Quality Control Chapter 10- Acceptance Sampling Systems PowerPoint presentation to accompany Besterfield Quality Control, 8e PowerPoints created by Rosida Coowar 1

Outline Lot-by-lot acceptance sampling plans for attributes Acceptance sampling plans for continuous production Acceptance sampling plans for variables 2

Learning Objectives When you have completed this chapter you should be able to: Determine the sampling plan using ANSI/ASQ Z1.4. Know the switching rules for ANSI/ASQ Z1.4. Categorize the various sampling plan systems in terms of lot-by-lot, continuous production, attributes or variables. 3

Learning Objectives-cont’d. When you have completed this chapter you should be able to: Describe the various sampling plan systems and know their function (advantages, disadvantages, purpose etc.). Determine the sampling plan using the Dodge Romig Tables Construct the OC Curve for a chain sampling plan. 4

Learning Objectives-cont’d. When you have completed this chapter you should be able to: Be able to use the Shainin Lot Plot Method. Determine the sampling plan ANSI/ASQ S1 Determine whether a lot is accepted or rejected using ANSI/ASQ Z1.9 5

Lot-by-Lot Acceptance Sampling Plans for Attributes Devised in 1942 at Bell Labs Later became MIL-STD-105E ISO-2859 ANSI/ASQ Z1.4 Wording & terminology changes Additional tables added 6

ANSI/ASQ Z1.4 This standard is applicable to: End items Components and raw materials Operations Materials in process Supplies in storage Maintenance operations Data or records 7

ANSI/ASQ Z1.4 Intended to be used for a continuing series of lots, but may be designed for isolated lots. Standard provides for single, double, and multiple sampling plans. Provision is also provided for normal, tightened, or reduced inspection. Plan is specified by the AQL, and sample-size code. 8

ANSI/ASQ Z1.4 Normal inspection is used at the start of inspection with changes being a function of recent quality history. Tightened inspection: Generally used when producer’s recent quality history has deteriorated. 9

ANSI/ASQ Z1.4 Reduced inspection: Used when the producer’s recent quality history has been exceptionally good. Decision concerning what type of plan to use is left to the responsible authority. Nonconformities are classified such as critical, major… 10

ANSI/ASQ Z1.4 11

Sample Size Code Letters 12

Comparison of Inspection levels 13

ANSI/ASQ Z1.4 AQL The AQL is the most important part of the standard since the AQL and sample size dictate the plan used. AQL is defined as the maximum percent nonconforming that can be considered satisfactory as a process average. Satisfactory = Producer’s risk, α Usually 0.05 14

ANSI/ASQ Z1.4 AQL AQL is specified by contract or responsible authority. AQL may be determine from historical data, empirical judgment, engineering information, experimentation, producer’s capability, consumer’s requirements. 15

ANSI/ASQ Z1.4 AQL AQL is specified by contract or responsible authority. AQL may be determine from historical data, empirical judgment, engineering information, experimentation, producer’s capability, consumer’s requirements. 17 16

ANSI/ASQ Z1.4 Sample Size Determined by lot size and inspection level Use of sample-size code Inspection level is determined by the responsible authority. 17 17

ANSI/ASQ Z1.4 Sample Size Different levels of inspection provide approximately the same protection to the producer, but different protections to the consumer. Plan provides for “special” levels to be used where relatively small sample sizes are necessary and large sampling risks must be tolerated. (S-1, S-2, S-3, S-4) 18 18

ANSI/ASQ Z1.4 Determine lot size Determine inspection level Implementation Determine lot size Determine inspection level Find sample-size code letter in table Determine AQL 19

ANSI/ASQ Z1.4 Determine type of sampling plan Implementation cont’d. Determine type of sampling plan Find sampling plan in appropriate table Start with normal inspection and change to tightened or reduced based on switching rules 20

AQL What an AQL means is that as long as a supplier maintains his/her process average (% defective) at the assigned AQL or lower, there is a very high probability that shipments from that supplier, when inspected using ASQ Z1.4 sampling plans, will be accepted.  21

AQL By the same token, there is a very high probability that shipments, when inspected using ASQ Z1.4 sampling plans, will be rejected if a supplier's process average (% defective) remains higher than the assigned AQL. 22

ANSI/ASQ Z1.4 Single sampling plans Start by identification of AQL, lot size, inspection level, and type of sampling plan. Locate appropriate plan parameters in tables. Double and Multiple Sampling Similar procedures as single sampling 23

ANSI/ASQ Z1.4 Normal, Tightened, and Reduced Inspection Start with normal inspection Switching Procedures Normal to tightened Institute when 2 out of 5 consecutive lots not accepted on original inspection Tightened to normal Institute when 5 consecutive lots accepted If not, then discontinue inspection under this plan 24

ANSI/ASQ Z1.4 Switching Procedures Normal to reduced Institute when: (all of the following) Preceding 10 lots on normal inspection have been accepted Total nonconforming in preceding 10 samples is less than number identified in Table 10-5. Production is at a steady rate Reduced inspection is considered desirable by responsible authority 25

ANSI/ASQ Z1.4 Switching Procedures Reduced to normal Institute when: (any of the following) A lot is not accepted Sampling procedure terminates with neither acceptance or rejection criteria have been met Production is irregular or delayed Other conditions 26

ANSI/ASQ Z1.4 Standard is designed for use where units of product are produced in a continuing series of lots or batches. If a sampling plan is desirable for a lot or batch of an isolated nature, it should be chosen based on the Limiting Quality (LQ) and consumer’s risk, b. These tables are included in the standard, but not the textbook. Or use ANSI/ASQ Standard Q3 27

ANSI/ASQ Standard Q3 Standard is used for inspection of isolated lots by attributes. Provides indexed tables by Limiting Quality, LQ. 28

ANSI/ASQ Standard Q3 Lot size and LQ must be known. Two Schemes: 1. Used for lots that are isolated or mixed or that have an unknown history as far as all parties know. Lot size and LQ must be known. Nominal values of the LQ are based on b=0.10 29

ANSI/ASQ Standard Q3 Two Schemes: 2. Used when a vendor is producing a continuous stream of lots and sends one or a few to a customer who will consider them as isolated lots. Occurs frequently when purchasing small quantities of raw materials. 30

Dodge-Romig Tables Tables for single and double sampling A set of inspection tables for lot-by-lot acceptance sampling by attributes. Tables are based on Limiting Quality (LQ) and Average Outgoing Quality Limit (AOQL). Tables for single and double sampling Advantage that the plan provides a minimum amount of inspection for a given inspection procedure. Desirable for in-house inspection 31

Dodge-Romig Tables Limiting Quality – LQ Based on the probability that a particular lot, which has percent nonconforming equal to the LQ, will be accepted. Probability is the consumer’s risk, β = 0.10 LQ plans give assurance that individual lots of poor quality will rarely be accepted. 32

Dodge-Romig Tables Observations about the LQ tables: As the lot size increases, the relative sample size decreases. The tables extend until the process average is one-half of the LQ. As the process average increases, a corresponding increase occurs in the amount inspected. 33

Dodge-Romig Tables Average Outgoing Quality Limit – AOQL Applicable when the inspected lot is a convenient subdivision of a flow of product for materials handling purposes (non-homogeneous) AOQL plan limits the amount of poor outgoing quality on an average basis, but gives no assurance on individual lots. 34

Dodge-Romig Tables Process average Type of nonconformance Obtained by the same techniques as for p-charts First 25 lots the average percent nonconforming is obtained Type of nonconformance Dodge-Romig tables do not provide for different categories or tightened inspection Different LQ or AOQL values may be used 35

Chain Sampling Inspection Plan A special type of lot-by-lot acceptance sampling plan for attributes designated as “Chain Sampling Plan ChSP-1”. Applicable to quality characteristics which involve destructive or costly tests. Use of small sample sizes Acceptance number, c=0 Poor shape of OC curve at the producer’s risk 36

Chain Sampling Inspection Plan Chain sampling uses the cumulative results of several samples Determination of the value of i, the number of previous samples, is determined by analysis of the OC curves for a given sample size. 37

Chain Sampling Inspection Plan Procedure: For each lot, select a sample of size n and test each for conformance to specifications. 38

Chain Sampling Inspection Plan Procedure: If the sample has 0 nonconforming units, accept the lot; if the sample has 2 or more nonconforming units, do not accept the lot; and if the sample has 1 nonconforming unit, it may be accepted provided that there are 0 nonconforming units in the previous i samples of size n. 39

Chain Sampling Diagram Current Lot i previous lots n=5 c=0 Last Lot Second- to-Last Lot Accept if 0 Nonconforming Units in n =5 or if 1 Nonconforming Unit & Zero Nonconforming Units in i Previous Lots Figure 10-4 Chain Sampling Diagram 40

Chain Sampling Inspection Plan Conditions for use of the Chain Sampling Plan: The lot should be one of continuing series of product that is sampled in substantially the order of production The consumer can normally expect the lots to be essentially the same quality. 41

Chain Sampling Inspection Plan Conditions for use of the Chain Sampling Plan: The consumer has confidence in the producer not to occasionally send an unacceptable lot that would have the optimum chance of acceptance. The quality characteristic is one that involves destructive or costly tests. 42

Sequential Sampling Used for costly or destructive tests Subgroup size of 1 – item by item plan Sequential sampling is similar to multiple sampling, except sequential sampling can, in theory, continue indefinitely. In practice, the plan is truncated after the number inspected is equal to three times the number inspected by a corresponding single sampling plan. Based on the Sequential Probability Ratio Test 43

Sequential Sampling Plan 44

Sequential Sampling Plan 45

Skip Lot Sampling Designated SkSP-1 and based on AOQL. A single sampling plan for minimizing inspection costs when there is a continuing supply of lots of raw materials, component parts, subassemblies, and finished parts from the same source. Applicable to chemical and physical characteristics that require laboratory analysis. 46

Procedure for SkSP-1 Plans Begin by inspecting every lot When i consecutive lots are found to be conforming Discontinue inspection of every lot Inspect a fraction, f, of the lots In a random manner When an inspected lot is found nonconforming Figure 10-7 Procedure SkSP-1 plans 47

ANSI/ASQ S1 Provides procedures to reduce the inspection effort when the supplier’s quality is superior. A skip-lot scheme used in conjunction with attribute lot-by-lot plans given in ASQ Z1.4 48

ANSI/ASQ S1 Requirements to use ANSI/ASQ S1 Have a documented system for controlling product quality and design changes Have instituted a system that is capable of detecting and correcting changes that might adversely affect quality. Not have experienced an organizational change that might adversely affect quality 49

ANSI/ASQ S1 Additional requirements of the product: Be of stable design Have been manufactured on a continuous basis for at least 6 months unless agreed to a longer period. Have been on normal and reduced inspection during the qualification period. Have maintained a quality level at or less than the AQL for at least 6 months. 50

ANSI/ASQ S1 Other: The previous 10 or more consecutive lots have been accepted The min cumulative sample size for the last 10 or more consecutive lots have been met. The acceptance numbers for the last 2 lots have been met 51

Sampling for Continuous Production Acceptance sampling for continuous production implies that manufacturing operations do not create lots as part of the normal part of the production process. Parts are produced by a continuous process on a conveyor or similar system. 51

Sampling for Continuous Production Plans for continuous production consist of alternating sequences of sampling inspection and screening (100%) inspection. Plans begin with 100% inspection and convert to sampling after a stated number of items are free of nonconformities. Sampling continues until a stated number of nonconforming units are found, at which time 100% inspection in reinstated. 53

Sampling for Continuous Production Applicable to attribute, nondestructive inspection of moving product. Inspection should be easy and rapid Process must be capable of manufacturing homogeneous product 54

Sampling for Continuous Production Developed by Dodge CSP-1, CSP-2, CSP-3 Later, MIL-STD-1235B 55

Sampling for Continuous Production CSP-1 Begins with 100% inspection of the product in the order of production until a certain number of successive units are free of nonconformities. 56

Sampling for Continuous Production CSP-1 Sampling inspection is then instituted Samples are selected in such a manner as to minimize any bias If a nonconformity occurs, sampling is discontinued and 100% inspection begins. 57

CSP-1 and CSP-F Plans 58

MIL-STD-1235B Designated by code letters Standard is composed of five different continuous sampling plans. Designated by code letters 59

MIL-STD-1235B Critical Major Minor Inspection is by attributes for nonconforming units using three classes of severity: Critical Major Minor Each of the plans incorporates a provision for discontinuance of inspection 60

Acceptance Sampling Plans for Variables Shainin Lot Plot ANSI/ASQ Z1.9-2003 61

Acceptance Sampling Plans for Variables Shainin Lot Plot Random sample of 10 subgroups of 5 each Find average and range Construct a histogram Calculate Xdouble bar, R bar Calculate ULL and LLL Compare to lot plots in Figure 10-15 62

Acceptance Sampling Plans for Variables ANSI/ASQ Z1.9-2003 Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming is an acceptance sampling system to be used on a continuing stream of lots for Acceptance Quality Limit (AQL) specified. 63

Acceptance Sampling Plans for Variables ANSI/ASQ Z1.9-2003 provides tightened, normal, and reduced plans to be used on measurements which are normally distributed. Variation may be measured by sample standard deviation, sample range, or known standard deviation. It is applicable only when the normality of the measurements is assured. 64