1. A cost of quality model proposed by Juran & Gryna defined the expected costs of three different product evaluation options:

Expected cost of no Inspection: NpA

Expected cost of sampling: nI + (N - n)pAP_a + (N - n)(1- P_a)I

Cost of examining every item if the lot is rejected (100% sorting, no rework).

Expected cost of 100% Inspection: NI

Where:

N = number of items in lot

n = number of items in sample

p = proportion defective in lot

A = damage cost incurred if defective slips through inspection

I = inspection cost per unit

P_a = probability the lot will be accepted (use binomial distribution to estimate)

Use the above model to estimate the costs associated with assessing a production lot containing 150 golf balls. If acceptance sampling is to be used, the engineer wants to employ a (20, 1) sampling plan. Marketing estimates if a bad golf ball slips through to the customer it will cost the company $0.25. Inspectors can check 500 golf balls per hour, and their average hourly wage (including benefits) is $18.00. The proportion defective has historically been around 5%.

1. What are the expected costs of the no inspection, sampling, and 100% inspection alternatives?

1. If a bad golf ball slipping through to the customer actually costs the company $0.50, and the acceptance number is tightened to 0 (keeping all other parameters the same), what are the expected costs of the three alternatives?

1. Answer the same question assuming the proportion defective jumps to 10%, butthe acceptance number is loosened to 2 (but still assume a $0.50 damage cost).

1. At Isogen Pharmaceuticals, the filling process for its asthma inhaler is set to dispense 120 milliliters (ml) of steroid solution per container. The average range for a sample of 6 containers is 7 ml.

1. What are the UCL_R and the LCL_R? Enter your responses rounded to two decimal places.

1. What are the UCL_X-bar and the LCL_X-bar? Enter your responses rounded to two decimal places.

1. As a hospital administrator of large hospital, you are concerned with the absenteeism among nurses’ aides. The issue has been raised by registered nurses, who feel they often have to perform work normally done by their aides. To get the facts, absenteeism data were gathered for the last three weeks, which is considered a representative period for future conditions. After taking random samples of 70 personnel files each day, the following data were produced:

Day	Aides Absent	Day	Aides Absent	Day	Aides Absent
1	2	6	3	11	6
2	4	7	7	12	6
3	6	8	7	13	12
4	2	9	1	14	2
5	6	10	2	15	2

Because your assessment of absenteeism is likely to come under careful scrutiny, you would like a type I error of only 1 percent. You want to be sure to identify any instances of unusual absences. If some are present, you will have to explore them on behalf of the registered nurses.

1. For the p-chart, find the upper and lower control limits. Enter your response rounded to three decimal places.

1. Based on your p-chart and the data from the last three weeks, what can we conclude about the absenteeism of nurses’ aides?

1. The proportion of absent aides from day 14 is above the UCL, so the process is not in control.
2. The proportion of absent aides from day 15 is below the LCL, so the process is not in control.
3. All sample proportions are within the control limits, so the process is in control.
4. The proportion of absent aides from day 13 is above the UCL, so the process is not in control.

1. An important aspect of customer service and satisfaction at the Big Country theme park is maintenance of the restrooms throughout the park. Customers expect the restrooms to be clean; odorless; well stocked with soap, paper towels, and toilet paper; and to have a comfortable temperature. In order to maintain quality, park quality-control inspectors randomly inspect restrooms daily (during the day and evening) and record the number of defects (incidences of poor maintenance). The goal of park management is approximately 10 defects per inspection period. Following a summary of the observations taken by these inspectors for 20 consecutive inspection periods:

Sample	Number Defective	Sample	Number Defective
1	7	11	14
2	14	12	10
3	6	13	11
4	9	14	12
5	12	15	9
6	3	16	13
7	11	17	7
8	7	18	15
9	7	19	11
10	8	20	16

1. Construct the appropriate control chart for this maintenance process using 3-sigma limits and calculate the UCL, LCL, and the central line (the proportion defective cannot be determined here, so the p-chart is not an option). Enter your responses rounded to two decimal places.

1. D0 pattern tests show any nonrandom patterns? (Yes or No)

1. Metropolitan Hospital is a city-owned and operated public hospital. Its emergency room is the largest and most prominent in the city. Approximately 70% of emergency cases in the city come or are sent to Metro General’s ER. As a result, the ER is often crowded and the staff is overworked, causing concern among hospital administrators and city officials about the quality of service and health care the ER is able to provide. One of the key quality attributes the administrators focus on is patient waiting time – that is, the time between when a patient checks in and registers and when the patient first sees an appropriate medical staff member. Hospital administration wants to monitor patient waiting time using statistical process control charts. At different times of the day over a period of several days, patient waiting times (in minutes) were recorded with the following results:

Sample (Subgroup)	Time 1	Time 2	Time 3	Time 4	Time 5
1	27	18	20	23	19
2	22	25	31	40	17
3	16	15	22	19	23
4	35	27	16	20	24
5	21	33	45	12	22
6	17	15	22	20	30
7	25	21	26	33	19
8	15	38	23	25	31
9	31	26	24	35	32
10	28	23	29	20	27

1. Develop an x-bar chart to be used in conjunction with R-chart to monitor patient waiting time. Enter the control chart parameters on the response sheet. Enter your responses rounded to two decimal places.

1. Does the process appear to be in a state of statistical control? Yes or no.

1. Management of a golf ball company has carefully screened and selected 12 dozen golf balls, and it is agreed that this sample contains 15 nonconforming balls (all for various cosmetic reasons). The balls are given to an inspector for classification into “good” and “bad” piles. The inspector ends up rejecting 7 good balls, and accepting 6 bad balls. The inspector classifies the remaining balls in the sample correctly.
   1. On average, what is the probability that this inspector will reject a golf ball?Enter your response rounded to three decimal places.

1. On average, what is the probability that this inspector will make a wrong decision?Enter your response rounded to three decimal places.

1. On average, what is the proportion of accepted units that are actually nonconforming? Enter your response rounded to three decimal places.

1. A lot of size 310 components is received. Management wants an AQL of 2.5%, and decides to use an attribute sampling plan to assess the quality of the lot. Using ANSI/ASQ Z1.4, Inspection Level II, the single sampling plan for normal inspection would be: n = _______ and c = ________. The probability that a lot with 7% nonconforming items will be accepted by this inspection plan is P_a = ______ (use 3 decimal places).

Response Sheet (one point per question – 33 points maximum)

No.	Question
1.a.	Cost of No Inspection ($/Lot) =
	Cost of Sampling ($/Lot) =
	Cost of 100% Inspection ($/Lot) =
1.b.	Cost of No Inspection ($/Lot) =
	Cost of Sampling ($/Lot)=
	Cost of 100% Inspection ($/Lot) =
1.c.	Cost of No Inspection ($/Lot) =
	Cost of Sampling ($/Lot) =
	Cost of 100% Inspection ($/Lot) =
2.a.	UCLR =
	LCLR =
2.b.	UCLX-bar =
	LCLX-bar =
3.a.	UCL =
	LCL =
3.b.	Multiple choice
4.a.	UCL =
	Central Line =
	LCL =
4.b.	Do pattern tests show any non-random patterns?
5.a.	UCLX-bar =
	Central line for X-bar chart =
	LCLX-bar =
	UCLR =
	Central line for range chart =
	LCLR =
5.b.	Is the process in statistical control?

Answer rating: 100% (QA)

A cost of quality model proposed by Juran Gryna defined the expected costs of three different product evaluation options Expected cost of no Inspection NpA Expected cost of sampling nI N npAP a N n1 P ... View the full answer