Question

A manufacturer purchases small bolts in cartons that usually contain several thousand bolts. Each shipment consists of a number of cartons. As a part of the acceptance procedure for these bolts, 400 bolts are selected at random from each carton and are subjected to visual inspection for certain defects. In a shipment of 10 cartons the respective percentage of defectives in the samples from each carton are 0, 0, 0.5, 0.75, 0, 2.0, 0.25, 0, 0.25 and 1.25. Does this shipment of bolts appear to exhibit statistical control with respect to the quality characteristics examined in the inspection?

Answer 1

We shall construct a p chart for fraction defectives. Define n=400=subgroup size and

Then

We compute   so that

UCL=.01558

LCL= -0.00558 , which is negative and hence, we take LCL as 0.

Then we create the following p chart

Since, a point lies outside the 3 sigma limit and 4 lie on the LCL, the process is suspected to be out of control.

Thus the shipment of bolts appear to exhibit lack of statistical control with respect to the quality characteristics examined in the inspection.

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