept lots only– Even if lots are of the same quality, sampling
will accept some lots and reject others
![Page 4: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/4.jpg)
Three aspects of sampling
• Quality cannot be inspected into the product– Acceptance sampling is an audit tool that
insures that the output of a process conforms to requirements
![Page 5: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/5.jpg)
The Acceptance-Sampling Problem
• Three approaches to lot sentencing:
1. Accept with no inspection
2. 100% inspection
3. Acceptance sampling
![Page 6: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/6.jpg)
The Acceptance-Sampling Problem
Why Acceptance Sampling and Not 100% Inspection?
• Testing can be destructive• Cost of 100% inspection is high• 100% inspection is not feasible
– Requires too much time– Can be inaccurate
• If vendor has excellent quality history
![Page 7: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/7.jpg)
The Acceptance-Sampling Problem
Advantages and Disadvantages of Sampling Advantages• Less expensive• Reduced damage• Reduces the amount of inspection errorDisadvantages• Risk of accepting “bad” lots, rejecting “good” lots• Less information generated• Requires planning and documentation
![Page 8: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/8.jpg)
The Acceptance-Sampling Problem
Types of Sampling Plans • There are variables sampling plans and attribute
sampling plans (this chapter is about attributes)
1. Single sampling plan
2. Double-sampling plan
3. Multiple-sampling plan
4. Sequential-sampling
![Page 9: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/9.jpg)
The Acceptance-Sampling Problem
Lot Formation
• Considerations before inspection:– Lots should be homogeneous
• Produced by the same machine, same operators, common raw materials, approximately the same time
![Page 10: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/10.jpg)
Lot Formation
• Considerations before inspection:– Larger lots more preferable than smaller lots
• More economical
– Lots should be conformable to the materials-handling systems used in both the vendor and consumer facilities.
![Page 11: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/11.jpg)
The Acceptance-Sampling Problem
Random Sampling• The units selected for inspection should be
chosen at random.
• If random samples are not used, bias can be introduced.
• If any judgment methods are used to select the sample, the statistical basis of the acceptance-sampling procedure is lost.
![Page 12: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/12.jpg)
Guidelines for Using acceptance Sampling
• It is a statement of the sample size to be used and the associated acceptance or rejection criteria.
• Sampling scheme is defined as the set of procedures consists of acceptance sampling plans in which lot sizes, sample sizes, and acceptance criteria along with the 100% inspection and sampling are related.
![Page 13: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/13.jpg)
• Acceptance sampling procedure depends upon the objectives and the history of the organization.
• Application of methodology is not static. It keep on moving from one level to another. e.g, we might begin with attribute sampling, and as our experience with the supplier increase then move to much less inspection and variable sampling
![Page 14: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/14.jpg)
Single-Sampling Plans For Attributes
Definition of a Single-Sampling Plan• A single sampling plan is defined by sample size, n, and the
acceptance number c. Say there are N total items in a lot. Choose n of the items at random. If more than c of the items are unacceptable, reject the lot.
• N = lot size
• n = sample size
• c = acceptance number
• d = observed number of defectives
• The acceptance or rejection of the lot is based on the results from a single sample - thus a single-sampling plan.
![Page 15: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/15.jpg)
Example
• N = 10000, n = 89, c = 2– From a lot of 10,000, take a sample of size 89– Observe the number of defectives, d– If d < 2, accept– Otherwise, reject
![Page 16: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/16.jpg)
Single-Sampling Plans For Attributes
The OC Curve• The operating-characteristic (OC) curve measures
the performance of an acceptance-sampling plan.
• The OC curve plots the probability of accepting the lot versus the lot fraction defective.
• The OC curve shows the probability that a lot submitted with a certain fraction defective will be either accepted or rejected.
![Page 17: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/17.jpg)
Example
• If p = .01, Pa = .9397
• If p = .02, Pa = .7366 means that 73.66% of lots will be expected to be accepted and 26.34% will be rejected
![Page 18: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/18.jpg)
Effect of n and c on OC curves
• Fig. 15.3 is the ideal OC curve– Pa = 1.0 until a level of quality that is
considered ‘bad’ is reached– But it can never be attained in practice.
![Page 19: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/19.jpg)
Effect of n and c on OC curves
OC curve for different values of n– By increasing the sample size, we get closer to
the ideal OC curve
![Page 20: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/20.jpg)
Effect of n and c on OC curves
OC curve for different values of c– As c is decreased, the OC curve shifts to the left– When c = 0, it is very hard on the vendor
![Page 21: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/21.jpg)
• Type A or Type B OC curves– In the type B OC curve, it is assumed that the samples
come from the large lot or from a stream of lots selected at random.
– Binomial distribution is used as p is constant– In the Type A OC curve, isolated lot of finite size is
used with size N– The exact probability distribution is ‘hypergeometric’
as p is not constant.– Type A OC curve will lie below Type B
![Page 22: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/22.jpg)
Rectifying inspection
• Acceptance sampling require corrective action when lots are rejected– 100% screening of rejected lots
– Defective items are removed, returned to the supplier, or replaced.
– Such sampling programs are known as “rectifying inspection programs”
– Affects the outgoing quality
– Fraction defective =po, average fraction defective = p1
![Page 23: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/23.jpg)
Rectifying inspection
Inspection activity
Rejected lots
Accepted lots
Incoming lots
Fraction defective p0
Fraction defective
0
Fraction defective
p0
Outgoing lots
Fraction defective p1<p0
![Page 24: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/24.jpg)
Average outgoing quality
• AOQ is the quality in the lot resulting from applying rectifying inspection– In a lot of size N, there will be
• n items in the sample that, after inspection, contain no defectives (all of the defectives were replaced)
• N-n items that, if the lot is rejected, also contain no defectives (the balance of the lot was inspected 100%)
• N-n items that, if the lot is accepted, contain p(N-n) defectives
![Page 25: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/25.jpg)
Average outgoing quality
• AOQ = [Pa p (N-n)]/N
• Example– N = 10000, n = 89, c = 2, p = .01
– Previously determined that Pa = .9397
– AOQ [(.9397)(.01)(10000-89)]/10000– AOQ = .0093
– Since (N-n)/N 1, AOQ ~ Pap
![Page 26: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/26.jpg)
AOQ curve for rectifying inspection
for n = 89, c = 2
• When incoming quality is very good, average fraction defective of outgoing lots is low
• When incoming quality is very poor, average fraction defective of outgoing lots is low
![Page 27: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/27.jpg)
![Page 28: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/28.jpg)
Average outgoing quality limit
• AOQL = .0155– No matter how bad the incoming lots are, the
outgoing quality level will never be worse than 1.55% fraction defective
![Page 29: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/29.jpg)
Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859)
Description of the Standard• Developed during World War II• MIL STD 105E is the most widely used
acceptance-sampling system for attributes• Gone through four revisions since 1950.• MIL STD 105E is a collection of sampling
schemes making it an acceptance-sampling system
![Page 30: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/30.jpg)
Military Standard 105E (ANSI/ASQC Z1.4 ISO 2859) Description of the Standard• Three types of sampling are provided for:
1. Single2. Double3. Multiple
• Provisions for each type of sampling plan include
1. Normal inspection2. Tightened inspection3. Reduced inspection
![Page 31: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/31.jpg)
Military Standard 105E
Description of the Standard• The acceptable quality level (AQL) is a primary focal
point of the standard• The AQL is generally specified in the contract or by the
authority responsible for sampling.• Different AQLs may be designated for different types of
defects.• Defects include critical defects, major defects, and
minor defects.• Tables for the standard provided are used to determine
the appropriate sampling scheme.
![Page 32: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/32.jpg)
Military Standard 105E
Description of the Standard• Switching Rules
– Normal to tightened– Tightened to normal– Normal to reduced– Reduced to normal– Discontinuance of inspection
![Page 33: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/33.jpg)
Military Standard 105E
Procedure1. Choose the AQL2. Choose the inspection level3. Determine the lot size4. Find the appropriate sample size code letter from Table
15-45. Determine the appropriate type of sampling plan to use
(single, double, multiple)6. Enter the appropriate table to find the type of plan to be
used.7. Determine the corresponding normal and reduced
inspection plans to be used when required.
![Page 34: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/34.jpg)
Military Standard 105E
Example• Suppose a product is submitted in lots of size
N = 2000. The AQL is 0.65%. Say we wanted to generate normal single-sampling plans.
• For lots of size 2000, (and general inspection level II) Table 15-4 indicates that the appropriate sample size code letter is K.
• From Table 15-5 for single-sampling plans under normal inspection, the normal inspection plan is n = 125, c = 2.
![Page 35: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/35.jpg)
![Page 36: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/36.jpg)
Military Standard 105E
Discussion• There are several points about the standard that
should be emphasized:1. MIL STD 105E is AQL-oriented2. The sample sizes selected for use in MIL STD 105E
are limited3. The sample sizes are related to the lot sizes.4. Switching rules from normal to tightened and from
tightened to normal are subject to some criticism.5. A common abuse of the standard is failure to use the
switching rules at all.
![Page 37: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/37.jpg)
Normal TightenedReduced
2 out of 5 consecutive lots
rejected
5 consecutivelots accepted
O Production steadyO 10 consecutive lots acceptedO Approved by responsible authority
O Lot rejectedO Irregular productionO Lot meets neither accept nor reject criteria
O Other conditions warrant return to normal inspection
“And” conditions
“Or” conditions
Start
10 consecutivelots remain on
tightened inspection
Discontinue
inspection
Switching rules
![Page 38: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/38.jpg)
Dodge-Romig Plans
• For rectifying inspection
• See Table 15-8 for an example for
AOQL = 3%– Indexed by lot size (N) and process average (p)
![Page 39: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/39.jpg)
Example
• N = 5000, p = .01
• Want a single sampling plan (w/rectifying inspection) with AOQL = 3%
• Read n = 65, c = 3 from the table
• These plans minimize ATI– Pa = .9957 at p = .01 (determined as previously)
– ATI = 65 + (1 - .9957)(5000 – 65) = 86.22
![Page 40: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/40.jpg)
Example, cont.
• Also, note that LTPD = 10.3%
• This is the point on the OC curve for which Pa = .10
– That is, this plan provides that 90% of incoming lots that are as bad as 10.3% defective will be rejected
![Page 41: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/41.jpg)
LTPD plans
• Can also develop a plan for a specified LTPD
• Table 14-9 is for LTPD = 1%
![Page 42: Chapter 15](https://reader030.fdocuments.net/reader030/viewer/2022032612/5681356e550346895d9cd458/html5/thumbnails/42.jpg)
Example
• N = 5000, p = .25%
• We want a single sampling plan (w/rectifying inspection) with LTPD of 1%
• Find n = 770, c = 4