To determine the process is in control or out of control using p-chart.
A company that produces nails has retained you as a consultant. The company presently produces six-, ten, and sixteen penny common nails. These nails are all produced on the same basic machines, with different wire gauges and dies. Currently, the company is using P charts, one chart for each machine. On a typical day about 35 machines are running. When a nail is inspected, its length, head shape, and point shape are assessed. The fraction defective is currently running at about 0.5 percent, and yesterday all of the machines were in statistical control.
Vendor 1 has proposed a plan where he will install a new vision inspection-sorting system which will 100 percent inspect, i.e., inspect for all three attributes currently being sampled., the nails, and identify and remove nails that do not meet specifications. The resolution of his system is such that it will inspect any of the six-, ten-, and sixteen penny nails currently in production. The vision inspection-sorting system is claimed to be 100 percent accurate in detecting nonconforming nails. The vendor further states that, since the inspection-sorting system is 100 percent accurate, the nail company will be able to totally discontinue its P chart procedures. He adds that the nail customers will be totally satisfied, since they will be receiving nails that meet all the requirements.
Vendor 2 has proposed that the nail company use its variables control chart software. She recommends that, since length is the most important quality characteristic, we should mix all of the sixpenny nails together (from all of the machines set up to produce sixpenny nails) and use only one set of control charts (X-bar and R) in order to save inspection and charting time. Vendor 2 also recommends that we follow this procedure for the ten penny and sixteen penny nails. She also claims that her mixing suggestion will minimize product sampling and will pay for her software in less than six months.
Your client, the nail company, has asked you to study the quality implication of the proposals and make a recommendation on possible courses of action.