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Seven Basic Quality tools documents


Definition of Quality Management -- it is a method for ensuring that all the activities necessary to design, develop and implement a product or service are effective and efficient with respect to the system and its performance. It is also a principle set by the company to endure the continuous advocacy of quality services and products, or the further improvement of it.





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Continuous Sampling Planning

Introduction

Lot acceptance sampling plans (LASP) are used during production to test units submitted forevaluation against certain hypotheses.  From a manufacturing perspective,LASP’s provide a check on a company’s quality control processes.  Most LASPsamples of a product are carried out in lots.

In standard sampling ahypotheses of the sample makes up the criteria by which the process is judged. These units are then accepted or rejected on the basis of the set forthhypothesis.  If a process has tested adequately, the lot or unit is acceptedand passed on to the retailer or customer.  If, however; quality control is notsufficient, sampling will prevent unacceptable product from leaving themanufacturer.  Accepting or rejecting a lot or unit is synonymous with notrejecting or rejecting the null hypothesis in the hypothesis test.  Becausegrouping into lots is not always advantages, continuous sampling as outlinedbelow, takes a slightly different approach to quality control in manufacturing. 

ContinuousSampling Defined

The concept ofcontinuous sampling planning originated in 1943 by Dodge.  Known as CSP-1,continuous sampling is used where product flow is continuous and not easilygrouped in lots.  Two parameters exist for continuous sampling.  One is thefrequency (f) and the second is the clearing number (i).  The frequency (f) isdefined by a number such as 1/20, 1/30, or 1/X.  The clearing number (i) is anumber such as 30 or 60.  A company checks all of its product until 100% of inumber of units are inspected and found to be defect free.  After 100% of inumber of units are found to be defect free 100% inspection is ceased, and oneout of every X number of units is checked.  The sampling continues until adefect is found.  After finding a defect the cycle repeats itself until 100% ofi number of units has been found to be defect free.  At this point the sample1/X will begin again.

Using ContinuousSampling

Carrying out acontinuous sampling plan is simple and can be carried out in 3 steps.  1.Inspect all i data.  2. If no defects are found, randomly sample fraction f ofdata and check again for defects.  3.  Whenever a defect is found, correct theflaw and repeat step 1.  There are two main parameters to consider whenexecuting a continuous sample.  All other relevant measurements for continuoussample planning can be derived from these two parameters.  The parameters withtheir variables defined can be seen in Figures 1 and 2.    

Figure 1 CSP-1 Parameters

 

 
 

 


AOQ Averageoutgoing quality for long-run CSP 1plan.

 

 

 


AFI Averagefraction inspected for long-run CSP 1plan.

 

 

 

            Figure2 AOQ and AFI Variables                  

f      Sampling frequency for short-run CSP – 1 plan

i      Clearance number for short-run CSP − 1 plan

p     Incoming quality level

pa    probability of accepting incoming unit

qi     = 1-p

N    Lot size

 

 
 








 

 

 


When a seriesdefects are gathered, a good continuous sampling plan will inspect 100% the rejectedunits and replace and defective parts or products.  In this case all defectsare made whole and accepted.  AOQ refers to the long term defect level of thissampling plan and 100% inspection of rejected units.  The average fractioninspected is simply the average of the fractions 1/X sampled.  Results can thenbe further analyzed by creating an Average Outgoing Quality Curve (Figure 3). An Average Outgoing Quality Curve plots the AOQ (Y-axis) against p, theincoming quality level (X-axis).  Figure 3 tells us that with high levels ofincoming quality (low p values); the average outgoing quality was also verygood. 

Figure 3 AverageOutgoing Quality Curve

A plot of the AOQ versus p is given below.

 

                     Plot of the AOQ versus p

 

When incomingquality begins to drop defective items are inspected and replaced, thusincreasing the average outgoing quality.  The curve in Figure 3 shows thatafter reaching a certain level p, AOQ begins to drop.  In other wordsdiminishing AOQ takes place as the value of p increases.  The maximum AOQ pointon the curve represents the worst possible quality that results from thecorrection of defects.

 

Example

Cart Racing isa technical sport and requires precision in driving abilities as well as inmechanics and cart workmanship.  Professional cart racers will have multiplerace carts and expect their carts to meet specific specifications.  One way toensure a race cart meets specifications is to run the cart on a DYNOmiteDynamometer.  A Dynamometer is always connected to a Data Acquisition Computerthat reads such information as true Hp, torque, RPM, elapsed time, etc.  Bydesignating a clearance number of say, 15, and a frequency of 1/5, a customcart builder could apply continuous sampling to Dynamometer testing to ensurehis carts meet certain criteria.  After running multiple samples the cartbuilder could figure out his AOQ level.  Putting the data in graph like that offigure three could show the cart builder his AOQ as compared to p, his or herincoming quality.  Using this data can provide further insight into wherequality originated and where quality improvement is still lacking.

How to get more information   

Roderick Lashley.  ApplyingStatistical Sampling Plans To Data Entry Procedures To Increase Data Quality. STATKING Consulting Inc.

 

Chen and Chau.  Joint Design ofEconomic Manufacturing Quantity, Sampling Plan and Specification Limits. Economic Quality Control, Vol 17, No. 2, 145-153.

 

Chen and Chau.  A Note on theContinuous Sampling Plan CSP-V.  Economic Quality Control, Vol 17, No. 2,235-239.

 

 



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