Sampling , Standards and quality , General studies , UPSC ESE

Sampling 

• It is a technique in which a random sample is drawn and on the basis of this random sample the decision of acceptance and rejection is taken. 

There are two way of inspection 

• 100% inspection. 
• Sampling inspection. 

100% inspection 

• It is generally expensive. 
• Handling by inspector can induce defect. 
• Can not used when the product destroy while inspection. 

Sampling inspection 

• 
  Sampling involve some risk : good lot is rejected that is producer risk ,bad lot is accepted that is consumer risk 

Acceptance sampling

• It is an important field of statistical quality control. 
• It is popularized by Dodge and Roming. 
• Originally applied by US military for testing of bullets in world war 2. 
• It is also known as "the middle of the road". 

Acceptance sampling for attributes 

• Counted using binomial. 
• It is based on go and no go gauge. 
• If the lot is having too many defective the lot is rejected otherwise accepted. 

Acceptance sampling for variables 

• It is also known as continuous measurement. 
• Usually measured by using mean and standard deviation. 

Sampling plan 

• The most important element of acceptance sampling is choosing an appropriate sampling plan which specify lot size and number of sample, size of each sample ,rule /criteria of acceptance and rejection. 

Types of sampling plan 

• Single sampling plan. 
• Double sampling plan. 
• Multiple sampling plan or sequential sampling plan 

Single sampling plan 

• When the decision of acceptance and rejection of the lot is based on only one sample then it is known as single sampling plan. 
• Flowchart for single sampling plan 
  

Double sampling plan 

• 
  When the decision of acceptance or rejection of lot may be based on two sample then it is known as double sampling plan. 
• Flow chart for double sampling plan. 
  

Sampling term 

AQL: acceptance  quality level 

• The percentage of defect of the lot at which the consumer are willing to accept the lot as good. 
• Example no electricity for 15 minutes in a day, Newspaper not delivered five times in a year. 

RQL: rejectable quality level 

LTPD:lot tolerance percentage defective

LQL: Limiting quality level. 

UQL: unacceptable quality level. 

• The upper limit on the percentage of defect of the lot at which the consumer is willing to accept the lot. 

Producer risk 

• It represent the probability that the lot containing the acceptable quality level will be rejected. 
• Good lot is rejected. 
• It is denoted by alpha. 
• It is also known as type 1 error. 
• It is 5% common. 

Consumer risk: 

• It represent the probability that the lot containing the defect exceeding RQL/LTPD/LQL/UQL will be accepted .
• Bad lot is accepted. 
• It is denoted by beta. 
• It is known as type 2 error. It is 10% common. 

OC curve (operating characteristic curve) 

• It is a graph between percentage defective or fraction defective in the incoming lot and the probability that the sampling plan will accept the lot. 
• It is used to measure the performance of sampling plan. 
• It can apply for all three types of sampling plan. 
• Pa is the probability of acceptance 
• % p = percentage defective 
  
• As the % defective increase the probability of acceptance will decrease. 
• At lower percentage defective the probability of acceptance is higher and at higher percentage defective the probability of acceptance is low. 

Types of oc curve. 

IQL: Indifference quality level 

• The percentage of defective in the lot at which the probability of acceptance is 50%. 

Note:

1.alpha=5% , at AQL = 0.02

• It means we consider it that 2% defective lot is to be good and we preferred to reject such batch not more than 5% of time. 

2. beta = 10% , at RQL= 0.08. 

• It means we consider it that 8% defective lot are poor and we prefer to accept these batch or such batch not more than 10% of time. 

Effect of acceptance number on OC curve keeping sampling size constant.

Effect of sample size on OC curve keeping acceptance number constant

Question : the maximum % defect that a consumer may find definitely acceptable?

Answer : LTPD

AOQ

• It represent the average % defective in the outgoing product after inspection including all accepted and all rejected.
• It is the another method to evaluate the goodness of sampling plan .
  

AOQL

• Average outgoing quality level
• The maximum value of average outgoing quality is known as AOQl
• (AOQ)max = AOQL

Note : AOQL value and the shape of AOQ curve depend on particular sampling plan . sampling plan are design such that there AOQL  does not exceed a certain specific value.

Question : if the probablity of acceptance of 1 % defective lot is 0.95 then what is value of AOQ?

Question : in an acceptance sampling plan develop for lot containing 1000 unit the sample size is 85 and acceptance number is 3 . The % defective of incoming lot is 2 % and the probablity of acceptance which is obtain from OC curve is 0.64 . What is value of AOQ?

Question : OC curve for 100 % inspection is :

Answer : ii