Ashutosh Bhardwaj

Pooled standard deviation is the weighted average standard deviation for two or more independent groups. Larger samples are given more weight in decision. There are two method of calculating pooled-standard deviation:
1.
2.
 
2nd method is supportive only when sample size is same for individual groups. lets us understand impact of both methods with the help of examples:
Suppose we have four individual groups of solar cell efficiency with same sample sizes ( shown in below table). Pooled standard deviation value will be “ 0.061826” by using first method . If we use second method then pooled standard deviation value will also be “0.061826” . Both methods are showing same pooled standard deviation value because 1st and 2nd methods will perform same in case of same sample sizes.
 

 
To discern between both methods, let's change sample size of Group-1 from value "6" to "5" and let's check pooled standard deviation for both methods. Now it shows different pooled standard deviation due to sample size non-equal for individual groups. In this case pooled-std deviation value " 0.0634" is acceptable. it indicates that "more weight given to larger samples".

As the name suggests, OEE is an overall measure that reflects performance from several aspects, it computes parameter of availability, performance  and quality into single key process indicator expressed as a percentage. Out of these parameters, performance rate (%) determines that “does the machine produce level of output that it should do” ? The simplest way of calculating the performance rate is “[Actual output / Predicted output ]% “
Actual output : we consider all parts including good and defective
Predicted output : Based upon actual availability and the machine cycle time
sometime, performance rate is mis - calculated due to :
 
Scenario-1: Team forgets to consider rejected part into actual output which results wrong performance rate like below example:
    Data Entry Unit   Case-1 Good product: 800 pcs   Defective Product: 200 pcs   Actual Output ( Good+Defective): 1000 pcs   Predicted Output: 1200 pcs   Performance Rate ( with defective part): 83.33% % Correct Performance Rate ( without defective part): 66.67% % Wrong  
Scenerio-2: Some time team adds old stock also in actual output for showing higher throughput which becomes higher than predicted output and result more than 100% performance rate.
Case-2 Good product: 800 pcs   Defective Product: 200 pcs   Actual Output ( Good+Defective): 1000 pcs   Old stock for posting: 300 pcs   Predicted Output: 1200 pcs   Performance Rate ( with defective part): 83.33% % Correct Performance Rate (  with old stock for posting): 108.33% % Wrong Scenerio-3: Actual output can never be more than predicted output otherwise performance shows more than 100% which indicates that cycle time is wrongly set.
Case-3 Good product: 1100 pcs   Defective Product: 200 pcs   Actual Output ( Good+Defective): 1300 pcs   Old stock for posting: 300 pcs   Predicted Output: 1200 pcs   Performance Rate ( with defective part): 108.33% % Wrong   In this case need to review ideal cycle time OEM and subject matter expert