IE 125: Chapter 10

rejectable quality level (RQL)

LTPD: ✓ Also called _______________________ and the limiting quality level (LQL) ✓ LTPD is a level of lot quality specified by the consumer, not a characteristic of the sampling plan

Single-sampling plan Double-sampling plan Multiple-sampling plan Sequential-sampling plan

Types of Sampling Plans

random sampling

Units selected for inspection from the lot should be chosen at random and they should be representative of all items in the lot • Prevent "salting" • Unless random samples are used, bias will be introduced • Assign a number to each item in the lot; code or serial number; three-digit random number • Stratify a lot

Sampling system

- a unified collection of one or more acceptance sampling schemes

Double-sampling plan

- following an initial sample, a decision is based on the information in that sample is made either to (1) accept the lot, (2) reject the lot, or (3) take a second sample. If the second sample is taken, the information from both the first and second sample is combined in order to reach a decision whether to accept or reject the lot.

Primary OC Curve

- gives the probability of acceptance as a function of lot or process quality

Break-even point (BEP)

- measure used to determine what approach to lot sentencing should be used

Multiple-sampling plan

- more than two samples may be required in order to reach a decision regarding the disposition of the lot

Single-sampling plan

- one sample of n units is selected at random from the lot, and the disposition of the lot is determined based on the information contained in that sample - n items, c acceptance number

curtailment

- possibility of rejecting a lot without complete inspection of the second sample

Sampling scheme

- set of procedures consisting of acceptance sampling plan in which lot sizes, sample sizes and acceptance or rejection criteria along with the amount of 100% inspection and sampling are related

Supplementary OC curves

- show the probability of lot acceptance and rejection on the first sample

Acceptance sampling plan

- statement of the sample size to be used and the associated acceptance or rejection criteria

Sequential-sampling plan

- units are selected from the lot one at a time, and following inspection of each unit, a decision is made either to accept the lot, reject the lot or select another unit

rectifying inspection programs

AS programs usually require corrective action when lots are rejected ➢ 100% inspection or screening of rejected lots, with all discovered defective items either removed for subsequent rework or returned to the supplier or replaced from a stock of known good items

1. It is usually *less expensive* because there is less inspection 2. There is *less handling* of the product, hence reduced damage 3. It is applicable to *destructive testing* 4. *Fewer personnel* are involved in inspection activities 5. It often greatly *reduces the amount of inspection error* 6. The *rejection of entire lots* as opposed to the simple return of defectives often *provides a stronger motivation to the vendor for quality improvements*

Acceptance sampling advantages relative to 100% inspection

1. There are *risks of accepting "bad" lots and rejecting "good" lots* 2. *Less information* is usually generated about the product or about the process that manufactured the product 3. Acceptance sampling *requires planning and documentation* of the acceptance sampling procedure whereas 100% inspection does not

Acceptance sampling disadvantages relative to 100% inspection

1. Accept with no inspection 2. 100% inspection 3. Acceptance sampling

Approaches to Lot Sentencing

1. It is the purpose of *acceptance sampling to sentence lots, not to estimate the lot quality*. Most acceptance sampling plans are not designed for estimation purposes. 2. Acceptance sampling plans *do not provide any direct form of quality control*. It simply accepts and rejects lot. 3. The most effective use of acceptance sampling is not to "inspect quality into the product" but rather as an *audit tool to ensure that the output of a process conforms to requirements*.

Aspects of Sampling

• administrative efficiency, • the type of information produced by the plan, • the average amount of inspection required by the procedure, and • the impact that a given procedure may have on the material flow in the manufacturing organization.

Factors to consider when selecting the type of sampling procedure

Design of sampling plan

The different types of sampling plans can be *designed so that a lot of specified quality has exactly the same probability of acceptance under all four types of sampling plans*

Acceptable Quality Level (AQL)

The poorest quality level for the supplier's process that a consumer would consider to be acceptable as a process average is called the ____________________

Lot tolerance percent defective (LTPD)

The protection obtained for individual lots of poor quality is established by the______________________________; quality level of a lot considered bad

▪ If the lot contains no defective items, no lots will be rejected, amount of inspection = n ▪ If the items are all defective, every lot will be submitted to 100% inspection, amount of inspection = N ▪ If the lot quality is 0 < p < 1, amount of inspection = between n and N

Total amount of inspection required by the sampling program

1. When testing is *destructive* 2. When the *cost of 100% inspection is extremely high* 3. When 100% inspection is *not technologically feasible or would require so much calendar time* that production scheduling would be seriously impacted 4. When there are many items to be inspected and the *inspection error rate is sufficiently high* that 100% inspection might cause a higher percentage of defective units to be passed than would occur with the use of a sampling plan 5. When the vendor has an *excellent quality history*, and some reduction in inspection from 100% is desired, but the vendor's *process capability is sufficiently low* as to make no inspection an unsatisfactory alternative 6. When there are *potentially serious product liability risks*, and although the vendor's process is satisfactory, a program for continuously monitoring the product is necessary 7. *Fatigue or boredom* caused by inspecting large numbers of items *leads to inspection errors*.

When to use acceptance sampling?

Average Outgoing Quality (AOQ)

_______________ is widely used for the evaluation of a rectifying sampling plan. ❑ The quality in the lot that results from the application of rectifying inspection; the average value of lot quality that would be obtained over a long sequence of lots from a process with fraction defective p ❑ Average fraction defective

Salting

intentionally adding defective items in lot

Lot sentencing

the decision to accept or reject a lot

Consumer's risk

the mistake of a customer's acceptance of a bad lot overlooked through sampling; the probability of a bad lot accepted (Type II error)

Producer's risk

the mistake of having a producer's good lot rejected through sampling; the probability of a good lot rejected (Type I error)

Binomial Approximation to the Hypergeometric distribution

used when n/N ≤ 0.1

Acceptance Sampling

• Concerned with inspection and decision making regarding products • During the 1930s and 1940s, it was one of the major components of the field of statistical quality control and was used primarily for incoming and receiving inspection • Decision: accept or reject the lot -- lot sentencing • Lot-disposition action

Lot Formation

• Lots should be homogeneous • Larger lots are preferred over smaller ones • Lots should be conformable to the materials-handling systems used in both the vendor and consumer facilities

100% inspection

• Used in situations where the component is extremely critical and passing any defectives would result in an unacceptably high failure cost at subsequent stages, or where the vendor's process capability is inadequate to meet specification

Accept with no inspection

• Useful in situations where either the vendor's process is so good that defective units are almost never encountered or where there is no economic justification to look for defective units

Average Outgoing Quality Limit (AOQL)

• worst possible average quality that would result from the rectifying inspection program • no matter how bad the fraction defective is in the incoming lots, the outgoing lots will never have a worse quality level on the average • _________ is an average level of quality, across a large stream of lots

MILITARY STANDARD 105E

▪ Sampling procedure for inspection by attributes developed during World War II and is the most widely used acceptance-sampling system for attributes in the world today ▪ A collection of sampling schemes; therefore an acceptance-sampling system ▪ Provides for three types of sampling: single, double, and multiple ▪ Primary focal point is the acceptable quality level (AQL) ▪ Different AQLs may be designated for different types of defects: critical, major, and minor ▪ Generally specified in contract or by authority responsible for sampling ▪ Sample size is determined by lot size and by choice of inspection level

supplier's manufacturing process smaller

✓ AQL is a property of the _________________________________, not a property of the sampling plan ✓ AQL should be set based on the criticality of the characteristic that is being inspected—the more critical the characteristic, the __________ the AQL should be

operating characteristic curve

✓ Describes how well an acceptance plan discriminates between good and bad lots; ✓ Shows the probability that a lot submitted with a certain fraction defective will be either accepted or rejected