hi evry one ,

i m a manufacturing engineer and i m engaged in a six sigma project : "Productivity enhancement on our packaging machine" .

the back groud of this project -- currently the average production of this machine is 73 shippers per shift although it's capcity is 100 shippers per shift .

and the production numbers varies from 50 shippers per shift to 105 shippers per shift.

In this situation how can i do Sigma Calculation ?

Ashish

Pls support me ........ 

Overview_of_Statistics.ppt 6-Sigma_Metrics_Calculator.xls

iceberg_melting.ppt

thanks Siva to give valuable presentation

but i m stiil not getting the answer to get the method of Sigma Calculation in manufacturing industry on production data.

where quality is not concern .
main concern area is variation in production no . machine doesn't meet the production target .
pls short out this problem

Ashish

The statistic that describes the capability of a process or a machine to produce jobs within a reasonable portion of the tolerance is called the Process Capability; this is denoted by Cp or PC ratio. The statistic is a measure of the variation in terms of ( ration or % of ) the width of the tolerance ( band) as available from the specification.

However a process may have a poor performance due to several reasons.

-input component- quality of conformance to requirements

- process parameters- operating conditions,speed, feed,etc

- machine condition - vibrations, alignments, geometric accuracies,etc

- method of inspection/acceptance

-external factors eg environmental, ambient conditions,

- the person operating the machine ( this is generally very less with modern machines as they reduce the dependance on operator)

sanjai

thanks for help

Dear Ashish,

We could possibly look at the problem in another way, though a bit in detail:

1) It seems the if the target of prodn is 100 pcs per hr on average then in order that there is no ( zero deviation ) from this target it is essential that the process is consistently able to give 100 jobs on the hour every hour.

Since this is not happenning. the degree of consistent behaviour of the packing process is measurable by a sigma level.or the std dev wrt to the target of 100.

In this case the sigma level shall be indicated by the deviaton from the target divided by the std dev of the prodn figures obtained over a period of time. Here if it is assumed the std dev is 3 with the spread of 103-100= 3 on one side and 50-100= 50 on the other . which when divided by the std dev 3 i.e 3/3= 1 and one side and 38/3=12 i.e the total spread is about 13.0 std dev, however only 1 std dev is worth considering as above the required prodn of more than 100. All other events would be called a deviation from reqmts of 100 since they produce less than the desired 100.

This corresponds to a low acceptance level of ( 1 std dev) 0.5 sigma.

2) Alternatively we could consider that the reqd prodn is not to be less than 100 job per hr , in which case it is a one sided reqmt. The spread is acceptable from 100 and beyond.Assume that the avg/mean is say 120 ( as close to 100 is desirable) . In which case the event of less than 100 /hr would be called a non conformance to reqmts. The consistency of the process is measured by the sigma level i.e the no of std dev that lie between the lower spec i.e 100 and the mean of the prodn rate say 120.considering that the std dev is 5.0 then the spread on this side corresponds to a 120-100/5= 4.0 std deviations. However all event with prodn beyond 100 are acceptable, then the spread beyond 120 is accceptable.

Consider that if we were to get a distribution with a avg of 105 and spread of 30 ( varies between 90 to 120) . in which case the events when the prodn has fallen below 100 are called non acceptable events. The probability of such an event is an indicator of the sigma value. Simply in other words (90-100/5)=2 std dev are in non acceptable zone below 100.

The Z score for the non conformance is considered as 2.0 which corresponds to acceptance sigma level of 5.0 ( a spread of 10 stdev against a desirable 12 std dev within acceptance zone) . Also the extent or % probability of such events can be predicted once the sigma level/ no of std dev on the side of acceptance are known. This can be done with the help of the normal probability tables in a book on statistics.

Sanjai.W

Dear Ashish,

The various approaches for productivity are as follows.

• Consider a lower specification limit only (no upper specification limit).
  
• Consider both limits. Lower specification limit to ensure that productivity never goes below a minimum specified value. Upper specification limit to ensure that productivity is never above a value (for example more than 105% may adversely affects machine life or increase maintenance costs).
  
• Consider upper specification limit only. This would safeguard against over-usage.
  

The approaches more likely to be used are number 1 and 2 as they make more business sense in most cases. Approach 3 may be counter productive if there are waiting orders or demand all the time.

To give examples for the first two let us consider the following:

• Lower Spec Limit = 100 pcs per hour. Mean = 125 pcs per hour, Std Dev = 5. The Sigma Level calculation shall be Z = (125-100)/5 = 5
  
• LSL = 100, USL = 150, Mean = 125, Std Dev = 5. Sigma Level calculation shall be Z upper = (150-125)/5 = 5 and Z lower = (125-100)/5 = 5
  

Both approaches take care of variation in productivity.

Regards,

VK

 thanks all of you

Hi ashish

i think Sigma Calculation of your prob can't be done without standard deviation for which we also require frequency of your data- i mean how many jobs made per shift not just range..