Acceptance level (AQL) of a lot inspection.pptx
- 1. cIC 1. The specification for a certain product characteristic are 0.005±0.0002in. The standard deviation & Mean are 0.0000429 & 0.0051 respetively. Calculate Cp and Cpk for this characteristic. Is this process capability acceptable? 2. The specification for a certain product characteristic are 50.05±0.05mm. Mean of the data is 50.04mm. The standard deviation is 0.01. Calculate Cp and Cpk for this characteristic. Is this process capability acceptable? Numerical on Process Capability Index
- 2. Solution 1: Usl= 0.005+0.0002= 0.0052 Lsl= 0.005- 0.0002= 0.0048 Mean= 0.0051, Standard deviation = 0.0000429 Find Cp & Cpk ϭ Cp= {Usl-Lsl)/6 (sigma) ϭ Cp= (0.0052-0.0048)/6* 0.0000429 Cp= 0.0004/0.0002574 Cp = 1.55 Cpk= min { (Usl- Mean)/3 (sigma), (Mean- Lsl)/ ϭ 3 (sigma) ϭ Cpk= min { (0.0052-0.0051)/3*0.0000429, (0051-0.0048)/3* 0.0000429} Cpk= min { 0.0001/0.0001287, 0.0003/0.0001287} Cpk = min { 0.77, 2.33} Cpk = 0.77, and since it is less than 1.33 the process is not capable.
- 3. Solution 2: Usl= 50.05+0.05= 50.1 Lsl= 50.05-0.05= 50.0 Mean= 50.04, Standard deviation =0.01 Find Cp & Cpk ϭ Cp= {Usl-Lsl)/6 (sigma) ϭ Cp= (50.1-50.00)/6* 0.01 Cp=0.1 /0.06 Cp = 1.67 Cpk= min { (Usl- Mean)/3 (sigma), (Mean- Lsl)/ ϭ 3 (sigma) ϭ Cpk= min { (50.1-50.04)/3*0.01, (50.04-50)/3* 0.01} Cpk= min { 0.06/0.03, 0.0004/0.03} Cpk = min { 2.0, 1.33} Cpk = 1.33, and since it is equal to 1.33 the process is capable.
- 4. 4 ACCEPTANCE SAMPLING Contents Sunjjoy Uvach 2. Reasons for Sampling Inspection cIC 1. Acceptance Sampling 3. Probability and the Operating Characteristic Curve 4. Lost Acceptance Sampling Plan (LASP) 5. Definitions of Basic Acceptance sampling terms 6. MIL STD 105D for Sampling
- 5. 5 Sunjjoy Uvach Producer cIC QUALITY Customer - If a lot is rejected during first sample then he has to take second sample or 100% inspection of the full lot which consumes time and money and delay in dispatches. Vehicle has to wait. - Customer should get consistent quality of material as per the terms and condition discussed earlier. - Producer should provide customer consistent quality of material as per the terms and condition discussed - If a lot passes the producer site and is rejected during inspection at their end the production line can stop in need of material and producer has to send person for inspection at customer’s end - A balance in Quality level to be ensured to satisfy the customer at all times by the producer. - A good sampling plan (which is agreed by both) helps in reducing the efforts in inspection both at producer and customer end.
- 6. 6 Quality Terms: 1. Quality Control: Day to day activity of Inspection & Control (Shop Floor) 2. Quality Assurance: To be designed in the product or service (Middle Management) 3. Quality Management: It is the mixture of Quality and Management for Sustenance & Delighted Customer. (Top Management)
- 7. 7 Sunjjoy Uvach cIC 1. Acceptance Quality Control - Individual sampling plans are used to protect against irregular degradation of levels of quality in submitted lots below that considered permissible by the customer. - A good sampling plan will also protect the producer in the sense that lots produced at permissible level of quality will have a good chance to be accepted by the plan.
- 8. 8 Sunjjoy Uvach cIC 2. Reasons for Sampling Inspection 1. If tests are destructive, necessitating sampling. It is obvious that 100% sampling will remove the defective parts but at the same time leaving no material for dispatch. 2. Process not in control, necessitating sampling to evaluate the product. An out of control condition implies erratic behavior that cannot be predicted. Therefore, to evaluate the product it is necessary to take a random sample of production after fixed time. 3. 100% inspection is inefficient; 0% is risky. The efficiency of 100% inspection is estimated at around 80% in screening the product. Under sampling, rejected pieces are returned, getting managements attention.
- 9. 9 Sunjjoy Uvach cIC 4. Special causes may occur after process inspection. Process control ends when the control chart is plotted, but the product moves on and is affected by subsequent causes on its way to the customer. Sampling the final or incoming product provides assurance against problems occurring after the process is complete. 5. Need for assurance while instituting process control. The process must operate for some time to implement control charts and achieve control. The product produced in this period of unknown control must be evaluated. Sampling is a way to evaluate this product and provide information useful in the start-up of process control.
- 10. 10 Sunjjoy Uvach cIC 6. Deliberate submission of defective material. A real world experience has shown that pressures of production or profit may lead to fraud. Sampling can help prevent this by detecting. 7. Process control may be impractical because of cost or lack of sophistication of personnel. It is sometimes not cost-effective to institute process control , yet the product needs to be evaluated. Sampling is also easier to implement. 8. 100% inspection does not promote process/product improvement. Sampling with feedback of information often leads to process improvement. 9. Customer mandates sampling plan. Customer may insist on mandatory sampling procedures which are to be met.
- 11. 11 Sunjjoy Uvach cIC 3. Probability and the Operating Characteristic Curve Undoubtedly the most important tool in acceptance quality control is probability theory. It is vital that the quality engineers are acquainted with probability theory. 3.1 Probability: Definition: “If there be a number of events of which one must happen and all are equally likely, and if one of a (smaller) number of these events will produce a certain results which cannot otherwise happen, the probability of this result is expressed by the ratio of this smaller to the whole number of events” (Whiteworth 1965, rule IV). Here the probability is defined as the ratio of favorable to total possible equally likely and mutually exclusive cases. Example: Chances of getting one ace from a pack of cards is 4/52=1/13 Total aces is 4 nos. & Pack of cards has 52 nos.
- 12. Sunjjoy Uvach 14 3.2. Operating Characteristic Curve cIC This curve shows the relation between probability of accepting a lot versus the per cent defectives. A fundamental use of probability with regard to acceptance sampling comes in describing the chances of a lot passing sampling inspection if it is composed of a given proportion defective. The very simplest sampling plan is, of course, as follows: 1. Sample one piece from the lot. 2. If it is good , accept the lot, 3. If it is defective, reject the lot. - If the sample has ¾ th ok pieces then chances of lot getting ok is 75% and getting rejected is 25%
- 13. 15 Sunjjoy Uvach cIC OC Curve n=1 & c=0 Here, we see that for any proposition defective p, the probability of acceptance Pa is just complimentary of p, i.e. Pa=1-p This is only true of the plan n (sample)=1, c (acceptance no.)=0 Here, OC curve gives at a glance a characterization of potential performance of the plan. Pa p 0.10.20.30.40.50.60.70.80.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
- 14. Sunjjoy Uvach 16 cIC For n=5 (samples), c=0 & p=0.005,0.01, 0.02,0.03.0.04 & 0.05 Probability of acceptance Pa for any proportion defective p can be computed as, Pa= (1-p) (1-p) (1-p) (1-p) (1-p)= (1-p)⁵ p (1-p) Pd=(1-p)⁵ 0.005 0.995 0.975 0.01 0.99 0.951 0.05 0.95 0.774 0.10 0.90 0.590 0.20 0.80 0.328 0.30 0.70 0.168 0.40 0.60 0.078 0.50 0.50 0.031 Pa p 0.005 0.010 0.050 0.100 0.200 0.300 0.400 0.500 0.000 0.200 0.400 0.600 0.800 1.000 1.200 Make O.C curve for following situation
- 15. Sunjjoy Uvach p cIC OC curve n=5, c=0 From fig it is clear that if the producer can maintain a defective less than 0.01 the product will be accepted 95% of time or more by the plan. 0.005 0.010 0.050 0.100 0.200 0.300 0.400 0.500 0.000 0.200 0.400 0.600 0.800 1.000 1.200 If the product is 13% defective then it will have a 50-50 % chance of acceptance. Pa
- 16. 18 Sunjjoy Uvach cIC The probability of observing exactly d defectives is given by the following binomial: Pd = f(d) = n! d!(n-d)! Pd (1-p)n-d The probability of acceptance is the probability that d, the no. of defectives, is less than or equal to c, the accept no. This means that P(d ≤ c) =∑ n! d!(n-d)! Pd (1-p)n-d Pa = c d=0 The probability of acceptance is the probability that d, the no. of defectives, is less than or equal to c, the accept no. This means that Using this formula with n=52, c=3 and p=0.01, 0.02,……….0.12, we find the result as in table
- 17. 19 Sunjjoy Uvach cIC Pa 0.998 0.980 0.930 0.845 0.739 0.620 0.502 0.394 0.300 0.223 0.162 0.115 p 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 OC Curve n=52,c=3
- 18. 20 Sunjjoy Uvach cIC 4. Lot Acceptance Sampling Plan (LASP) LASP is a sampling scheme and a set of rules for making decisions for accepting/rejecting a lot. LASP are following types: 1. Single sampling plans 2. Double sampling plans 3. Multiple sampling plans 4. Sequential sampling plans 5. Skip lot sampling plans 1. Single sampling plans: These are usually denoted as (n,c) plans, for a sample size n, where the lot is rejected if there are more than c defectives. This is the easiest of plans but not cost effective considering the nos of lots to be inspected.
- 19. 21 Sunjjoy Uvach cIC 2. Double sampling plans: After the first sample is tested , there are three possibilities a) Accept the lot, b) Reject the lot, c) No decision (Indecisiveness) If decision is c then another sample is taken and combined result is evaluated to take the decision. 3. Multiple sampling plans: This is an extension of double sampling plan where more than two lots are inspected to make a decision. The advantage is that small sample sizes are taken. 4. Sequential sampling plans: This is the ultimate extension of multiple sampling where items are selected from a lot one at a time and after it’s inspection a decision of either accepting/rejecting the lot or take another sample 5. Skip lot sampling plans: In this only some of the lots in offering are inspected.
- 20. 22 Sunjjoy Uvach cIC 5. Definitions of Basic Acceptance sampling terms 1. AQL (Acceptance Quality Level): AQL is a percentage defective that is the baseline requirement for the quality of the producer’s product. The producer would like to design a sampling plan such that there is high probability of accepting a lot that has a defect level ≤ AQL 2. LTPD (Lot Tolerance Percentage Defective): LTPD is a designated high defect level that would be unacceptable to the consumer. Consumer will want a sampling plan which will have low probability of accepting a lot having defect level as high as LTPD. 3. Type 1 error (Producer’s risk): This is the probability that a (n,c) sampling plan will be rejecting a lot having defect level equal to AQL. It is represented by ‘α’. It ranges from 0.2 to 0.01 4. Type 2 error (Consumer’s risk): This is the probability that a (n,c) sampling plan will be accepting a lot having defect level equal to LTPD. It is represented by ‘β’. It ranges from 0.2 to 0.01
- 21. 23 Sunjjoy Uvach cIC 5. Average Outgoing Quality (AOQ): AOQ represents .’the average % defective in the outgoing products after inspection. Example: Calculate sample size and AOQ for single sampling plan using following data of acceptance sampling: 1) Probability of acceptance of a 0.5% defectives is 0.525 2) Lot size= 10,000 nos 3) Acceptance no. =1 4) np= 1.6 {=sample size (n) X defectives in sample(p)} 5) Defectives in the sample not to be replaced Rejection in the lot Total qty. in the lot (N-n) N AOQ = =PaXP’ Pa – Probability of acceptance, P’- percentage defective N= Lot size n= Sample size
- 22. Solution:
- 23. 25 Sunjjoy Uvach cIC Sr. No Point shown in Fig. Probability of Acceptance, Pa Description 1 A’ 100% Zero Defectives 2 A 95% 5% Defectives 3 B’ 0% 100% Defectives 4 B 10% 90% Defectives 5 AQL Higher Acceptance Quality Level 6 IQL 50% Indifference Quality Level 7 LTPD Lower Lot Tolerance Percentage Defective 8 Producer’s Risk ---------- Risk of rejecting a good lot 9 Consumer’s risk ----------- Risk of accepting a bad lot 6. Actual OC Curve
- 24. 26 Sunjjoy Uvach cIC 6. MIL STD 105D for Sampling
- 25. Engineering Engineers Questions are Welcome Thanks for Patience