ME 418 Quality in Manufacturing ISE Quality Control and Industrial Statistics CHAPTER 07 ACCEPTANCE SAMPLING PLANS.

Transcription

1 University of Hail College of Engineering ME 418 Quality in Manufacturing ISE Quality Control and Industrial Statistics CHAPTER 07 ACCEPTANCE SAMPLING PLANS Professor Mohamed Aichouni Acceptance Sampling Acceptance sampling is a method used to accept or reject product based on a random sample of the product. The purpose of acceptance sampling is to sentence lots (accept or reject) rather than to estimate the quality of a lot. Acceptance sampling plans do not improve quality. The nature of sampling is such that acceptance sampling will accept some lots and reject others even though they are of the same quality. The most effective use of acceptance sampling is as an auditing tool to help ensure that the output of a process meets requirements. 1

2 Acceptance Sampling Take a Sample Size n, Accept if c or less. Producer Risk is a good lot will be rejected and sent back. Consumer Risk is a bad lot will be accepted. Acceptance Sampling Flow Chart 2

3 Acceptance Sampling N : sample size sampling Inspect the sample : cعدد القبول Acceptance number Accept the lot Reject the lot 5 N Terminology As mentioned acceptance sampling can reject good lots and accept bad lots. More formally: Producers risk refers to the probability of rejecting a good lot. AQL (Acceptable Quality Level) - the numerical definition of a good lot; associated with Producer`s risk. The ANSI/ASQC standard describes AQL as the maximum percentage or proportion of nonconforming items or number of nonconformities in a batch that can be considered satisfactory as a process average 3

4 Terminology Consumers Risk refers to the probability of accepting a bad lot where: LTPD (Lot Tolerance Percent Defective) - the numerical definition of a bad or poor lot. described by the ANSI/ASQC standard as the percentage or proportion of nonconforming items or noncomformities in a batch for which the customer wishes the probability of acceptance to be a specified low value. Limiting Quality Level - Numerical definition of a poor lot, associated with the consumer s risk. Types of Sampling Plans Sampling Plans by Attributes: Single sampling plan by attributes Double sampling plan by attributes Sequential sampling plan 8 4

5 Single Sampling Operating Characteristic (OC) curve The Operating Characteristic Curve is typically used to represent the four parameters (Producers Risk, Consumers Risk, AQL and LTPD) of the sampling plan. P on the x axis represents the percent defective in the lot. 5

6 Ideal Operating Characteristics Curve (100% Inspection) 100% P(Accept Whole Shipment) P of Acceptance 0% 0 Always Accept Always Reject Proportion of non Conforming Actual OC Curves Are determined by sample size [n] and acceptance number [c]. Accept the lot if c or fewer nonconforming are obtained, reject if more. OK to assume Binomial distribution (if lot size is 10x sample size). Calculate P accept for range of incoming p levels. 6

7 Actual OC Curves 100% P(Accept Whole Shipment) P < 100 % Risk to accept bad lot and/or reject a good lot Accept the lot Reject the lot 0% Cut-Off Proportion of non Conforming 13 Actual OC Curves and the Producer`s Risk and Consumer`s Risk = 0.05 AQL P of acceptance = LTPD for AQL LTPD Good Indifference zone lot Proportion of non conforming Bad lot 7

8 Sample problem Given a lot size of N=2000, a sample size n=50, and an acceptance number c=2. Calculate the OC curve for this plan. Probability of accepting is obtaining c=2 or less nonconforming items in samples of size n=50. Vary p from 0 to 0.15 (what if p =.) OC for possible sampling plans 16 8

9 Vary n and c Double Sampling In an effort to reduce the amount of inspection double (or multiple) sampling is used. Whether or not the sampling effort will be reduced depends on the defective proportions of incoming lots. Typically, four parameters are specified: n 1 = c 1 = n 2 = c 2 = number of units in the first sample acceptance number for the first sample number of units in the second sample acceptance number for both samples 9

10 Procedure A double sampling plan proceeds as follows: A random sample of size n 1 is drawn from the lot. If the number of defective units (say d 1 ) c 1 the lot is accepted. If d 1 c 2 the lot is rejected. If neither of these conditions are satisfied a second sample of size n 2 is drawn from the lot. If the number of defectives in the combined samples (d 1 + d 2 ) > c 2 the lot is rejected. If not the lot is accepted. Double Sampling Plan 10

11 Double Sampling Plan Application of double sampling requires that a first sample of size n1 is taken at random from the (large) lot. The number of defectives is then counted and compared to the first sample's acceptance number a1 and rejection number r1. Denote the number of defectives in sample 1 by d1 and in sample 2 by d2, then: If d1<= a1, the lot is accepted. If d1 >= r1, the lot is rejected. If a1 < d1 < r1, a second sample is taken. If a second sample of size n2 is taken, the number of defectives, d2, is counted. The total number of defectives is D2 = d1 + d2. Now this is compared to the acceptance number a2 and the rejection number r2 of sample 2. In double sampling, r2 = a2 + 1 to ensure a decision on the sample. If D2 <= a2, the lot is accepted. If D2 >= r2, the lot is rejected. Designing Acceptance Plans This should be performed on agreement between the producer and the consumer. Each party work to reduce the risk, by varying n and c to obtain different OC curves. Single and multiple sampling plans can be used. Refer to standard published Standards (MIL-STD- 105D, Dodge Romig Tables). 11

12 Acceptance Sampling Plans on Minitab Minitab perform all the necessary calculations to design acceptance sampling plans. og/applying-statistics-inquality-projects/attributeacceptance-samplingfor-an-acceptancenumber-of-0 Examples will be worked out next sessions International Standards on Sampling Plans ISO :1995 Sampling procedures for inspection by attributes -- Part 0: Introduction to the ISO 2859 attribute sampling system ISO :1999 Sampling procedures for inspection by attri butes -- Part 1: Sampling schemes indexed by acceptance quality limit (AQL) for lot - by - lot inspection ISO :1999/Cor 1:2001 ISO :1985 Sampling procedures for inspection by attributes -- Part 2: Sampling plans indexed by limiting quality (LQ) for isolated lot i nspection ISO :1991 Sampling procedures for inspection by attributes -- Part 3: Skip - lot sampling procedures ISO :2002 Sampling procedures for inspection by attributes -- Part 4: Procedures for assessment of declared quality levels ISO 3951:1989 Sampling procedures and charts for inspection by variables for percent nonconforming ISO 8422:1991 Sequential sampling plans for inspection by attributes ISO 8422:1991/Cor 1:1993 ISO 8423:1991 ISO 8423:1991/Cor 1:1993 ISO/TR 8550:1994 ISO 10725:2000 Sequential sampling plans for inspection by variables for percent nonconforming (known stan dard deviation) Guide for the selection of an acceptance sampling system, scheme or plan for inspection of discrete items in lots Acceptance sampling plans and procedures for the inspection of bulk materials ISO :2003 Statistical aspects of sampling from bulk materials -- Part 1: General principles ISO :2001 Statistical aspects of sampling from bulk materials -- Part 2: Sampling of particulate materials 12

13 Conclusion Lecture Finished "Quality control truly begins and ends with education", K. Ishikawa (1990). Any Question? Yes Ask questions No Teachers answers Train your self (Google, YouTube, course webpage End (See you next lecture) University of Hail College of Engineering ME 418 Quality in Manufacturing ISE Quality Control and Industrial Statistics CHAPTER 06 PART 2 ACCEPTANCE SAMPLING PLANS EXAMPLES ON MINITAB Professor Mohamed Aichouni

14 Acceptance Sampling Plans on Minitab Acceptance Sampling Plans on Minitab This graph represents the probability to accept a batch for a given proportion of defectives. 14

15 Acceptance Sampling Plans on Minitab Acceptance Sampling Plans on Minitab 15

16 Acceptance Sampling Plans on Minitab 16