How do you make a plan of experimentation that can identify the important factors and interactions that contribute to both defects and quality? (maximum to 50 total trials per experiment)

ABC Co manufactures a biscuit product consisting of two biscuit wafers, with a mock cream filling in between, and fully enrobed in chocolate. Management would like to improve the process, and intend to conduct planned experiments on it. Currently, knowledge of the process is very low within the factory. Management know that they have problems with (1) biscuit defects, and with (2) variations in quality, that have led to customer complaints, and this is losing them money. Biscuits are produced in batches of 100,000 with ten biscuits packed into in each pack (so that means 10,000 packs are produced per batch). Each pack produces $8 revenue for ABC Co (after retail and transportation costs are removed), so this implies a maximum of $80,000 of gross revenue per batch. Costs of production total $30,000 per batch, and so the nett revenue is $50,000 after production costs are subtracted. The maximum possible revenue is further reduced by the quality problems outlined below, however (table 1 summarises). Defects are measured as the % defects in a random sample taken from a batch. Currently, defects result in approximately 12% of product not being rejected as not fit for sale (12% x 10,000 = 1,200 packs per 10,000. This amounts to $9,600 of lost revenue per batch. For this reason, every 1% reduction in defects will produce $800 additional revenue per batch, and every 1% increase in defects will reduce revenue by the same amount. Product Quality is measured by consumer panels, using 4 measurement dimensions each scored out of 5, therefore producing a total quality score out of 20. The average score for ABC's product quality is currently 14, and marketing has predicted (from benchmarking with other products) that each 1 unit improvement in average quality is expected to produce a $1000 increase in gross revenue per batch (and vice versa) due to increased sales. Table 1 Cost / Revenue element Batch size Total revenue to ABC Production costs Current Cost of defects Current quality level Revenue / Cost Per batch 100,000 biscuits or 10,000 packs $80,000 $30,000 12% rejected product loss of $9,600) 14 out of a possible 20 (opportunity cost of $6000) Low (-1) High (+1) Mixture A Mixture B slow fast less 200C more 250 C 10 mins 15 mins 10 C 18 C Factor Why included? Mixing It is believed that there may be batch-to-batch variation, especially for quality. Forming The forming process might create inconsistencies and lead to defects Spraying Spraying with oil might affect the flavour Cooking temp The temperature of cooking might lead to defects, and to reduced flavour Cooking time The time in the over might lead to burning, and cause defects and poor flavour Cooling temp The temperature at which biscuits are cooled might lead to defects Cooling time The time at which biscuits are cooled might lead to defects Filling amount The amount of filling might be causing complaints about quality Enrobing The temperature of enrobing might lead to chocolate temp inconsistency, and quality complaints Packaging The packaging process could be a source of defects speed Line speed Line speed might be causing problems due to insufficient time on certain stages, linked to the above 5 mins 30 mins thin thick 40C 60C slow fast 20 RPM 60 RPM ABC Co manufactures a biscuit product consisting of two biscuit wafers, with a mock cream filling in between, and fully enrobed in chocolate. Management would like to improve the process, and intend to conduct planned experiments on it. Currently, knowledge of the process is very low within the factory. Management know that they have problems with (1) biscuit defects, and with (2) variations in quality, that have led to customer complaints, and this is losing them money. Biscuits are produced in batches of 100,000 with ten biscuits packed into in each pack (so that means 10,000 packs are produced per batch). Each pack produces $8 revenue for ABC Co (after retail and transportation costs are removed), so this implies a maximum of $80,000 of gross revenue per batch. Costs of production total $30,000 per batch, and so the nett revenue is $50,000 after production costs are subtracted. The maximum possible revenue is further reduced by the quality problems outlined below, however (table 1 summarises). Defects are measured as the % defects in a random sample taken from a batch. Currently, defects result in approximately 12% of product not being rejected as not fit for sale (12% x 10,000 = 1,200 packs per 10,000. This amounts to $9,600 of lost revenue per batch. For this reason, every 1% reduction in defects will produce $800 additional revenue per batch, and every 1% increase in defects will reduce revenue by the same amount. Product Quality is measured by consumer panels, using 4 measurement dimensions each scored out of 5, therefore producing a total quality score out of 20. The average score for ABC's product quality is currently 14, and marketing has predicted (from benchmarking with other products) that each 1 unit improvement in average quality is expected to produce a $1000 increase in gross revenue per batch (and vice versa) due to increased sales. Table 1 Cost / Revenue element Batch size Total revenue to ABC Production costs Current Cost of defects Current quality level Revenue / Cost Per batch 100,000 biscuits or 10,000 packs $80,000 $30,000 12% rejected product loss of $9,600) 14 out of a possible 20 (opportunity cost of $6000) Low (-1) High (+1) Mixture A Mixture B slow fast less 200C more 250 C 10 mins 15 mins 10 C 18 C Factor Why included? Mixing It is believed that there may be batch-to-batch variation, especially for quality. Forming The forming process might create inconsistencies and lead to defects Spraying Spraying with oil might affect the flavour Cooking temp The temperature of cooking might lead to defects, and to reduced flavour Cooking time The time in the over might lead to burning, and cause defects and poor flavour Cooling temp The temperature at which biscuits are cooled might lead to defects Cooling time The time at which biscuits are cooled might lead to defects Filling amount The amount of filling might be causing complaints about quality Enrobing The temperature of enrobing might lead to chocolate temp inconsistency, and quality complaints Packaging The packaging process could be a source of defects speed Line speed Line speed might be causing problems due to insufficient time on certain stages, linked to the above 5 mins 30 mins thin thick 40C 60C slow fast 20 RPM 60 RPM