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Assignment - Group Case Analysis

TQM 603 Statistical Quality Control

Description of Assignment Task

1- Analyze and evaluate the improving service quality in the choice of your company.

2- Describe the process of improvement tools that are applied in this company

3- Recommend quality improvements in this company.

Course Learning Outcomes

3. Implement the control charts for variables and attributes.

4. Analyze the process and measurement system capability.

5. Develop exponentially weighted moving average and Control Charts for monitoring variability.

Case -1.

Many quality characteristics cannot be conveniently represented numerically. Control charts for quality characteristics that are expressed as variables. Although these control charts enjoy widespread application, they are not universally applicable, because not all quality characteristics can be expressed with variables data.

Suppose one examine a container and classify it into one of the two categories called conforming or nonconforming, depending on whether the container meets the requirements on one or more quality characteristics. Abu Dhabi National paper mill uses a control chart to monitor the imperfection in finished rolls of paper. Production output is inspected for 20 days, and the resulting data are shown in Table 1.

Table : 1 shows the data on imperfections in rolls of papers

Day	Number of rolls produced	Totsl number of Imperfections	Day	Number of Rolls Produced	Total Number of Imperfections
1	18	12	11	18	18
2	18	14	12	18	18
3	24	20	13	18	9
4	22	18	14	20	10
5	22	15	15	20	14
6	22	12	16	20	13
7	20	11	17	24	16
8	20	15	18	24	18
9	20	15	19	22	20
10	20	10	20	21	17

a) Use these data to set up a control chart for nonconformities per roll of paper. Does the process appear to be in statistical control?

b) What center line and control limits would you recommend for controlling current production?

c) Consider the papermaking process andset up a u chart based on an average sample size to control this process.

d) Set up a standardized u chart for this paper making process with the help of the data available in table 1.

Case-2.

CUSUM and the EWMA offer considerable performance improvement relative to Shewhart charts. CUSUM and EWMA control charts are very useful in phase II process-monitoring situations survey of several univariate process control techniques, including methods for short production runs and monitoring techniques suitable for processes in which the data are auto correlated.

Kittlitz presents data on machinery break-down in Waco, Texas, for the years 2009–2018 (data taken from the Waco, December 29, 2018). There were 29 machinery break-down in 2018. Table 2 gives the dates of the 2018machinery break-down and the number of days between each break-down.

Table: 2 shows the Machinery Break-down data from Waco Texas

Month	Date	Days Between	Month	Date	Days Between
January	20		July	8	2
February	23	34	July	9	1
February	25	2	July	26	17
March	5	8	September	9	45
March	10	5	September	22	13
April	4	25	September	24	2
May	7	33	October	1	7
May	24	17	October	4	3
May	28	4	October	8	4
June	7	10	October	19	11
June	16*	9.25	November	2	14
June	16*	0.50	November	25	23
June	22*	5.25	December	28	33
June	25	3	December	29	1
July	6	11

The * refers to the fact that two machinery break-down occurred on June 16 and were determined to have occurred 12 hours apart.

(a) Plot the days-between-machinery break-down data on a normal probability plot. Does the assumption of a normal distribution seem reasonable for these data?

(b) Transform the data using the 0.2777 root of the data. Plot the transformed data on a normal probability plot. Does this plot indicate that the transformation has been successful in making the new data more closely resemble data from a normal distribution?

(c) Transform the data using the fourth root (0.25) of the data. Plot the transformed data on a normal probability plot. Does this plot indicate that the transformation has been successful in making the new data more closely resemble data from a normal distribution? Is the plot very different from the one in part (b)?

(d) Construct an individual control chart using the transformed data from part (b).

(e) Construct an individual control chart using the transformed data from part (c). How similar is it to the one you constructed in part (d)?

(f) Is the process stable? Provide a practical interpretation of the control chart.

(g) Consider the Machinery break-down data in table 2 and Set up an EWMA control chart for this process with λ = 0.1 and L = 2.7. Does potential non-normality in the data pose a concern here?

(h) Analyse the Machinery break-down data in table 2 using amoving average control chart with w = 5. Does potentialnon-normality in the data pose a concern here?