1 IES 331 Quality Control Chapter 14 Acceptance Sampling for Attributes – Single Sampling Plan and Military Standard Week 13 August 30 – September 1, 2005

Dr. Karndee Prichanont IES331 1/ Acceptance Sampling  Another area of quality control and improvement  Closely connected with inspection and testing of product  Inspection can occur at many points in a process Acceptance Sampling: the inspection and classification of a sample of nits selected at random from a larger batch or lot and ultimate decision about disposition of the lot – Lot Disposition or Lot Sentencing Acceptance Sampling: the inspection and classification of a sample of nits selected at random from a larger batch or lot and ultimate decision about disposition of the lot – Lot Disposition or Lot Sentencing Two common points of inspection

Dr. Karndee Prichanont IES331 1/ Acceptance Sampling

Dr. Karndee Prichanont IES331 1/ approaches for sentencing 1. _________________ 2. ____________________ 3. ___________________ Inspect every item in the lot, then remove the defective units by discarding, reworking, or returning to suppliers For critical process. Defective input may result high failure cost From new supplier when 100% inspection is too costly Trusted supplier with potential risk For low cost or low impact material on the subsequent process From trusted supplier

Dr. Karndee Prichanont IES331 1/ Advantages and Disadvantages of Sampling Advantages  Less expensive because of less inspection ___________________  Rejection on entire lot motivates quality improvement for suppliers Disadvantages  Risk of _______________  Requires planning and documentation  Require extensive study on customer’s requirement

Dr. Karndee Prichanont IES331 1/ Types of Sampling Plan Sampling Plan for Variables Sampling Plan for Attributes 1. Single-sampling plan 2. Double-sampling plan 3. Multiple-sampling plan 4. Sequential sampling plan ___________________________ _____________________________

Dr. Karndee Prichanont IES331 1/ Lot Formation 1. Lots should be ______________ produced on the same machines, by same operators, from common raw materials, at approximately the same time period 2. Larger lots are better than smaller lots 3. Lots should be conformable to the material handling systems ___________________________________

Dr. Karndee Prichanont IES331 1/ Random Sampling  Inspected units should be selected at random  Inspected units should represent all items in the lot  Potential bad story ____________________ __________________

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes  A lot of size N has been submitted for inspection  Sample size n  Acceptance number of defective c  Lot sentencing is based on one sample of size n N = 10,000 n = 89 Example N = 10,000 n= 89 c = 2 Example N = 10,000 n= 89 c = 2

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes The OC Curve  Operating characteristic (OC) curve  Also refer to Chapter 2; Page 78 Curve plots the probability of accepting the lot (P a ) versus the lot fraction defective (p)

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes The OC Curve

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes Ideal OC curve  Theoretically, it can be achieved by ___________________  Due to sampling, ideal OC curve cannot be perfectly achieved.  If sample size (n) _______, the OC curve shape will approach the ideal OC curve

Dr. Karndee Prichanont IES331 1/ n Single-Sampling Plans for Attributes Effects of n on OC curves __________,  As sample size (n) __________, the OC curve shape will approach the ideal OC curve  Note that c is kept in proportional to n  ____________________

Dr. Karndee Prichanont IES331 1/ c Single-Sampling Plans for Attributes Effects of c on OC curves  Changing acceptance number (c) does not significantly change the shape  _____________________ _____________________

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes OC curve Acceptable quality level (AQL)  The poorest quality level for the supplier’s process that a consumer would consider to be acceptable  A property of the supplier’s manufacturing process, not a property of the sampling plan Lot tolerance percent defective (LTPD)  The protection obtained for individual lots of poor quality  Also called rejectable quality level (RQL) and the limiting quality level (LQL)  LTPD is a level of lot quality specified _____________, not a characteristic of the sampling plan  Sampling plans can be designed to have specified performance at the AQL and the LTPD points ______________________________________

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes Type-A and Type-B OC Curves

Dr. Karndee Prichanont IES331 1/ Designing a single-sampling plan with a specified OC curve To construct sampling plan such that Probability of acceptance for lots with fraction defective p 1 Probability of acceptance for lots with fraction defective p 2

Dr. Karndee Prichanont IES331 1/ Binomial Nomograph

Dr. Karndee Prichanont IES331 1/ Single-Sampling Plans for Attributes Rectifying Inspection  When the lot is rejected, it requires corrective action

Dr. Karndee Prichanont IES331 1/ Average outgoing quality - AOQ Given the lot size of N, sample size of n, and fraction defective of p  n items in the sample that, after inspection, contain no defectives, because all discovered defectives are replaced  N – n items that, if the lot is rejected, also contain no defectives  N – n items that, if the lot is accepted p(N-n) defectives If N >> n, then

Dr. Karndee Prichanont IES331 1/ Average outgoing quality - AOQ

Dr. Karndee Prichanont IES331 1/ 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

Dr. Karndee Prichanont IES331 1/ Military Standard 105E

Dr. Karndee Prichanont IES331 1/ Military Standard 105E Procedure 1. Choose the AQL 2. Choose the inspection level 3. Determine the lot size 4. Fine the appropriate sample size code letter (from Table 14-4) 5. Determine the appropriate type of sampling plan to use (single) 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

Dr. Karndee Prichanont IES331 1/ Discussion of Military Standard  Several points about MIL STD 105E should be emphasized:  MIL STD 105E is AQL-oriented  Not all possible sample sizes are possible (2,3,5,8,13,20,32,50, etc.)  Sample sizes are related to lot sizes  Switching rules are subject to criticism for both misswitching between inspection plans and discontinuation even though there has been no actual quality deterioration