In the following confusion matrix for a fault diagnosis system for 33kV switchge

Question

In the following confusion matrix for a fault diagnosis system for 33kV switchgear there are 5 types of possible fault identified: a- control system, b-lubrication, c- mechanism, d- contact wear, e- flat battery. Calculate: (i) The true positive rate for lubrication faults 10% (ii) The false positive rate for contact wear 10% (iii)The Positive Predictive Value (PPV) for flat batteries 20% (iv)The sensitivity for mechanism faults 20% (v) The specificity for mechanism faults 20% (vi)The most prevalent fault and its prevalence 20%

Explanation / Answer

(i) True Positive Rate of Lubrication faults (b) = TP/(TP+FN) = 7/(6+7+5+3+1) =0.318

(ii) False Positive Rate of Contact Wear (d) = FP/(FP+TP) =(3+1+3+1)/(3+1+3+1+3) = 0.727

(iii) PPV of flat batteries (e) = TP/(TP+FP) = 8/(8+3+1+1+1) =  0.571

(iv) Sensitivity for mechanism faults (c) = True Positive Rate = TP/(TP+FN) = 4/(3+9+4+1+1) = 0.222

(v) Specificity for mechanism faults (c) = True Negative Rate = TN/(TN+FP) =((3+4+6+7)+(1+1+3+1)+(10+6+2+4)+(3+3+3+8) )/(5+3+5+4+(3+4+6+7)+(1+1+3+1)+(10+6+2+4)+(3+3+3+8)) =0.793

(vi) most prevalent fault is (d) Contact Wear

Prevalence = (Total Actual)/N = 25/100 = 0.25

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